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Updated WEEK05
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Kevin Thomas
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@@ -1,6 +1,6 @@
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?# Week 5: Integers and Floats in Embedded Systems: Debugging and Hacking Integers and Floats w/ Intermediate GPIO Output Assembler Analysis
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# 📘 Week 5: Integers and Floats in Embedded Systems: Debugging and Hacking Integers and Floats w/ Intermediate GPIO Output Assembler Analysis
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## ? What You'll Learn This Week
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## 🎯 What You'll Learn This Week
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By the end of this tutorial, you will be able to:
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- Understand how integers and floating-point numbers are stored in memory
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@@ -25,10 +25,10 @@ In C programming for embedded systems, we have special integer types that tell t
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+-----------------------------------------------------------------+
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| Integer Types - Different Sizes for Different Needs |
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| |
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| uint8_t: 1 byte (0 to 255) - like a small box |
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| int8_t: 1 byte (-128 to 127) - can hold negatives! |
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| uint16_t: 2 bytes (0 to 65,535) - medium box |
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| uint32_t: 4 bytes (0 to 4 billion) - big box |
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| uint8_t: 1 byte (0 to 255) - like a small box |
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| int8_t: 1 byte (-128 to 127) - can hold negatives! |
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| uint16_t: 2 bytes (0 to 65,535) - medium box |
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| uint32_t: 4 bytes (0 to 4 billion) - big box |
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| |
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+-----------------------------------------------------------------+
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```
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@@ -42,83 +42,9 @@ The difference between `uint8_t` and `int8_t` is whether the number can be **neg
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| `uint8_t` | `u` | 0 to 255 | Ages, counts, always positive |
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| `int8_t` | none | -128 to 127 | Temperature, can be negative |
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Let's review the code in `0x000b_integer-data-type`.
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```assembly
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#include <stdio.h>
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#include "pico/stdlib.h"
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int main(void) {
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uint8_t age = 43;
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int8_t range = -42;
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stdio_init_all();
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__asm volatile (
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"ldr r3, =0x40038000\n" // address of PADS_BANK0_BASE
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"ldr r2, =0x40028004\n" // address of IO_BANK0 GPIO0.ctrl
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"movs r0, #16\n" // GPIO16 (start pin)
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"init_loop:\n" // loop start
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"lsls r1, r0, #2\n" // pin * 4 (pad offset)
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"adds r4, r3, r1\n" // PADS base + offset
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"ldr r5, [r4]\n" // load current config
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"bic r5, r5, #0x180\n" // clear OD+ISO
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"orr r5, r5, #0x40\n" // set IE
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"str r5, [r4]\n" // store updated config
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"lsls r1, r0, #3\n" // pin * 8 (ctrl offset)
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"adds r4, r2, r1\n" // IO_BANK0 base + offset
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"ldr r5, [r4]\n" // load current config
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"bic r5, r5, #0x1f\n" // clear FUNCSEL bits [4:0]
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"orr r5, r5, #5\n" // set FUNCSEL = 5 (SIO)
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"str r5, [r4]\n" // store updated config
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"mov r4, r0\n" // pin
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"movs r5, #1\n" // bit 1; used for OUT/OE writes
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"mcrr p0, #4, r4, r5, c4\n" // gpioc_bit_oe_put(pin,1)
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"adds r0, r0, #1\n" // increment pin
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"cmp r0, #20\n" // stop after pin 18
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"blt init_loop\n" // loop until r0 == 20
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);
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uint8_t pin = 16;
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while (1) {
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__asm volatile (
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"mov r4, %0\n" // pin
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"movs r5, #0x01\n" // bit 1; used for OUT/OE writes
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"mcrr p0, #4, r4, r5, c0\n" // gpioc_bit_out_put(16, 1)
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:
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: "r"(pin)
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: "r4","r5"
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);
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sleep_ms(500);
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__asm volatile (
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"mov r4, %0\n" // pin
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"movs r5, #0\n" // bit 0; used for OUT/OE writes
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"mcrr p0, #4, r4, r5, c0\n" // gpioc_bit_out_put(16, 0)
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:
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: "r"(pin)
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: "r4","r5"
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);
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sleep_ms(500);
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pin++;
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if (pin > 18) pin = 16;
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printf("age: %d\r\n", age);
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printf("range: %d\r\n", range);
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}
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}
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```
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### Breaking Down the Code
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#### The Integer Variables
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This program declares two integer variables that demonstrate the difference between **signed** and **unsigned** types:
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Let's say a program declares two integer variables that demonstrate the difference between **signed** and **unsigned** types:
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```c
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uint8_t age = 43;
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@@ -127,48 +53,6 @@ int8_t range = -42;
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The variable `age` is a `uint8_t` - an **unsigned** 8-bit integer that can only hold values from `0` to `255`. Since age is always a positive number, unsigned is the right choice. The variable `range` is an `int8_t` - a **signed** 8-bit integer that can hold values from `-128` to `127`. The signed type allows it to represent negative numbers like `-42`. Under the hood, negative values are stored using **two's complement** encoding: the CPU flips all the bits of `42` (`0x2A`) and adds `1`, producing `0xD6`, which is how `-42` lives in a single byte of memory.
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#### GPIO Initialization with Inline Assembly
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Instead of using the Pico SDK's `gpio_init()`, `gpio_set_dir()`, and `gpio_set_function()` helpers, this program configures GPIO pins **directly at the register level** using inline assembly. This gives us a window into how the hardware actually works on the RP2350.
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The initialization loop configures GPIO pins 16 through 19 (our red, green, blue, and yellow LEDs) in three steps per pin:
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**Step 1 - Configure the pad.** Each GPIO pin has a pad control register in `PADS_BANK0` starting at base address `0x40038000`. The code calculates the offset as `pin * 4`, loads the current register value, clears the **OD** (output disable) and **ISO** (isolation) bits with `bic r5, r5, #0x180`, and sets the **IE** (input enable) bit with `orr r5, r5, #0x40`. This ensures the pad is electrically active and ready to drive output.
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**Step 2 - Set the pin function.** Each GPIO pin has a control register in `IO_BANK0` starting at `0x40028004`. The offset is `pin * 8` because each pin's control block is 8 bytes wide. The code clears the `FUNCSEL` field (bits `[4:0]`) and sets it to `5`, which selects the **SIO** (Single-cycle I/O) function. SIO is the mode that lets software directly control pin state through the GPIO coprocessor.
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**Step 3 - Enable the output driver.** The instruction `mcrr p0, #4, r4, r5, c4` writes to the RP2350's GPIO coprocessor. Coprocessor register `c4` controls the **output enable** - with `r4` holding the pin number and `r5` set to `1`, this tells the hardware "this pin is an output." The `mcrr` (Move to Coprocessor from two ARM Registers) instruction is how the Cortex-M33 on the RP2350 talks to its dedicated GPIO coprocessor, bypassing the normal memory-mapped I/O path for single-cycle pin control.
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#### The Blink Loop with Inline Assembly
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Inside the `while (1)` loop, the program uses two inline assembly blocks to toggle the current LED on and off:
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```c
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"mcrr p0, #4, r4, r5, c0\n" // gpioc_bit_out_put(pin, 1)
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```
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This time the coprocessor register is `c0` instead of `c4`. Register `c0` controls the **output value** - setting `r5 = 1` drives the pin HIGH (LED on), and `r5 = 0` drives it LOW (LED off). Each toggle is followed by `sleep_ms(500)` for a half-second delay, creating a visible blink.
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The GCC extended assembly syntax `"r"(pin)` tells the compiler to load the C variable `pin` into a general-purpose register and make it available as `%0` inside the assembly block. The clobber list `"r4","r5"` warns the compiler that those registers are modified, so it won't store anything important there.
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#### The Pin Cycling and Print Statements
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After each on/off cycle, the program increments `pin` and wraps it back to `16` when it exceeds `18`:
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```c
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pin++;
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if (pin > 18) pin = 16;
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```
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This cycles through GPIO 16, 17, and 18 - red, green, and blue LEDs - creating a rotating blink pattern. Finally, `printf` prints both integer variables over UART so we can observe their values on the serial terminal:
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```
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age: 43
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range: -42
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```
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> Tip: **Why use inline assembly instead of the SDK?** This program is designed to teach you what happens *beneath* the SDK. When you call `gpio_put(16, 1)` in normal Pico code, the SDK ultimately does the same coprocessor write - `mcrr p0, #4, r4, r5, c0`. By writing the assembly directly, you can see exactly how the RP2350 hardware is controlled, which is essential knowledge for reverse engineering and binary patching.
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---
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## Part 2: Understanding Floating-Point Data Types
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@@ -198,13 +82,89 @@ A **float** is a number that can have a decimal point. Unlike integers which can
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+-----------------------------------------------------------------+
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```
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### How to Compute This by Hand (42.5 -> IEEE 754)
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Use this exact process any time you need to encode a decimal float manually.
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1. Determine the sign bit.
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- `42.5` is positive, so `sign = 0`.
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2. Convert the number to binary.
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- Integer part: `42 = 101010 (base 2)`
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- Fractional part: use repeated multiply-by-2 on the fraction.
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- Start with `0.5`
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- `0.5 * 2 = 1.0` -> integer part is `1` (this is the first binary fractional bit)
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- Remaining fractional part is now `0.0`, so we stop.
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- Therefore `0.5 = 0.1 (base 2)`.
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- Combined: `42.5 = 101010.1 (base 2)`
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3. Normalize to the form `1.xxxxx * 2^n`.
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- `101010.1 (base 2) = 1.010101 (base 2) * 2^5`
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- So the true exponent is `n = 5`.
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4. Compute the stored exponent (bias 127 for float).
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- `stored exponent = n + 127 = 5 + 127 = 132`
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- `132` in binary is `10000100` (8 bits).
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> Tip: **Why 127?** The exponent field is 8 bits wide, giving $2^8 = 256$ total values. Half of that range should represent negative exponents and half positive. The midpoint is $(2^8 / 2) - 1 = 127$. So a stored exponent of `127` means a real exponent of **0**, values below `127` are negative exponents, and values above `127` are positive exponents. Doubles use an 11-bit exponent field so their midpoint (bias) is $( 2^{11} / 2) - 1 = 1023$ instead.
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5. Build the mantissa (fraction bits).
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- Take bits after the leading `1.` from `1.010101` -> `010101`
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- Pad with zeros to 23 bits:
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- `01010100000000000000000`
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6. Assemble all fields.
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- `sign | exponent | mantissa`
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- `0 | 10000100 | 01010100000000000000000`
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- Full 32-bit pattern:
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- `01000010001010100000000000000000`
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7. Convert the 32-bit binary to hex (group by 4 bits).
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- `0100 0010 0010 1010 0000 0000 0000 0000`
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- `4 2 2 A 0 0 0 0`
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- Final result: `0x422A0000`
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Quick decode check (reverse direction, fully expanded):
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Given the 32-bit pattern:
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- `0 | 10000100 | 01010100000000000000000`
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Decode it field by field:
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1. Sign bit
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- Sign bit is `0` -> number is positive.
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- So the sign multiplier is `(+1)`.
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2. Exponent field
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- Exponent bits are `10000100`.
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- Convert to decimal: `10000100 (base 2) = 132`.
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- Float bias is `127`, so true exponent is:
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- `132 - 127 = 5`.
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3. Mantissa field
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- Stored mantissa bits are `01010100000000000000000`.
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- IEEE 754 normal numbers use an implicit leading `1`, so significand becomes:
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- `1.010101 (base 2)`.
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4. Rebuild the value
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- Formula: `value = (+1) * 1.010101 (base 2) * 2^5`.
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- Shift binary point right by 5:
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- `1.010101 * 2^5 = 101010.1 (base 2)`.
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5. Convert `101010.1 (base 2)` to decimal
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- Integer part: `101010 = 32 + 8 + 2 = 42`
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- Fraction part: `.1 = 1/2 = 0.5`
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- Total: `42 + 0.5 = 42.5`
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So the decoded value is exactly `42.5`.
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### Float vs Integer - Key Differences
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| Property | Integer (`uint8_t`) | Float (`float`) |
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| -------------- | ---------------------- | --------------------------- |
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| **Size** | 1 byte | 4 bytes |
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| **Precision** | Exact | ~7 decimal digits |
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| **Range** | 0 to 255 | ?3.4 * 10++ |
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| **Range** | 0 to 255 | ±3.4 × 10^38 |
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| **Encoding** | Direct binary | IEEE 754 (sign/exp/mantissa)|
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| **printf** | `%d` | `%f` |
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@@ -228,6 +188,10 @@ int main(void) {
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}
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```
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> Note: `fav_num` is declared inside `main`, so by C rules it is an automatic (stack) variable. In optimized embedded builds, the compiler may avoid creating a real stack slot and instead materialize the value from read-only constant storage (typically `.rodata` and/or an ARM literal pool).
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>
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> An ARM **literal pool** is a small table of constants that the assembler places near code in memory. Instead of encoding a large immediate value directly in an instruction, the CPU executes a load instruction (such as `ldr`) that reads the constant from that nearby table. That is why Ghidra can show constant loads rather than a classic stack local.
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**What this code does:**
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1. Declares a `float` variable `fav_num` and initializes it to `42.5`
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2. Initializes the serial output
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@@ -260,7 +224,7 @@ The program is printing `42.500000` because `printf` with `%f` defaults to 6 dec
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---
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## ? Part 2.5: Setting Up Ghidra for Float Analysis
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## 🔧 Part 2.5: Setting Up Ghidra for Float Analysis
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### Step 3: Start Ghidra
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@@ -313,7 +277,7 @@ Wait for analysis to complete (watch the progress bar in the bottom right).
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---
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## ? Part 2.6: Navigating and Resolving Functions
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## 🔍 Part 2.6: Navigating and Resolving Functions
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### Step 8: Find the Functions
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@@ -347,7 +311,7 @@ For `main`, let's also fix the return type:
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---
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## ? Part 2.7: Analyzing the Main Function
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## 🔬 Part 2.7: Analyzing the Main Function
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### Step 11: Examine Main in Ghidra
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@@ -357,6 +321,7 @@ You'll see something like:
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```c
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int main(void)
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{
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undefined4 uVar1;
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undefined4 extraout_r1;
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@@ -384,7 +349,7 @@ int main(void)
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1. Click on `FUN_100030ec`
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2. Right-click -> **Edit Function Signature**
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3. Change to: `int __wrap_printf(char *format,...)`
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3. Change to: `int printf(char *format,...)`
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4. Check the **Varargs** checkbox (printf takes variable arguments!)
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5. Click **OK**
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@@ -394,17 +359,18 @@ Look at the decompiled code after resolving functions:
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```c
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int main(void)
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{
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undefined4 uVar1;
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undefined4 extraout_r1;
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undefined4 uVar2;
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undefined4 extraout_r1_00;
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FUN_10002f5c();
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stdio_init_all();
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uVar1 = DAT_1000024c;
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uVar2 = extraout_r1;
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do {
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FUN_100030ec(DAT_10000250,uVar2,0,uVar1);
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printf(DAT_10000250,uVar2,0,uVar1);
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uVar2 = extraout_r1_00;
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} while( true );
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}
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@@ -472,7 +438,7 @@ Now let's check it. IEEE 754 uses a simple rule for the sign bit:
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```
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r3 = 0x40454000 = 0100 0000 0100 0101 0100 0000 0000 0000
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^
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r3 bit 31 = 0 -> sign = 0 -> Positive number
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r3 bit 31 = 0 -> sign = 0 -> Positive number
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```
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The topmost bit of r3 is `0`, so the number is **positive**. If that bit were `1` instead (e.g. `0xC0454000`), the number would be negative (`-42.5`).
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@@ -507,35 +473,35 @@ This means the number is scaled by $2^5 = 32$. In other words, the mantissa gets
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- **High 20 bits of mantissa** (bits 51-32) = bits 19-0 of r3:
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```
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r3 bits 19-0: 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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r3 bits 19-0: 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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```
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- **Low 32 bits of mantissa** (bits 31-0) = all of r2:
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```
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r2 = 0x00000000 -> 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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r2 = 0x00000000 -> 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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```
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Full 52-bit mantissa:
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```
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0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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?? top 20 bits from r3 -> ?? bottom 32 bits from r2 (all zero) ->
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<- top 20 bits from r3 -> <- bottom 32 bits from r2 (all zero) ->
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```
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IEEE 754 always prepends an **implied leading `1`**, so the actual value represented is:
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||||
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||||
```
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1.010101 00000... (the 1. is implicit, not stored)
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1.010101 00000... (the 1. is implicit, not stored)
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```
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**4. Reconstruct the value**
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$$1.010101_2 \times 2^5$$
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$$1.010101\text{ (base 2)} \times 2^5$$
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Shift the binary point 5 places right:
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$$101010.1_2$$
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$$101010.1\text{ (base 2)}$$
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||||
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||||
Now convert each bit position to decimal:
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||||
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@@ -547,9 +513,9 @@ Now convert each bit position to decimal:
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||||
| `0` (bit 2) | $2^2$ | 0 |
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||||
| `1` (bit 1) | $2^1$ | 2 |
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||||
| `0` (bit 0) | $2^0$ | 0 |
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||||
| `1` (bit ?1) | $2^{-1}$ | 0.5 |
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| `1` (bit -1) | $2^{-1}$ | 0.5 |
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||||
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$$32 + 8 + 2 + 0.5 = \mathbf{42.5} ?$$
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$$32 + 8 + 2 + 0.5 = \mathbf{42.5}$$
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||||
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||||
### Step 16: Examine the Assembly
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||||
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||||
@@ -559,49 +525,47 @@ Look at the **Listing** window (assembly view). Find the main function:
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||||
*************************************************************
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||||
* FUNCTION
|
||||
*************************************************************
|
||||
undefined FUN_10000234 ()
|
||||
undefined <UNASSIGNED> <RETURN>
|
||||
FUN_10000234+1 XREF[1,1]: 1000018c (c) , 1000018a (*)
|
||||
FUN_10000234
|
||||
10000234 38 b5 push {r3,r4,r5,lr}
|
||||
10000236 02 f0 91 fe bl FUN_10002f5c undefined FUN_10002f5c()
|
||||
1000023a 00 24 movs r4,#0x0
|
||||
1000023c 03 4d ldr r5,[DAT_1000024c ] = 40454000h
|
||||
int __stdcall main (void )
|
||||
int r0:4 <RETURN>
|
||||
main+1 XREF[1,1]: 1000018c (c) , 1000018a (*)
|
||||
main
|
||||
10000234 38 b5 push {r3,r4,r5,lr}
|
||||
10000236 02 f0 91 fe bl stdio_init_all bool stdio_init_all(void)
|
||||
1000023a 00 24 movs r4,#0x0
|
||||
1000023c 03 4d ldr r5,[DAT_1000024c ] = 40454000h
|
||||
LAB_1000023e XREF[1]: 10000248 (j)
|
||||
1000023e 22 46 mov r2,r4
|
||||
10000240 2b 46 mov r3,r5
|
||||
10000242 03 48 ldr r0=>s_fav_num:_%f_100034a8 ,[DAT_10000250 ] = "fav_num: %f\r\n"
|
||||
1000023e 22 46 mov r2,r4
|
||||
10000240 2b 46 mov r3,r5
|
||||
10000242 03 48 ldr r0=>s_fav_num:_%f_100034a8 ,[DAT_10000250 ] = "fav_num: %f\r\n"
|
||||
= 100034A8h
|
||||
10000244 02 f0 52 ff bl FUN_100030ec undefined FUN_100030ec()
|
||||
10000248 f9 e7 b LAB_1000023e
|
||||
10000244 02 f0 52 ff bl printf int printf(char * format, ...)
|
||||
10000248 f9 e7 b LAB_1000023e
|
||||
1000024a 00 ?? 00h
|
||||
1000024b bf ?? BFh
|
||||
DAT_1000024c XREF[1]: FUN_10000234:1000023c (R)
|
||||
1000024c 00 40 45 40 undefine 40454000h
|
||||
DAT_10000250 XREF[1]: FUN_10000234:10000242 (R)
|
||||
10000250 a8 34 00 10 undefine 100034A8h ? -> 100034a8
|
||||
|
||||
DAT_1000024c XREF[1]: main:1000023c (R)
|
||||
1000024c 00 40 45 40 undefine 40454000h
|
||||
DAT_10000250 XREF[1]: main:10000242 (R)
|
||||
10000250 a8 34 00 10 undefine 100034A8h * -> 100034a8
|
||||
```
|
||||
|
||||
> ? **Key Insight:** The `mov.w r2, #0x0` loads the low 32 bits (all zeros) and `ldr r3, [DAT_...]` loads the high 32 bits (`0x40454000`) of the double. Together, `r2:r3` = `0x40454000_00000000` = `42.5` as a double.
|
||||
> 💡 **Key Insight:** The `mov.w r2, #0x0` loads the low 32 bits (all zeros) and `ldr r3, [DAT_...]` loads the high 32 bits (`0x40454000`) of the double. Together, `r2:r3` = `0x40454000_00000000` = `42.5` as a double.
|
||||
|
||||
### Step 17: Find the Format String
|
||||
|
||||
In the Listing view, click on the data reference to find the format string:
|
||||
|
||||
```
|
||||
s_fav_num:_%f_100034a8 XREF[1]: FUN_10000234:10000242 (*)
|
||||
100034a8 66 61 76 ds "fav_num: %f\r\n"
|
||||
5f 6e 75
|
||||
6d 3a 20
|
||||
|
||||
s_fav_num:_%f_100034a8 XREF[1]: main:10000242 (*)
|
||||
100034a8 66 61 76 ds "fav_num: %f\r\n"
|
||||
5f 6e 75
|
||||
6d 3a 20
|
||||
```
|
||||
|
||||
This confirms `printf` is called with the format string `"fav_num: %f\r\n"` and the double-precision value of `42.5`.
|
||||
|
||||
---
|
||||
|
||||
## ? Part 2.8: Patching the Float - Changing 42.5 to 99.0
|
||||
## ✏️ Part 2.8: Patching the Float - Changing 42.5 to 99.0
|
||||
|
||||
### Step 18: Calculate the New IEEE 754 Encoding
|
||||
|
||||
@@ -611,15 +575,15 @@ We want to change `42.5` to `99.0`. First, we need to figure out the double-prec
|
||||
|
||||
| Division | Quotient | Remainder |
|
||||
|---------------|----------|-----------|
|
||||
| 99 ? 2 | 49 | **1** |
|
||||
| 49 ? 2 | 24 | **1** |
|
||||
| 24 ? 2 | 12 | **0** |
|
||||
| 12 ? 2 | 6 | **0** |
|
||||
| 6 ? 2 | 3 | **0** |
|
||||
| 3 ? 2 | 1 | **1** |
|
||||
| 1 ? 2 | 0 | **1** |
|
||||
| 99 ÷ 2 | 49 | **1** |
|
||||
| 49 ÷ 2 | 24 | **1** |
|
||||
| 24 ÷ 2 | 12 | **0** |
|
||||
| 12 ÷ 2 | 6 | **0** |
|
||||
| 6 ÷ 2 | 3 | **0** |
|
||||
| 3 ÷ 2 | 1 | **1** |
|
||||
| 1 ÷ 2 | 0 | **1** |
|
||||
|
||||
Read remainders bottom-to-top: $99_{10} = 1100011_2$
|
||||
Read remainders bottom-to-top: 99 (base 10) = 1100011 (base 2)
|
||||
|
||||
**Step B - Convert the fractional part (.0) to binary:**
|
||||
|
||||
@@ -627,18 +591,18 @@ There is no fractional part - `.0` is exactly zero, so the fractional binary is
|
||||
|
||||
**Step C - Combine:**
|
||||
|
||||
$$99.0_{10} = 1100011.0_2$$
|
||||
$$99.0\text{ (base 10)} = 1100011.0\text{ (base 2)}$$
|
||||
|
||||
**Step D - Normalize to IEEE 754 form** (move the binary point so there's exactly one `1` before it):
|
||||
|
||||
$$1100011.0_2 = 1.100011_2 \times 2^6$$
|
||||
$$1100011.0\text{ (base 2)} = 1.100011\text{ (base 2)} \times 2^6$$
|
||||
|
||||
We shifted the binary point 6 places left, so the exponent is **6**.
|
||||
|
||||
**Step E - Extract the IEEE 754 fields:**
|
||||
|
||||
1. **Sign:** `0` (positive)
|
||||
2. **Exponent:** $6 + 1023 = 1029 = 10000000101_2$
|
||||
2. **Exponent:** $6 + 1023 = 1029 = 10000000101\text{ (base 2)}$
|
||||
3. **Mantissa:** `1000110000000000...` (everything after the `1.`, padded with zeros to 52 bits)
|
||||
4. **Full double:** `0x4058C00000000000`
|
||||
|
||||
@@ -654,7 +618,7 @@ Since `r2` stays `0x00000000`, we only need to patch the high word loaded into `
|
||||
Look in the Listing view for the data that loads the high word of the double:
|
||||
|
||||
```
|
||||
10000248 00 40 45 40 undefined4 40454000h
|
||||
1000024c 00 40 45 40 undefined4 40454000h
|
||||
```
|
||||
|
||||
This is the 32-bit constant that gets loaded into `r3` - the high word of our double `42.5`.
|
||||
@@ -662,16 +626,15 @@ This is the 32-bit constant that gets loaded into `r3` - the high word of our do
|
||||
### Step 20: Patch the Constant
|
||||
|
||||
1. Click on Window -> Bytes
|
||||
2. Click on Pencil Icon in Bytes Editor
|
||||
2. Right-click and select **Patch Data**
|
||||
3. Change `00404540` to `00C05840`
|
||||
2. Click on the Pencil icon to enable byte editing
|
||||
3. At address `1000024c`, overwrite `00 40 45 40` with `00 C0 58 40` (little-endian for `0x40454000 -> 0x4058C000`)
|
||||
4. Press Enter
|
||||
|
||||
This changes the high word from `0x40454000` (42.5 as double) to `0x4058C000` (99.0 as double).
|
||||
|
||||
---
|
||||
|
||||
## ? Part 2.9: Export and Test the Hacked Binary
|
||||
## 🚀 Part 2.9: Export and Test the Hacked Binary
|
||||
|
||||
### Step 21: Export the Patched Binary
|
||||
|
||||
@@ -686,7 +649,7 @@ This changes the high word from `0x40454000` (42.5 as double) to `0x4058C000` (9
|
||||
**Open a terminal and navigate to your project directory:**
|
||||
|
||||
```powershell
|
||||
cd C:\Users\assem.KEVINTHOMAS\OneDrive\Documents\Embedded-Hacking\0x000e_floating-point-data-type
|
||||
cd C:\Users\flare-vm\Desktop\Embedded-Hacking-main\0x000e_floating-point-data-type
|
||||
```
|
||||
|
||||
**Run the conversion command:**
|
||||
@@ -710,7 +673,7 @@ fav_num: 99.000000
|
||||
...
|
||||
```
|
||||
|
||||
? **BOOM! We hacked the float!** The value changed from `42.5` to `99.0`!
|
||||
🎉 **BOOM! We hacked the float!** The value changed from `42.5` to `99.0`!
|
||||
|
||||
---
|
||||
|
||||
@@ -748,7 +711,7 @@ A **double** (short for "double-precision floating-point") is like a `float` but
|
||||
| **Precision** | ~7 decimal digits | ~15 decimal digits |
|
||||
| **Exponent** | 8 bits (bias 127) | 11 bits (bias 1023) |
|
||||
| **Mantissa** | 23 bits | 52 bits |
|
||||
| **Range** | ?3.4 * 10++ | ?1.8 * 10+++? |
|
||||
| **Range** | ±3.4 × 10^38 | ±1.8 × 10^308 |
|
||||
| **printf** | `%f` | `%lf` |
|
||||
| **ARM passing** | Promoted to double | Native in `r2:r3` |
|
||||
|
||||
@@ -806,7 +769,7 @@ The program is printing `42.525250` because `printf` with `%lf` defaults to 6 de
|
||||
|
||||
---
|
||||
|
||||
## ? Part 3.5: Setting Up Ghidra for Double Analysis
|
||||
## 🔧 Part 3.5: Setting Up Ghidra for Double Analysis
|
||||
|
||||
### Step 3: Start Ghidra
|
||||
|
||||
@@ -859,7 +822,7 @@ Wait for analysis to complete (watch the progress bar in the bottom right).
|
||||
|
||||
---
|
||||
|
||||
## ? Part 3.6: Navigating and Resolving Functions
|
||||
## 🔍 Part 3.6: Navigating and Resolving Functions
|
||||
|
||||
### Step 8: Find the Functions
|
||||
|
||||
@@ -893,7 +856,7 @@ For `main`, let's also fix the return type:
|
||||
|
||||
---
|
||||
|
||||
## ? Part 3.7: Analyzing the Main Function
|
||||
## 🔬 Part 3.7: Analyzing the Main Function
|
||||
|
||||
### Step 11: Examine Main in Ghidra
|
||||
|
||||
@@ -901,48 +864,9 @@ Click on `main` (or `FUN_10000234`). Look at the **Decompile** window:
|
||||
|
||||
You'll see something like:
|
||||
|
||||
```c
|
||||
void FUN_10000238(void)
|
||||
{
|
||||
undefined4 uVar1;
|
||||
undefined4 uVar2;
|
||||
undefined4 extraout_r1;
|
||||
undefined4 uVar3;
|
||||
undefined4 extraout_r1_00;
|
||||
undefined4 in_r3;
|
||||
|
||||
uVar2 = DAT_10000258;
|
||||
uVar1 = DAT_10000254;
|
||||
FUN_10002f64();
|
||||
uVar3 = extraout_r1;
|
||||
do {
|
||||
FUN_100030f4(DAT_10000250,uVar3,uVar1,uVar2,in_r3);
|
||||
uVar3 = extraout_r1_00;
|
||||
} while( true );
|
||||
}
|
||||
```
|
||||
|
||||
### Step 12: Resolve stdio_init_all
|
||||
|
||||
1. Click on `FUN_10002f64`
|
||||
2. Right-click -> **Edit Function Signature**
|
||||
3. Change to: `bool stdio_init_all(void)`
|
||||
4. Click **OK**
|
||||
|
||||
### Step 13: Resolve printf
|
||||
|
||||
1. Click on `FUN_100030f4`
|
||||
2. Right-click -> **Edit Function Signature**
|
||||
3. Change the name to `printf`
|
||||
4. Check the **Varargs** checkbox (printf takes variable arguments!)
|
||||
5. Click **OK**
|
||||
|
||||
### Step 14: Understand the Double Encoding
|
||||
|
||||
Look at the decompiled code after resolving functions:
|
||||
|
||||
```c
|
||||
int main(void)
|
||||
|
||||
{
|
||||
undefined4 uVar1;
|
||||
undefined4 uVar2;
|
||||
@@ -961,6 +885,46 @@ int main(void)
|
||||
}
|
||||
```
|
||||
|
||||
### Step 12: Resolve stdio_init_all
|
||||
|
||||
1. Click on `FUN_10002f64`
|
||||
2. Right-click -> **Edit Function Signature**
|
||||
3. Change to: `bool stdio_init_all(void)`
|
||||
4. Click **OK**
|
||||
|
||||
### Step 13: Resolve printf
|
||||
|
||||
1. Click on `FUN_100030f4`
|
||||
2. Right-click -> **Edit Function Signature**
|
||||
3. Change to: `int printf(char *format,...)`
|
||||
4. Check the **Varargs** checkbox (printf takes variable arguments!)
|
||||
5. Click **OK**
|
||||
|
||||
### Step 14: Understand the Double Encoding
|
||||
|
||||
Look at the decompiled code after resolving functions:
|
||||
|
||||
```c
|
||||
int main(void)
|
||||
|
||||
{
|
||||
undefined4 uVar1;
|
||||
undefined4 uVar2;
|
||||
undefined4 extraout_r1;
|
||||
undefined4 uVar3;
|
||||
undefined4 extraout_r1_00;
|
||||
|
||||
uVar2 = DAT_10000258;
|
||||
uVar1 = DAT_10000254;
|
||||
stdio_init_all();
|
||||
uVar3 = extraout_r1;
|
||||
do {
|
||||
printf(DAT_10000250,uVar3,uVar1,uVar2);
|
||||
uVar3 = extraout_r1_00;
|
||||
} while( true );
|
||||
}
|
||||
```
|
||||
|
||||
**Where's `double fav_num = 42.52525`?** It's been optimized into immediate values!
|
||||
|
||||
This time we see **two** non-zero values: `0x645a1cac` and `0x4045433b`. Unlike the float example where the low word was `0x0`, a double with a fractional part like `42.52525` needs **all 52 mantissa bits** - so both halves carry data.
|
||||
@@ -974,7 +938,7 @@ A 64-bit double is passed in two 32-bit registers:
|
||||
|
||||
Together they form `0x4045433B645A1CAC` - the IEEE 754 **double-precision** encoding of `42.52525`.
|
||||
|
||||
> ? **Key Difference from Float:** In the float example, `r2` was `0x00000000` because `42.5` has a clean fractional part. But `42.52525` has a repeating binary fraction, so the low 32 bits are non-zero (`0x645A1CAC`). This means **both** registers matter when patching doubles with complex fractional values!
|
||||
> 💡 **Key Difference from Float:** In the float example, `r2` was `0x00000000` because `42.5` has a clean fractional part. But `42.52525` has a repeating binary fraction, so the low 32 bits are non-zero (`0x645A1CAC`). This means **both** registers matter when patching doubles with complex fractional values!
|
||||
|
||||
### Step 15: Verify the Double Encoding
|
||||
|
||||
@@ -992,12 +956,10 @@ Bit: 63 62-52 (11 bits) 51-32 (20 bits) 3
|
||||
+---+-----------------------+------------------------------------------+------------------------------------------+
|
||||
| 0 | 1 0 0 0 0 0 0 0 1 0 0 | 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 | 01100100010110100001110010101100 |
|
||||
+---+-----------------------+------------------------------------------+------------------------------------------+
|
||||
Sign Exponent (11) Mantissa high 20 bits Mantissa low 32 bits
|
||||
(from r3 bits 19-0) (from r2)
|
||||
Sign Exponent (11) Mantissa high 20 bits Mantissa low 32 bits
|
||||
(from r3 bits 19-0) (from r2)
|
||||
```
|
||||
|
||||
> ? **Key Difference from 42.5:** In the `42.5` example, r2 was `0x00000000` because `42.5` has a clean fractional part (`.5` = exactly one binary digit). But `42.52525` has a repeating binary fraction, so the low 32 bits are **non-zero** (`0x645A1CAC`). Every bit of both registers matters here!
|
||||
|
||||
**Step-by-step field extraction:**
|
||||
|
||||
**1. Sign bit**
|
||||
@@ -1007,7 +969,7 @@ The sign bit is bit 63 of the 64-bit double, which is bit 31 of r3 (the high reg
|
||||
```
|
||||
r3 = 0x4045433B = 0100 0000 0100 0101 0100 0011 0011 1011
|
||||
^
|
||||
r3 bit 31 = 0 -> sign = 0 -> Positive number ?
|
||||
r3 bit 31 = 0 -> sign = 0 -> Positive number ✓
|
||||
```
|
||||
|
||||
**2. Exponent - bits 62-52 = bits 30-20 of r3**
|
||||
@@ -1042,29 +1004,29 @@ r3 bits 19-0: 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1
|
||||
- **Low 32 bits of mantissa** (bits 31-0) = all of r2:
|
||||
|
||||
```
|
||||
r2 = 0x645A1CAC -> 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0
|
||||
r2 = 0x645A1CAC -> 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0
|
||||
```
|
||||
|
||||
Full 52-bit mantissa:
|
||||
|
||||
```
|
||||
0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 1 1 0 1 1 | 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 0 0
|
||||
?? top 20 bits from r3 -> ?? bottom 32 bits from r2 ->
|
||||
<- top 20 bits from r3 -> <- bottom 32 bits from r2 ->
|
||||
```
|
||||
|
||||
IEEE 754 always prepends an **implied leading `1`**, so the actual value represented is:
|
||||
|
||||
```
|
||||
1.0101010000110011101101100100010110100001110010101100 (the 1. is implicit, not stored)
|
||||
1.0101010000110011101101100100010110100001110010101100 (the 1. is implicit, not stored)
|
||||
```
|
||||
|
||||
**4. Reconstruct the value**
|
||||
|
||||
$$1.0101010000110011101101100100..._2 \times 2^5$$
|
||||
$$1.0101010000110011101101100100...\text{ (base 2)} \times 2^5$$
|
||||
|
||||
Shift the binary point 5 places right:
|
||||
|
||||
$$101010.10000110011101101100100010110100001110010101100_2$$
|
||||
$$101010.10000110011101101100100010110100001110010101100\text{ (base 2)}$$
|
||||
|
||||
**Integer part** (`101010`):
|
||||
|
||||
@@ -1083,25 +1045,25 @@ $$32 + 8 + 2 = \mathbf{42}$$
|
||||
|
||||
| Bit position | Power of 2 | Decimal value |
|
||||
|---|---|---|
|
||||
| `1` (bit ?1) | $2^{-1}$ | 0.5 |
|
||||
| `0` (bit ?2) | $2^{-2}$ | 0 |
|
||||
| `0` (bit ?3) | $2^{-3}$ | 0 |
|
||||
| `0` (bit ?4) | $2^{-4}$ | 0 |
|
||||
| `0` (bit ?5) | $2^{-5}$ | 0 |
|
||||
| `1` (bit ?6) | $2^{-6}$ | 0.015625 |
|
||||
| `1` (bit ?7) | $2^{-7}$ | 0.0078125 |
|
||||
| `0` (bit ?8) | $2^{-8}$ | 0 |
|
||||
| `0` (bit ?9) | $2^{-9}$ | 0 |
|
||||
| `1` (bit ?10) | $2^{-10}$ | 0.0009765625 |
|
||||
| `1` (bit ?11) | $2^{-11}$ | 0.00048828125 |
|
||||
| `1` (bit ?12) | $2^{-12}$ | 0.000244140625 |
|
||||
| `1` (bit -1) | $2^{-1}$ | 0.5 |
|
||||
| `0` (bit -2) | $2^{-2}$ | 0 |
|
||||
| `0` (bit -3) | $2^{-3}$ | 0 |
|
||||
| `0` (bit -4) | $2^{-4}$ | 0 |
|
||||
| `0` (bit -5) | $2^{-5}$ | 0 |
|
||||
| `1` (bit -6) | $2^{-6}$ | 0.015625 |
|
||||
| `1` (bit -7) | $2^{-7}$ | 0.0078125 |
|
||||
| `0` (bit -8) | $2^{-8}$ | 0 |
|
||||
| `0` (bit -9) | $2^{-9}$ | 0 |
|
||||
| `1` (bit -10) | $2^{-10}$ | 0.0009765625 |
|
||||
| `1` (bit -11) | $2^{-11}$ | 0.00048828125 |
|
||||
| `1` (bit -12) | $2^{-12}$ | 0.000244140625 |
|
||||
| ... | ... | *(remaining 35 bits add smaller and smaller fractions)* |
|
||||
|
||||
First 12 fractional bits sum: $0.5 + 0.015625 + 0.0078125 + 0.0009765625 + 0.00048828125 + 0.000244140625 \approx 0.5251$
|
||||
|
||||
The remaining 35 fractional bits refine this to $\approx 0.52525$. This is because `0.52525` is a **repeating fraction** in binary - it can never be represented with a finite number of bits, so double precision stores the closest possible 52-bit approximation.
|
||||
|
||||
$$42 + 0.52525 = \mathbf{42.52525} ?$$
|
||||
$$42 + 0.52525 = \mathbf{42.52525} \checkmark$$
|
||||
|
||||
### Step 16: Examine the Assembly
|
||||
|
||||
@@ -1111,58 +1073,57 @@ Look at the **Listing** window (assembly view). Find the main function:
|
||||
*************************************************************
|
||||
* FUNCTION
|
||||
*************************************************************
|
||||
undefined FUN_10000238 ()
|
||||
undefined <UNASSIGNED> <RETURN>
|
||||
FUN_10000238+1 XREF[1,1]: 1000018c (c) , 1000018a (*)
|
||||
FUN_10000238
|
||||
10000238 38 b5 push {r3,r4,r5,lr}
|
||||
1000023a 06 a5 adr r5,[0x10000254 ]
|
||||
1000023c d5 e9 00 45 ldrd r4,r5,[r5,#0x0 ]=>DAT_10000254 = 645A1CACh
|
||||
int __stdcall main (void )
|
||||
int r0:4 <RETURN>
|
||||
main+1 XREF[1,1]: 1000018c (c) , 1000018a (*)
|
||||
main
|
||||
10000238 38 b5 push {r3,r4,r5,lr}
|
||||
1000023a 06 a5 adr r5,[0x10000254 ]
|
||||
1000023c d5 e9 00 45 ldrd r4,r5,[r5,#0x0 ]=>DAT_10000254 = 645A1CACh
|
||||
= 4045433Bh
|
||||
10000240 02 f0 90 fe bl FUN_10002f64 undefined FUN_10002f64()
|
||||
10000240 02 f0 90 fe bl stdio_init_all bool stdio_init_all(void)
|
||||
LAB_10000244 XREF[1]: 1000024e (j)
|
||||
10000244 22 46 mov r2,r4
|
||||
10000246 2b 46 mov r3,r5
|
||||
10000248 01 48 ldr r0=>s_fav_num:_%lf_100034b0 ,[DAT_10000250 ] = "fav_num: %lf\r\n"
|
||||
10000244 22 46 mov r2,r4
|
||||
10000246 2b 46 mov r3,r5
|
||||
10000248 01 48 ldr r0=>s_fav_num:_%lf_100034b0 ,[DAT_10000250 ] = "fav_num: %lf\r\n"
|
||||
= 100034B0h
|
||||
1000024a 02 f0 53 ff bl FUN_100030f4 undefined FUN_100030f4()
|
||||
1000024e f9 e7 b LAB_10000244
|
||||
DAT_10000250 XREF[1]: FUN_10000238:10000248 (R)
|
||||
10000250 b0 34 00 10 undefine 100034B0h ? -> 100034b0
|
||||
DAT_10000254 XREF[1]: FUN_10000238:1000023c (R)
|
||||
10000254 ac 1c 5a 64 undefine 645A1CACh
|
||||
DAT_10000258 XREF[1]: FUN_10000238:1000023c (R)
|
||||
10000258 3b 43 45 40 undefine 4045433Bh
|
||||
1000024a 02 f0 53 ff bl printf int printf(char * format, ...)
|
||||
1000024e f9 e7 b LAB_10000244
|
||||
DAT_10000250 XREF[1]: main:10000248 (R)
|
||||
10000250 b0 34 00 10 undefine 100034B0h ? -> 100034b0
|
||||
DAT_10000254 XREF[1]: main:1000023c (R)
|
||||
10000254 ac 1c 5a 64 undefine 645A1CACh
|
||||
DAT_10000258 XREF[1]: main:1000023c (R)
|
||||
10000258 3b 43 45 40 undefine 4045433Bh
|
||||
```
|
||||
|
||||
> ? **Key Insight:** Notice that **both** `r2` and `r3` are loaded from data constants using `ldr`. Compare this to the float example where `r2` was loaded with `mov.w r2, #0x0`. Because `42.52525` requires all 52 mantissa bits, neither word can be zero - the compiler must store both halves as separate data constants.
|
||||
> 💡 **Key Insight:** Notice that **both** `r2` and `r3` are loaded from data constants using `ldr`. Compare this to the float example where `r2` was loaded with `mov.w r2, #0x0`. Because `42.52525` requires all 52 mantissa bits, neither word can be zero - the compiler must store both halves as separate data constants.
|
||||
|
||||
### Step 17: Find the Format String
|
||||
|
||||
In the Listing view, click on the data reference to find the format string:
|
||||
|
||||
```
|
||||
s_fav_num:_%lf_100034b0 XREF[1]: FUN_10000238:10000248 (*)
|
||||
100034b0 66 61 76 ds "fav_num: %lf\r\n"
|
||||
5f 6e 75
|
||||
6d 3a 20
|
||||
|
||||
s_fav_num:_%lf_100034b0 XREF[1]: main:10000248 (*)
|
||||
100034b0 66 61 76 ds "fav_num: %lf\r\n"
|
||||
5f 6e 75
|
||||
6d 3a 20
|
||||
```
|
||||
|
||||
This confirms `printf` is called with the format string `"fav_num: %lf\r\n"` and the double-precision value of `42.52525`.
|
||||
|
||||
---
|
||||
|
||||
## ? Part 3.8: Patching the Double - Changing 42.52525 to 99.99
|
||||
## ✏️ Part 3.8: Patching the Double - Changing 42.52525 to 99.99
|
||||
|
||||
### Step 18: Calculate the New IEEE 754 Encoding
|
||||
|
||||
We want to change `42.52525` to `99.99`. First, we need to figure out the double-precision encoding of `99.99`:
|
||||
|
||||
1. $99.99 = 1.5623... \times 2^6 = 1.100011111111..._2 \times 2^6$
|
||||
1. $99.99 = 1.5623... \times 2^6 = 1.100011111111...\text{ (base 2)} \times 2^6$
|
||||
2. **Sign:** `0` (positive)
|
||||
3. **Exponent:** $6 + 1023 = 1029 = 10000000101_2$
|
||||
4. **Mantissa:** `1000111111010111000010100011110101110000101000111..._2$
|
||||
3. **Exponent:** $6 + 1023 = 1029 = 10000000101\text{ (base 2)}$
|
||||
4. **Mantissa:** `1000111111010111000010100011110101110000101000111... (base 2)`
|
||||
5. **Full double:** `0x4058FF5C28F5C28F`
|
||||
|
||||
| Register | Old Value | New Value |
|
||||
@@ -1178,35 +1139,35 @@ Look in the Listing view for the two data constants:
|
||||
|
||||
**Low word (loaded into `r2`):**
|
||||
```
|
||||
10000254 ac 1c 5a 64 undefined4 645A1CACh
|
||||
10000254 ac 1c 5a 64 undefined4 645A1CACh
|
||||
```
|
||||
|
||||
**High word (loaded into `r3`):**
|
||||
```
|
||||
10000258 3b 43 45 40 undefined4 4045433Bh
|
||||
10000258 3b 43 45 40 undefined4 4045433Bh
|
||||
```
|
||||
|
||||
### Step 20: Patch Both Constants
|
||||
|
||||
**Patch the low word:**
|
||||
1. Click on the data at address `10000254` containing `645A1CAC`
|
||||
2. Right-click and select **Patch Data**
|
||||
3. Change `645A1CAC` to `28F5C28F` -> `8FC2F528`
|
||||
2. Open the Bytes window and enable byte editing (Pencil icon)
|
||||
3. Overwrite bytes `ac 1c 5a 64` with `8f c2 f5 28` (little-endian for `0x645A1CAC -> 0x28F5C28F`)
|
||||
4. Press Enter
|
||||
|
||||
**Patch the high word:**
|
||||
1. Click on the data at address `10000258` containing `4045433B`
|
||||
2. Right-click and select **Patch Data**
|
||||
3. Change `4045433B` to `4058FF5C` -> `5CFF5840`
|
||||
2. Keep byte editing enabled in the Bytes window
|
||||
3. Overwrite bytes `3b 43 45 40` with `5c ff 58 40` (little-endian for `0x4045433B -> 0x4058FF5C`)
|
||||
4. Press Enter
|
||||
|
||||
This changes the full 64-bit double from `0x4045433B645A1CAC` (42.52525) to `0x4058FF5C28F5C28F` (99.99).
|
||||
|
||||
> ? **Key Difference from Float Patching:** When we patched the float `42.5`, we only needed to change one word (the high word in `r3`) because the low word was all zeros. With `42.52525 -> 99.99`, **both** words change. Always check whether the low word is non-zero before patching!
|
||||
> 💡 **Key Difference from Float Patching:** When we patched the float `42.5`, we only needed to change one word (the high word in `r3`) because the low word was all zeros. With `42.52525 -> 99.99`, **both** words change. Always check whether the low word is non-zero before patching!
|
||||
|
||||
---
|
||||
|
||||
## ? Part 3.9: Export and Test the Hacked Binary
|
||||
## 🚀 Part 3.9: Export and Test the Hacked Binary
|
||||
|
||||
### Step 21: Export the Patched Binary
|
||||
|
||||
@@ -1221,7 +1182,7 @@ This changes the full 64-bit double from `0x4045433B645A1CAC` (42.52525) to `0x4
|
||||
**Open a terminal and navigate to your project directory:**
|
||||
|
||||
```powershell
|
||||
cd C:\Users\assem.KEVINTHOMAS\OneDrive\Documents\Embedded-Hacking\0x0011_double-floating-point-data-type
|
||||
cd C:\Users\flare-vm\Desktop\Embedded-Hacking-main\0x0011_double-floating-point-data-type
|
||||
```
|
||||
|
||||
**Run the conversion command:**
|
||||
@@ -1245,11 +1206,11 @@ fav_num: 99.990000
|
||||
...
|
||||
```
|
||||
|
||||
? **BOOM! We hacked the double!** The value changed from `42.52525` to `99.99`!
|
||||
🎉 **BOOM! We hacked the double!** The value changed from `42.52525` to `99.99`!
|
||||
|
||||
---
|
||||
|
||||
## ? Part 3.95: Summary - Float and Double Analysis
|
||||
## 📊 Part 3.95: Summary - Float and Double Analysis
|
||||
|
||||
### What We Accomplished
|
||||
|
||||
@@ -1293,7 +1254,7 @@ fav_num: 99.990000
|
||||
| - Split into high/low words |
|
||||
+-----------------------------------------------------------------+
|
||||
| 5. Patch the constant(s) in Ghidra |
|
||||
| - Right-click -> Patch Data |
|
||||
| - Edit bytes in the Bytes window (Pencil mode) |
|
||||
| - Replace the old encoding with the new one |
|
||||
+-----------------------------------------------------------------+
|
||||
| 6. Export -> Convert to UF2 -> Flash -> Verify |
|
||||
@@ -1307,7 +1268,7 @@ fav_num: 99.990000
|
||||
|
||||
---
|
||||
|
||||
## ? Key Takeaways
|
||||
## 💡 Key Takeaways
|
||||
|
||||
1. **Integers have fixed sizes** - `uint8_t` is 1 byte (0-255), `int8_t` is 1 byte (-128 to 127). The `u` prefix means unsigned.
|
||||
|
||||
@@ -1325,7 +1286,7 @@ fav_num: 99.990000
|
||||
|
||||
---
|
||||
|
||||
## ? Glossary
|
||||
## 📖 Glossary
|
||||
|
||||
| Term | Definition |
|
||||
| ----------------------- | ------------------------------------------------------------------------------ |
|
||||
@@ -1349,7 +1310,7 @@ fav_num: 99.990000
|
||||
|
||||
---
|
||||
|
||||
## ? Additional Resources
|
||||
## 📚 Additional Resources
|
||||
|
||||
### GPIO Coprocessor Reference
|
||||
|
||||
@@ -1388,6 +1349,4 @@ The RP2350 GPIO coprocessor instructions:
|
||||
|
||||
**Remember:** Every binary you encounter in the real world can be analyzed and understood using these same techniques. Whether it's an integer, a float, or a double - it's all just bits waiting to be decoded. Practice makes perfect!
|
||||
|
||||
Happy hacking! ?
|
||||
|
||||
|
||||
Happy hacking! 🎉
|
||||
|
||||
@@ -0,0 +1,79 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
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.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
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.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
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<rect class="bg" width="1200" height="800"/>
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|
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<!-- Background grid decoration -->
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<g opacity="0.06">
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<line x1="200" y1="0" x2="200" y2="800" stroke="#00ff41" stroke-width="1"/>
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<line x1="400" y1="0" x2="400" y2="800" stroke="#00ff41" stroke-width="1"/>
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<line x1="600" y1="0" x2="600" y2="800" stroke="#00ff41" stroke-width="1"/>
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<line x1="800" y1="0" x2="800" y2="800" stroke="#00ff41" stroke-width="1"/>
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<line x1="1000" y1="0" x2="1000" y2="800" stroke="#00ff41" stroke-width="1"/>
|
||||
</g>
|
||||
|
||||
<!-- Hex rain decoration -->
|
||||
<g opacity="0.04" font-family="'Courier New',monospace" font-size="14" fill="#00ff41">
|
||||
<text x="50" y="80">4F 70 65 6E 4F 43 44</text>
|
||||
<text x="900" y="120">10 00 02 34 08 B5 01</text>
|
||||
<text x="150" y="180">47 44 42 20 52 45 56</text>
|
||||
<text x="800" y="240">20 08 20 00 FF AA 00</text>
|
||||
<text x="80" y="350">52 50 32 33 35 30 00</text>
|
||||
<text x="950" y="380">0A 0A 0F 12 12 1A 1A</text>
|
||||
<text x="100" y="520">41 52 4D 76 38 2D 4D</text>
|
||||
<text x="870" y="560">00 FF 41 00 D4 FF 88</text>
|
||||
<text x="60" y="680">47 48 49 44 52 41 00</text>
|
||||
<text x="920" y="720">FF 00 40 C0 C0 C0 00</text>
|
||||
</g>
|
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<!-- Corner accents -->
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<polyline points="1170,30 1170,80 1120,80" fill="none" stroke="#00ff41" stroke-width="2" opacity="0.3"/>
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<polyline points="30,770 30,720 80,720" fill="none" stroke="#00ff41" stroke-width="2" opacity="0.3"/>
|
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<polyline points="1170,770 1170,720 1120,720" fill="none" stroke="#00ff41" stroke-width="2" opacity="0.3"/>
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||||
|
||||
<!-- Top accent line -->
|
||||
<rect x="100" y="140" width="1000" height="2" fill="#00ff41" opacity="0.4"/>
|
||||
|
||||
<!-- Course Title -->
|
||||
<text x="600" y="210" text-anchor="middle" font-family="'Courier New',monospace" font-size="56" font-weight="bold" fill="#00ff41">Embedded Systems</text>
|
||||
<text x="600" y="278" text-anchor="middle" font-family="'Courier New',monospace" font-size="56" font-weight="bold" fill="#00ff41">Reverse Engineering</text>
|
||||
|
||||
<!-- Divider -->
|
||||
<rect x="300" y="310" width="600" height="2" fill="#00d4ff" opacity="0.6"/>
|
||||
|
||||
<!-- Week Number -->
|
||||
<text x="600" y="380" text-anchor="middle" font-family="'Courier New',monospace" font-size="42" font-weight="bold" fill="#00d4ff">// WEEK 05</text>
|
||||
|
||||
<!-- Week Topic -->
|
||||
<text x="600" y="440" text-anchor="middle" font-family="'Courier New',monospace" font-size="28" fill="#c0c0c0">Integers and Floats in Embedded Systems:</text>
|
||||
<text x="600" y="478" text-anchor="middle" font-family="'Courier New',monospace" font-size="28" fill="#c0c0c0">Debugging and Hacking Integers and Floats</text>
|
||||
<text x="600" y="516" text-anchor="middle" font-family="'Courier New',monospace" font-size="28" fill="#c0c0c0">w/ Intermediate GPIO Output Analysis</text>
|
||||
|
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<!-- Bottom accent line -->
|
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<rect x="100" y="570" width="1000" height="2" fill="#00ff41" opacity="0.4"/>
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||||
|
||||
<!-- University -->
|
||||
<text x="600" y="635" text-anchor="middle" font-family="'Courier New',monospace" font-size="36" font-weight="bold" fill="#ffaa00">George Mason University</text>
|
||||
|
||||
<!-- Bottom badge -->
|
||||
<rect x="400" y="670" width="400" height="40" rx="20" fill="none" stroke="#00ff41" stroke-width="1.5" opacity="0.5"/>
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||||
<text x="600" y="697" text-anchor="middle" font-family="'Courier New',monospace" font-size="20" fill="#00ff41" opacity="0.7">RP2350 // ARM Cortex-M33</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 4.5 KiB |
@@ -0,0 +1,77 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
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<style>
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.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
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|
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<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">Integer Data Types</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">Fixed-Size Types for Embedded Systems</text>
|
||||
|
||||
<!-- uint8_t -->
|
||||
<rect x="40" y="110" width="540" height="155" rx="8" class="pnl"/>
|
||||
<text x="310" y="148" text-anchor="middle" class="sub">uint8_t</text>
|
||||
<text x="60" y="185" class="grn">Unsigned 8-bit</text>
|
||||
<text x="360" y="185" class="txt">1 byte</text>
|
||||
<text x="60" y="218" class="txt">Range:</text>
|
||||
<text x="200" y="218" class="amb">0 to 255</text>
|
||||
<text x="60" y="245" class="dim">Ages, counts, always positive</text>
|
||||
|
||||
<!-- int8_t -->
|
||||
<rect x="620" y="110" width="540" height="155" rx="8" class="pnl"/>
|
||||
<text x="890" y="148" text-anchor="middle" class="sub">int8_t</text>
|
||||
<text x="640" y="185" class="red">Signed 8-bit</text>
|
||||
<text x="940" y="185" class="txt">1 byte</text>
|
||||
<text x="640" y="218" class="txt">Range:</text>
|
||||
<text x="780" y="218" class="amb">-128 to 127</text>
|
||||
<text x="640" y="245" class="dim">Temperature, can be negative</text>
|
||||
|
||||
<!-- uint16_t -->
|
||||
<rect x="40" y="285" width="540" height="155" rx="8" class="pnl"/>
|
||||
<text x="310" y="323" text-anchor="middle" class="sub">uint16_t</text>
|
||||
<text x="60" y="360" class="grn">Unsigned 16-bit</text>
|
||||
<text x="360" y="360" class="txt">2 bytes</text>
|
||||
<text x="60" y="393" class="txt">Range:</text>
|
||||
<text x="200" y="393" class="amb">0 to 65,535</text>
|
||||
<text x="60" y="420" class="dim">Sensor readings, medium values</text>
|
||||
|
||||
<!-- uint32_t -->
|
||||
<rect x="620" y="285" width="540" height="155" rx="8" class="pnl"/>
|
||||
<text x="890" y="323" text-anchor="middle" class="sub">uint32_t</text>
|
||||
<text x="640" y="360" class="cyn">Unsigned 32-bit</text>
|
||||
<text x="940" y="360" class="txt">4 bytes</text>
|
||||
<text x="640" y="393" class="txt">Range:</text>
|
||||
<text x="780" y="393" class="amb">0 to ~4 billion</text>
|
||||
<text x="640" y="420" class="dim">Addresses, timestamps</text>
|
||||
|
||||
<!-- Code Example -->
|
||||
<rect x="40" y="460" width="1120" height="150" rx="8" class="pnl"/>
|
||||
<text x="600" y="498" text-anchor="middle" class="sub">Code Example</text>
|
||||
<rect x="60" y="515" width="1080" height="80" rx="6" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="80" y="548" class="amb">uint8_t age = 43;</text>
|
||||
<text x="500" y="548" class="dim">// unsigned, 0-255</text>
|
||||
<text x="80" y="578" class="red">int8_t range = -42;</text>
|
||||
<text x="500" y="578" class="dim">// signed, -128 to 127</text>
|
||||
|
||||
<!-- Key Insight -->
|
||||
<rect x="40" y="630" width="1120" height="150" rx="8" class="pnl"/>
|
||||
<text x="600" y="668" text-anchor="middle" class="sub">Key Insight</text>
|
||||
<text x="60" y="700" class="txt">The</text>
|
||||
<text x="120" y="700" class="grn">u</text>
|
||||
<text x="145" y="700" class="txt">prefix means</text>
|
||||
<text x="370" y="700" class="cyn">unsigned</text>
|
||||
<text x="540" y="700" class="txt">(no negatives)</text>
|
||||
<text x="60" y="730" class="txt">Without</text>
|
||||
<text x="210" y="730" class="grn">u</text>
|
||||
<text x="235" y="730" class="txt">= signed (allows negatives)</text>
|
||||
<text x="60" y="760" class="dim">Choose the smallest type that fits your data</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 3.7 KiB |
@@ -0,0 +1,79 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
|
||||
.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
||||
.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
|
||||
.sub{font:bold 28px 'Courier New',monospace;fill:#00d4ff}
|
||||
.txt{font:24px 'Courier New',monospace;fill:#c0c0c0}
|
||||
.dim{font:20px 'Courier New',monospace;fill:#888}
|
||||
.grn{font:bold 24px 'Courier New',monospace;fill:#00ff41}
|
||||
.red{font:bold 24px 'Courier New',monospace;fill:#ff0040}
|
||||
.cyn{font:bold 24px 'Courier New',monospace;fill:#00d4ff}
|
||||
.amb{font:bold 24px 'Courier New',monospace;fill:#ffaa00}
|
||||
.badge{stroke:#00ff41;rx:14}
|
||||
</style>
|
||||
<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">Two's Complement</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">How Negative Numbers are Stored</text>
|
||||
|
||||
<!-- Step-by-step: -42 encoding -->
|
||||
<rect x="40" y="110" width="1120" height="280" rx="8" class="pnl"/>
|
||||
<text x="600" y="148" text-anchor="middle" class="sub">Encoding -42 as int8_t</text>
|
||||
|
||||
<rect x="60" y="170" width="340" height="90" rx="6" fill="#0a0a0f" stroke="#00d4ff" stroke-width="1"/>
|
||||
<text x="230" y="200" text-anchor="middle" class="cyn">Step 1: Start</text>
|
||||
<text x="230" y="235" text-anchor="middle" class="txt">42 = 0x2A</text>
|
||||
|
||||
<rect x="420" y="170" width="340" height="90" rx="6" fill="#0a0a0f" stroke="#ffaa00" stroke-width="1"/>
|
||||
<text x="590" y="200" text-anchor="middle" class="amb">Step 2: Flip</text>
|
||||
<text x="590" y="235" text-anchor="middle" class="txt">~0x2A = 0xD5</text>
|
||||
|
||||
<rect x="780" y="170" width="340" height="90" rx="6" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="950" y="200" text-anchor="middle" class="grn">Step 3: Add 1</text>
|
||||
<text x="950" y="235" text-anchor="middle" class="txt">0xD5+1 = 0xD6</text>
|
||||
|
||||
<text x="60" y="300" class="txt">Binary:</text>
|
||||
<text x="200" y="300" class="grn">00101010</text>
|
||||
<text x="400" y="300" class="amb">-></text>
|
||||
<text x="450" y="300" class="amb">11010101</text>
|
||||
<text x="650" y="300" class="grn">-></text>
|
||||
<text x="700" y="300" class="red">11010110</text>
|
||||
|
||||
<text x="60" y="340" class="dim">Result: -42 stored as 0xD6 in memory</text>
|
||||
<text x="60" y="368" class="dim">Top bit = 1 means negative</text>
|
||||
|
||||
<!-- Comparison Table -->
|
||||
<rect x="40" y="410" width="1120" height="200" rx="8" class="pnl"/>
|
||||
<text x="600" y="448" text-anchor="middle" class="sub">Signed vs Unsigned: Same Bits!</text>
|
||||
|
||||
<text x="80" y="488" class="cyn">Hex</text>
|
||||
<text x="280" y="488" class="cyn">Binary</text>
|
||||
<text x="580" y="488" class="cyn">uint8_t</text>
|
||||
<text x="800" y="488" class="cyn">int8_t</text>
|
||||
|
||||
<line x1="60" y1="500" x2="1140" y2="500" stroke="#1a1a2e" stroke-width="1"/>
|
||||
|
||||
<text x="80" y="530" class="amb">0x2A</text>
|
||||
<text x="280" y="530" class="txt">00101010</text>
|
||||
<text x="580" y="530" class="grn">42</text>
|
||||
<text x="800" y="530" class="grn">42</text>
|
||||
|
||||
<text x="80" y="565" class="amb">0xD6</text>
|
||||
<text x="280" y="565" class="txt">11010110</text>
|
||||
<text x="580" y="565" class="grn">214</text>
|
||||
<text x="800" y="565" class="red">-42</text>
|
||||
|
||||
<text x="60" y="590" class="dim">Same byte 0xD6 = 214 unsigned, -42 signed</text>
|
||||
|
||||
<!-- GDB Verification -->
|
||||
<rect x="40" y="630" width="1120" height="150" rx="8" class="pnl"/>
|
||||
<text x="600" y="668" text-anchor="middle" class="sub">GDB Verification</text>
|
||||
|
||||
<rect x="60" y="688" width="1080" height="75" rx="6" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="80" y="718" class="grn">(gdb)</text>
|
||||
<text x="180" y="718" class="txt">x/1xb &range</text>
|
||||
<text x="80" y="745" class="amb">0x200003e7:</text>
|
||||
<text x="300" y="745" class="red">0xd6</text>
|
||||
<text x="440" y="745" class="dim">// -42 in memory</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 3.6 KiB |
@@ -0,0 +1,75 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
|
||||
.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
||||
.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
|
||||
.sub{font:bold 28px 'Courier New',monospace;fill:#00d4ff}
|
||||
.txt{font:24px 'Courier New',monospace;fill:#c0c0c0}
|
||||
.dim{font:20px 'Courier New',monospace;fill:#888}
|
||||
.grn{font:bold 24px 'Courier New',monospace;fill:#00ff41}
|
||||
.red{font:bold 24px 'Courier New',monospace;fill:#ff0040}
|
||||
.cyn{font:bold 24px 'Courier New',monospace;fill:#00d4ff}
|
||||
.amb{font:bold 24px 'Courier New',monospace;fill:#ffaa00}
|
||||
.badge{stroke:#00ff41;rx:14}
|
||||
</style>
|
||||
<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">Inline Assembly GPIO</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">Direct Hardware Control via ASM</text>
|
||||
|
||||
<!-- Init Loop -->
|
||||
<rect x="40" y="110" width="1120" height="310" rx="8" class="pnl"/>
|
||||
<text x="600" y="148" text-anchor="middle" class="sub">GPIO Init Loop (pins 16-19)</text>
|
||||
|
||||
<rect x="60" y="168" width="340" height="120" rx="6" fill="#0a0a0f" stroke="#00d4ff" stroke-width="1"/>
|
||||
<text x="230" y="198" text-anchor="middle" class="cyn">1. Config Pad</text>
|
||||
<text x="80" y="228" class="dim">PADS_BANK0</text>
|
||||
<text x="80" y="255" class="dim">Clear OD+ISO, set IE</text>
|
||||
<text x="80" y="275" class="amb">0x40038000</text>
|
||||
|
||||
<rect x="420" y="168" width="340" height="120" rx="6" fill="#0a0a0f" stroke="#ffaa00" stroke-width="1"/>
|
||||
<text x="590" y="198" text-anchor="middle" class="amb">2. Set Function</text>
|
||||
<text x="440" y="228" class="dim">IO_BANK0</text>
|
||||
<text x="440" y="255" class="dim">FUNCSEL = 5 (SIO)</text>
|
||||
<text x="440" y="275" class="grn">0x40028004</text>
|
||||
|
||||
<rect x="780" y="168" width="340" height="120" rx="6" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="950" y="198" text-anchor="middle" class="grn">3. Enable Out</text>
|
||||
<text x="800" y="228" class="dim">GPIO Coprocessor</text>
|
||||
<text x="800" y="255" class="dim">mcrr p0,#4,r4,r5,c4</text>
|
||||
<text x="800" y="275" class="red">Output Enable</text>
|
||||
|
||||
<text x="60" y="330" class="txt">Loop: r0 = 16 to 19</text>
|
||||
<text x="400" y="330" class="dim">Red, Green, Blue, Yellow LEDs</text>
|
||||
<text x="60" y="398" class="dim">Each pin: pad config + function select + OE</text>
|
||||
|
||||
<!-- Blink Loop -->
|
||||
<rect x="40" y="440" width="540" height="190" rx="8" class="pnl"/>
|
||||
<text x="310" y="478" text-anchor="middle" class="sub">Blink Loop</text>
|
||||
|
||||
<rect x="60" y="498" width="500" height="40" rx="4" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="80" y="525" class="grn">mcrr p0,#4,r4,r5,c0</text>
|
||||
|
||||
<text x="60" y="565" class="txt">r4 = pin, r5 = value</text>
|
||||
<text x="60" y="595" class="dim">c0 = output value register</text>
|
||||
<text x="60" y="615" class="dim">r5=1 ON, r5=0 OFF</text>
|
||||
|
||||
<!-- Pin Cycling -->
|
||||
<rect x="620" y="440" width="540" height="190" rx="8" class="pnl"/>
|
||||
<text x="890" y="478" text-anchor="middle" class="sub">Pin Cycling</text>
|
||||
|
||||
<rect x="640" y="498" width="500" height="75" rx="6" fill="#0a0a0f" stroke="#ffaa00" stroke-width="1"/>
|
||||
<text x="660" y="528" class="amb">pin++;</text>
|
||||
<text x="660" y="558" class="txt">if (pin > 18) pin=16;</text>
|
||||
|
||||
<text x="640" y="600" class="dim">Cycles: 16 -> 17 -> 18 -> 16</text>
|
||||
<text x="640" y="620" class="dim">Red -> Green -> Blue -> repeat</text>
|
||||
|
||||
<!-- Key Takeaway -->
|
||||
<rect x="40" y="650" width="1120" height="130" rx="8" class="pnl"/>
|
||||
<text x="600" y="688" text-anchor="middle" class="sub">Why Inline Assembly?</text>
|
||||
<text x="60" y="722" class="txt">gpio_put(16,1) calls</text>
|
||||
<text x="390" y="722" class="grn">mcrr</text>
|
||||
<text x="470" y="722" class="txt">underneath</text>
|
||||
<text x="60" y="752" class="dim">Inline ASM shows what the SDK does at hardware level</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 3.7 KiB |
@@ -0,0 +1,83 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
|
||||
.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
||||
.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
|
||||
.sub{font:bold 28px 'Courier New',monospace;fill:#00d4ff}
|
||||
.txt{font:24px 'Courier New',monospace;fill:#c0c0c0}
|
||||
.dim{font:20px 'Courier New',monospace;fill:#888}
|
||||
.grn{font:bold 24px 'Courier New',monospace;fill:#00ff41}
|
||||
.red{font:bold 24px 'Courier New',monospace;fill:#ff0040}
|
||||
.cyn{font:bold 24px 'Courier New',monospace;fill:#00d4ff}
|
||||
.amb{font:bold 24px 'Courier New',monospace;fill:#ffaa00}
|
||||
.badge{stroke:#00ff41;rx:14}
|
||||
</style>
|
||||
<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">IEEE 754 Float</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">32-bit Single Precision Encoding</text>
|
||||
|
||||
<!-- Field Layout -->
|
||||
<rect x="40" y="110" width="1120" height="170" rx="8" class="pnl"/>
|
||||
<text x="600" y="147" text-anchor="middle" class="sub">Float Bit Layout (32 bits)</text>
|
||||
|
||||
<rect x="60" y="172" width="80" height="30" rx="4" fill="#0a0a0f" stroke="#ff0040" stroke-width="2"/>
|
||||
<text x="100" y="192" text-anchor="middle" class="red">S</text>
|
||||
|
||||
<rect x="150" y="172" width="350" height="30" rx="4" fill="#0a0a0f" stroke="#ffaa00" stroke-width="2"/>
|
||||
<text x="325" y="192" text-anchor="middle" class="amb">Exponent (8)</text>
|
||||
|
||||
<rect x="510" y="172" width="630" height="30" rx="4" fill="#0a0a0f" stroke="#00ff41" stroke-width="2"/>
|
||||
<text x="825" y="192" text-anchor="middle" class="grn">Mantissa (23)</text>
|
||||
|
||||
<text x="100" y="227" text-anchor="middle" class="dim">1 bit</text>
|
||||
<text x="100" y="243" text-anchor="middle" class="dim">sign</text>
|
||||
|
||||
<text x="325" y="227" text-anchor="middle" class="dim">8 bits</text>
|
||||
<text x="325" y="243" text-anchor="middle" class="dim">bias=127</text>
|
||||
|
||||
<text x="825" y="227" text-anchor="middle" class="dim">23 bits</text>
|
||||
<text x="825" y="243" text-anchor="middle" class="dim">+implicit 1</text>
|
||||
|
||||
<!-- Formula -->
|
||||
<rect x="40" y="300" width="1120" height="110" rx="8" class="pnl"/>
|
||||
<text x="600" y="325" text-anchor="middle" class="sub">Decode Formula</text>
|
||||
<text x="60" y="350" class="txt">Value = (-1)^sign × 2^(exp-127) × (1 + mantissa)</text>
|
||||
<text x="60" y="370" class="dim">Sign determines +/- Exponent scales with bias 127 Mantissa adds precision</text>
|
||||
<text x="60" y="385" class="dim">Special cases: exp=0 or 255 (denorm, inf, NaN)</text>
|
||||
|
||||
<!-- Example: 42.5 -->
|
||||
<rect x="40" y="430" width="1120" height="255" rx="8" class="pnl"/>
|
||||
<text x="600" y="455" text-anchor="middle" class="sub">Decode Example: 42.5</text>
|
||||
|
||||
<text x="80" y="485" class="red">Sign Bit: 0</text>
|
||||
<text x="400" y="485" class="dim">Positive number</text>
|
||||
|
||||
<text x="80" y="515" class="amb">Exponent: 10000100</text>
|
||||
<text x="450" y="515" class="dim">= 132 decimal</text>
|
||||
|
||||
<text x="80" y="545" class="txt">Bias subtraction: 132 - 127 = 5</text>
|
||||
|
||||
<text x="80" y="575" class="grn">Mantissa: 01010100...0</text>
|
||||
<text x="450" y="575" class="dim">= 1.010101</text>
|
||||
|
||||
<text x="80" y="605" class="txt">Combine: 1.010101 × 2^5 = 42.5</text>
|
||||
|
||||
<text x="80" y="635" class="cyn">Hex: 0x422A0000</text>
|
||||
|
||||
<text x="80" y="661" class="dim">Binary: 01000010001010100000000000000000</text>
|
||||
|
||||
<!-- Float vs Integer -->
|
||||
<rect x="40" y="705" width="1120" height="100" rx="8" class="pnl"/>
|
||||
<text x="600" y="729" text-anchor="middle" class="sub">32-bit Storage Comparison</text>
|
||||
|
||||
<text x="60" y="759" class="cyn">Integer:</text>
|
||||
<text x="200" y="759" class="txt">Exact values</text>
|
||||
<text x="430" y="759" class="dim">Range: -2.1B to +2.1B</text>
|
||||
<text x="860" y="759" class="red">No decimals</text>
|
||||
|
||||
<text x="60" y="781" class="amb">Float:</text>
|
||||
<text x="200" y="781" class="txt">Approximate values</text>
|
||||
<text x="470" y="781" class="dim">Range: ±10^38</text>
|
||||
<text x="810" y="781" class="grn">~7 sig digits</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 3.8 KiB |
@@ -0,0 +1,76 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
|
||||
.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
||||
.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
|
||||
.sub{font:bold 28px 'Courier New',monospace;fill:#00d4ff}
|
||||
.txt{font:24px 'Courier New',monospace;fill:#c0c0c0}
|
||||
.dim{font:20px 'Courier New',monospace;fill:#888}
|
||||
.grn{font:bold 24px 'Courier New',monospace;fill:#00ff41}
|
||||
.red{font:bold 24px 'Courier New',monospace;fill:#ff0040}
|
||||
.cyn{font:bold 24px 'Courier New',monospace;fill:#00d4ff}
|
||||
.amb{font:bold 24px 'Courier New',monospace;fill:#ffaa00}
|
||||
.badge{stroke:#00ff41;rx:14}
|
||||
</style>
|
||||
<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">Float in Ghidra</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">Analyzing 42.5 in the Binary</text>
|
||||
|
||||
<!-- Decompiled View -->
|
||||
<rect x="40" y="110" width="540" height="280" rx="8" class="pnl"/>
|
||||
<text x="310" y="148" text-anchor="middle" class="sub">Decompiled main()</text>
|
||||
|
||||
<rect x="60" y="168" width="500" height="205" rx="6" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="80" y="198" class="txt">int main(void) {</text>
|
||||
<text x="100" y="228" class="cyn">stdio_init_all();</text>
|
||||
<text x="100" y="258" class="txt">uVar1 = DAT_1000024c;</text>
|
||||
<text x="100" y="288" class="txt">do {</text>
|
||||
<text x="120" y="318" class="amb">printf(fmt,0,uVar1);</text>
|
||||
<text x="100" y="348" class="txt">} while(true);</text>
|
||||
|
||||
<!-- Key Discovery -->
|
||||
<rect x="620" y="110" width="540" height="280" rx="8" class="pnl"/>
|
||||
<text x="890" y="148" text-anchor="middle" class="sub">Key Discovery</text>
|
||||
|
||||
<text x="640" y="190" class="txt">printf with %f always</text>
|
||||
<text x="640" y="220" class="txt">receives a</text>
|
||||
<text x="830" y="220" class="red">double</text>
|
||||
<text x="960" y="220" class="txt">(64-bit)</text>
|
||||
|
||||
<text x="640" y="260" class="dim">C promotes float to double</text>
|
||||
<text x="640" y="290" class="dim">for variadic functions!</text>
|
||||
|
||||
<rect x="640" y="310" width="500" height="60" rx="4" fill="#0a0a0f" stroke="#ffaa00" stroke-width="2"/>
|
||||
<text x="890" y="348" text-anchor="middle" class="amb">42.5 sent as double</text>
|
||||
|
||||
<!-- Register Pair -->
|
||||
<rect x="40" y="410" width="1120" height="180" rx="8" class="pnl"/>
|
||||
<text x="600" y="448" text-anchor="middle" class="sub">Register Pair r2:r3</text>
|
||||
|
||||
<rect x="60" y="470" width="520" height="50" rx="4" fill="#0a0a0f" stroke="#00d4ff" stroke-width="1"/>
|
||||
<text x="80" y="510" class="cyn">r2 (low):</text>
|
||||
<text x="260" y="510" class="grn">0x00000000</text>
|
||||
|
||||
<rect x="600" y="470" width="540" height="50" rx="4" fill="#0a0a0f" stroke="#ffaa00" stroke-width="1"/>
|
||||
<text x="620" y="510" class="amb">r3 (high):</text>
|
||||
<text x="810" y="510" class="grn">0x40454000</text>
|
||||
|
||||
<text x="60" y="565" class="txt">Combined: 0x4045400000000000</text>
|
||||
<text x="680" y="565" class="grn">= 42.5</text>
|
||||
|
||||
<!-- Assembly -->
|
||||
<rect x="40" y="610" width="1120" height="170" rx="8" class="pnl"/>
|
||||
<text x="600" y="648" text-anchor="middle" class="sub">Assembly View</text>
|
||||
|
||||
<rect x="60" y="668" width="1080" height="90" rx="6" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="80" y="698" class="grn">1000023a</text>
|
||||
<text x="260" y="698" class="amb">00 24</text>
|
||||
<text x="380" y="698" class="txt">movs r4, #0x0</text>
|
||||
<text x="640" y="698" class="dim">// r2 = 0</text>
|
||||
|
||||
<text x="80" y="733" class="grn">1000023c</text>
|
||||
<text x="260" y="733" class="amb">03 4d</text>
|
||||
<text x="380" y="733" class="txt">ldr r5,[DAT...]</text>
|
||||
<text x="640" y="733" class="dim">// r3 = 0x40454000</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 3.5 KiB |
@@ -0,0 +1,87 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
|
||||
.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
||||
.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
|
||||
.sub{font:bold 28px 'Courier New',monospace;fill:#00d4ff}
|
||||
.txt{font:24px 'Courier New',monospace;fill:#c0c0c0}
|
||||
.dim{font:20px 'Courier New',monospace;fill:#888}
|
||||
.grn{font:bold 24px 'Courier New',monospace;fill:#00ff41}
|
||||
.red{font:bold 24px 'Courier New',monospace;fill:#ff0040}
|
||||
.cyn{font:bold 24px 'Courier New',monospace;fill:#00d4ff}
|
||||
.amb{font:bold 24px 'Courier New',monospace;fill:#ffaa00}
|
||||
.badge{stroke:#00ff41;rx:14}
|
||||
</style>
|
||||
<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">Patching Float</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">Changing 42.5 to 99.0 in Ghidra</text>
|
||||
|
||||
<!-- Calculate New Encoding -->
|
||||
<rect x="40" y="110" width="1120" height="230" rx="8" class="pnl"/>
|
||||
<text x="600" y="148" text-anchor="middle" class="sub">Calculate 99.0 as Double</text>
|
||||
|
||||
<text x="60" y="188" class="txt">99 decimal =</text>
|
||||
<text x="290" y="188" class="grn">1100011</text>
|
||||
<text x="440" y="188" class="txt">binary</text>
|
||||
|
||||
<text x="60" y="223" class="txt">Normalize:</text>
|
||||
<text x="250" y="223" class="amb">1.100011 x 2^6</text>
|
||||
|
||||
<text x="60" y="258" class="red">Sign:</text>
|
||||
<text x="160" y="258" class="txt">0</text>
|
||||
<text x="300" y="258" class="amb">Exp:</text>
|
||||
<text x="380" y="258" class="txt">6+1023 = 1029</text>
|
||||
|
||||
<text x="60" y="293" class="grn">Mantissa:</text>
|
||||
<text x="240" y="293" class="txt">100011000...0</text>
|
||||
|
||||
<text x="60" y="328" class="dim">Full double: 0x4058C00000000000</text>
|
||||
|
||||
<!-- Before vs After -->
|
||||
<rect x="40" y="360" width="540" height="200" rx="8" class="pnl"/>
|
||||
<text x="310" y="398" text-anchor="middle" class="sub">Before (42.5)</text>
|
||||
|
||||
<rect x="60" y="418" width="500" height="50" rx="4" fill="#0a0a0f" stroke="#ff0040" stroke-width="1"/>
|
||||
<text x="80" y="448" class="cyn">r2:</text>
|
||||
<text x="160" y="448" class="red">0x00000000</text>
|
||||
|
||||
<rect x="60" y="478" width="500" height="50" rx="4" fill="#0a0a0f" stroke="#ff0040" stroke-width="1"/>
|
||||
<text x="80" y="508" class="cyn">r3:</text>
|
||||
<text x="160" y="508" class="red">0x40454000</text>
|
||||
|
||||
<text x="60" y="548" class="dim">Output: fav_num: 42.500000</text>
|
||||
|
||||
<rect x="620" y="360" width="540" height="200" rx="8" class="pnl"/>
|
||||
<text x="890" y="398" text-anchor="middle" class="sub">After (99.0)</text>
|
||||
|
||||
<rect x="640" y="418" width="500" height="50" rx="4" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="660" y="448" class="cyn">r2:</text>
|
||||
<text x="740" y="448" class="grn">0x00000000</text>
|
||||
<text x="960" y="450" class="dim">same!</text>
|
||||
|
||||
<rect x="640" y="478" width="500" height="50" rx="4" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="660" y="508" class="cyn">r3:</text>
|
||||
<text x="740" y="508" class="grn">0x4058C000</text>
|
||||
<text x="960" y="510" class="amb">changed</text>
|
||||
|
||||
<text x="640" y="548" class="dim">Output: fav_num: 99.000000</text>
|
||||
|
||||
<!-- Patch Steps -->
|
||||
<rect x="40" y="580" width="1120" height="200" rx="8" class="pnl"/>
|
||||
<text x="600" y="618" text-anchor="middle" class="sub">Patch in Ghidra</text>
|
||||
|
||||
<rect x="60" y="640" width="340" height="65" rx="6" fill="#0a0a0f" stroke="#00d4ff" stroke-width="1"/>
|
||||
<text x="230" y="668" text-anchor="middle" class="cyn">1. Window: Bytes</text>
|
||||
<text x="230" y="690" text-anchor="middle" class="dim">Open byte editor</text>
|
||||
|
||||
<rect x="420" y="640" width="340" height="65" rx="6" fill="#0a0a0f" stroke="#ffaa00" stroke-width="1"/>
|
||||
<text x="590" y="668" text-anchor="middle" class="amb">2. Find 00404540</text>
|
||||
<text x="590" y="690" text-anchor="middle" class="dim">High word of 42.5</text>
|
||||
|
||||
<rect x="780" y="640" width="340" height="65" rx="6" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="950" y="668" text-anchor="middle" class="grn">3. Patch 00C05840</text>
|
||||
<text x="950" y="690" text-anchor="middle" class="dim">High word of 99.0</text>
|
||||
|
||||
<text x="60" y="748" class="dim">Only one word to patch (low word is 0)</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 4.0 KiB |
@@ -0,0 +1,75 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
|
||||
.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
||||
.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
|
||||
.sub{font:bold 28px 'Courier New',monospace;fill:#00d4ff}
|
||||
.txt{font:24px 'Courier New',monospace;fill:#c0c0c0}
|
||||
.dim{font:20px 'Courier New',monospace;fill:#888}
|
||||
.grn{font:bold 24px 'Courier New',monospace;fill:#00ff41}
|
||||
.red{font:bold 24px 'Courier New',monospace;fill:#ff0040}
|
||||
.cyn{font:bold 24px 'Courier New',monospace;fill:#00d4ff}
|
||||
.amb{font:bold 24px 'Courier New',monospace;fill:#ffaa00}
|
||||
.badge{stroke:#00ff41;rx:14}
|
||||
</style>
|
||||
<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">Double Precision</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">IEEE 754 64-bit Floating Point</text>
|
||||
|
||||
<!-- Bit Layout -->
|
||||
<rect x="40" y="110" width="1120" height="175" rx="8" class="pnl"/>
|
||||
<text x="600" y="148" text-anchor="middle" class="sub">64-Bit Layout</text>
|
||||
|
||||
<rect x="60" y="168" width="80" height="72" rx="4" fill="#ff0040" stroke="#ff0040" stroke-width="1" opacity="0.3"/>
|
||||
<text x="100" y="197" text-anchor="middle" class="red">Sign</text>
|
||||
<text x="100" y="218" text-anchor="middle" class="dim">1 bit</text>
|
||||
|
||||
<rect x="160" y="168" width="300" height="72" rx="4" fill="#ffaa00" stroke="#ffaa00" stroke-width="1" opacity="0.2"/>
|
||||
<text x="310" y="197" text-anchor="middle" class="amb">Exponent</text>
|
||||
<text x="310" y="218" text-anchor="middle" class="dim">11 bits (bias 1023)</text>
|
||||
|
||||
<rect x="480" y="168" width="660" height="72" rx="4" fill="#00ff41" stroke="#00ff41" stroke-width="1" opacity="0.2"/>
|
||||
<text x="810" y="197" text-anchor="middle" class="grn">Mantissa (Fraction)</text>
|
||||
<text x="810" y="218" text-anchor="middle" class="dim">52 bits</text>
|
||||
|
||||
<text x="60" y="272" class="dim">Formula: (-1)^S x 1.Mantissa x 2^(Exp-1023)</text>
|
||||
|
||||
<!-- 42.52525 Example -->
|
||||
<rect x="40" y="305" width="1120" height="190" rx="8" class="pnl"/>
|
||||
<text x="600" y="340" text-anchor="middle" class="sub">Encoding 42.52525</text>
|
||||
|
||||
<text x="60" y="378" class="cyn">Sign:</text>
|
||||
<text x="170" y="378" class="txt">0 (positive)</text>
|
||||
|
||||
<text x="60" y="408" class="amb">Exponent:</text>
|
||||
<text x="230" y="408" class="txt">5 + 1023 = 1028</text>
|
||||
<text x="530" y="408" class="dim">= 0x404 (hex)</text>
|
||||
|
||||
<text x="60" y="438" class="grn">Mantissa:</text>
|
||||
<text x="230" y="438" class="txt">0101010000110011...</text>
|
||||
|
||||
<text x="60" y="468" class="dim">Full 64-bit hex:</text>
|
||||
<text x="310" y="468" class="grn">0x4045433B645A1CAC</text>
|
||||
|
||||
<!-- Float vs Double Comparison -->
|
||||
<rect x="40" y="515" width="540" height="265" rx="8" class="pnl"/>
|
||||
<text x="310" y="553" text-anchor="middle" class="sub">Float (32-bit)</text>
|
||||
|
||||
<text x="60" y="590" class="txt">Size: 4 bytes</text>
|
||||
<text x="60" y="620" class="txt">Exp: 8 bits</text>
|
||||
<text x="60" y="650" class="txt">Mantissa: 23 bits</text>
|
||||
<text x="60" y="680" class="txt">Precision: ~7 digits</text>
|
||||
<text x="60" y="710" class="txt">Bias: 127</text>
|
||||
<text x="60" y="740" class="dim">1 register (ARM)</text>
|
||||
|
||||
<rect x="620" y="515" width="540" height="265" rx="8" class="pnl"/>
|
||||
<text x="890" y="553" text-anchor="middle" class="sub">Double (64-bit)</text>
|
||||
|
||||
<text x="640" y="590" class="grn">Size: 8 bytes</text>
|
||||
<text x="640" y="620" class="grn">Exp: 11 bits</text>
|
||||
<text x="640" y="650" class="grn">Mantissa: 52 bits</text>
|
||||
<text x="640" y="680" class="grn">Precision: ~15 digits</text>
|
||||
<text x="640" y="710" class="grn">Bias: 1023</text>
|
||||
<text x="640" y="740" class="dim">2 registers (r2:r3)</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 3.5 KiB |
@@ -0,0 +1,71 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
|
||||
.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
||||
.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
|
||||
.sub{font:bold 28px 'Courier New',monospace;fill:#00d4ff}
|
||||
.txt{font:24px 'Courier New',monospace;fill:#c0c0c0}
|
||||
.dim{font:20px 'Courier New',monospace;fill:#888}
|
||||
.grn{font:bold 24px 'Courier New',monospace;fill:#00ff41}
|
||||
.red{font:bold 24px 'Courier New',monospace;fill:#ff0040}
|
||||
.cyn{font:bold 24px 'Courier New',monospace;fill:#00d4ff}
|
||||
.amb{font:bold 24px 'Courier New',monospace;fill:#ffaa00}
|
||||
.badge{stroke:#00ff41;rx:14}
|
||||
</style>
|
||||
<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">Double in Ghidra</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">Analyzing 42.52525 in memory</text>
|
||||
|
||||
<!-- Decompiled View -->
|
||||
<rect x="40" y="110" width="540" height="230" rx="8" class="pnl"/>
|
||||
<text x="310" y="148" text-anchor="middle" class="sub">Decompiled main()</text>
|
||||
|
||||
<rect x="60" y="168" width="500" height="150" rx="4" fill="#0a0a0f" stroke="#1a1a2e" stroke-width="1"/>
|
||||
<text x="80" y="198" class="cyn">int main(void) {</text>
|
||||
<text x="110" y="228" class="txt">double fav_num</text>
|
||||
<text x="110" y="258" class="amb"> = 42.52525;</text>
|
||||
<text x="110" y="288" class="txt">stdio_init_all();</text>
|
||||
<text x="80" y="308" class="cyn">}</text>
|
||||
|
||||
<!-- Key Difference from Float -->
|
||||
<rect x="620" y="110" width="540" height="230" rx="8" class="pnl"/>
|
||||
<text x="890" y="148" text-anchor="middle" class="sub">Key Difference</text>
|
||||
|
||||
<text x="640" y="188" class="txt">Float (42.5):</text>
|
||||
<text x="640" y="218" class="dim">r2 = 0x00000000 (zero!)</text>
|
||||
<text x="640" y="248" class="dim">r3 = 0x40454000</text>
|
||||
|
||||
<text x="640" y="288" class="grn">Double (42.52525):</text>
|
||||
<text x="640" y="318" class="amb">r2 = 0x645A1CAC (non-zero!)</text>
|
||||
|
||||
<!-- Register Pair -->
|
||||
<rect x="40" y="360" width="1120" height="170" rx="8" class="pnl"/>
|
||||
<text x="600" y="398" text-anchor="middle" class="sub">Register Pair r2:r3</text>
|
||||
|
||||
<rect x="60" y="418" width="520" height="55" rx="4" fill="#0a0a0f" stroke="#ffaa00" stroke-width="1"/>
|
||||
<text x="80" y="445" class="amb">r3 (HIGH):</text>
|
||||
<text x="280" y="445" class="grn">0x4045433B</text>
|
||||
|
||||
<rect x="620" y="418" width="520" height="55" rx="4" fill="#0a0a0f" stroke="#ffaa00" stroke-width="1"/>
|
||||
<text x="640" y="445" class="amb">r2 (LOW):</text>
|
||||
<text x="830" y="445" class="grn">0x645A1CAC</text>
|
||||
|
||||
<text x="60" y="510" class="dim">Combined: 0x4045433B645A1CAC = 42.52525</text>
|
||||
|
||||
<!-- Assembly View -->
|
||||
<rect x="40" y="550" width="1120" height="230" rx="8" class="pnl"/>
|
||||
<text x="600" y="588" text-anchor="middle" class="sub">Assembly (ldrd)</text>
|
||||
|
||||
<rect x="60" y="608" width="700" height="140" rx="4" fill="#0a0a0f" stroke="#1a1a2e" stroke-width="1"/>
|
||||
<text x="80" y="638" class="cyn">ldrd r2,r3,[PC,#0x10]</text>
|
||||
<text x="80" y="668" class="dim">; Loads BOTH words at once</text>
|
||||
<text x="80" y="698" class="dim">; r2 gets low word</text>
|
||||
<text x="80" y="728" class="dim">; r3 gets high word</text>
|
||||
|
||||
<rect x="780" y="608" width="360" height="140" rx="4" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="800" y="648" class="grn">ldrd = Load</text>
|
||||
<text x="800" y="678" class="grn">Register</text>
|
||||
<text x="800" y="708" class="grn">Doubleword</text>
|
||||
<text x="800" y="738" class="dim">ARM Cortex-M33</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 3.4 KiB |
@@ -0,0 +1,88 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
|
||||
.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
||||
.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
|
||||
.sub{font:bold 28px 'Courier New',monospace;fill:#00d4ff}
|
||||
.txt{font:24px 'Courier New',monospace;fill:#c0c0c0}
|
||||
.dim{font:20px 'Courier New',monospace;fill:#888}
|
||||
.grn{font:bold 24px 'Courier New',monospace;fill:#00ff41}
|
||||
.red{font:bold 24px 'Courier New',monospace;fill:#ff0040}
|
||||
.cyn{font:bold 24px 'Courier New',monospace;fill:#00d4ff}
|
||||
.amb{font:bold 24px 'Courier New',monospace;fill:#ffaa00}
|
||||
.badge{stroke:#00ff41;rx:14}
|
||||
</style>
|
||||
<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">Patching Double</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">Changing 42.52525 to 99.99</text>
|
||||
|
||||
<!-- New Encoding Calc -->
|
||||
<rect x="40" y="110" width="1120" height="160" rx="8" class="pnl"/>
|
||||
<text x="600" y="148" text-anchor="middle" class="sub">99.99 as IEEE 754 Double</text>
|
||||
|
||||
<text x="60" y="188" class="cyn">Sign:</text>
|
||||
<text x="160" y="188" class="txt">0</text>
|
||||
<text x="300" y="188" class="amb">Exp:</text>
|
||||
<text x="390" y="188" class="txt">6 + 1023 = 1029</text>
|
||||
|
||||
<text x="60" y="223" class="grn">Result:</text>
|
||||
<text x="200" y="223" class="grn">0x4058FF5C28F5C28F</text>
|
||||
|
||||
<text x="60" y="253" class="dim">r3 (HIGH) = 0x4058FF5C</text>
|
||||
<text x="540" y="253" class="dim">r2 (LOW) = 0x28F5C28F</text>
|
||||
|
||||
<!-- Before vs After -->
|
||||
<rect x="40" y="290" width="540" height="240" rx="8" class="pnl"/>
|
||||
<text x="310" y="328" text-anchor="middle" class="sub">Before (42.52525)</text>
|
||||
|
||||
<rect x="60" y="348" width="500" height="50" rx="4" fill="#0a0a0f" stroke="#ff0040" stroke-width="1"/>
|
||||
<text x="80" y="373" class="cyn">r3:</text>
|
||||
<text x="150" y="373" class="red">0x4045433B</text>
|
||||
|
||||
<rect x="60" y="408" width="500" height="50" rx="4" fill="#0a0a0f" stroke="#ff0040" stroke-width="1"/>
|
||||
<text x="80" y="433" class="cyn">r2:</text>
|
||||
<text x="150" y="433" class="red">0x645A1CAC</text>
|
||||
|
||||
<text x="60" y="485" class="dim">printf: 42.525250</text>
|
||||
<text x="60" y="515" class="dim">Both words non-zero</text>
|
||||
|
||||
<rect x="620" y="290" width="540" height="240" rx="8" class="pnl"/>
|
||||
<text x="890" y="328" text-anchor="middle" class="sub">After (99.99)</text>
|
||||
|
||||
<rect x="640" y="348" width="500" height="50" rx="4" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="660" y="373" class="cyn">r3:</text>
|
||||
<text x="730" y="373" class="grn">0x4058FF5C</text>
|
||||
<text x="940" y="380" class="amb">changed</text>
|
||||
|
||||
<rect x="640" y="408" width="500" height="50" rx="4" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="660" y="433" class="cyn">r2:</text>
|
||||
<text x="730" y="433" class="grn">0x28F5C28F</text>
|
||||
<text x="940" y="440" class="amb">changed</text>
|
||||
|
||||
<text x="640" y="485" class="dim">printf: 99.990000</text>
|
||||
<text x="640" y="515" class="dim">BOTH words changed!</text>
|
||||
|
||||
<!-- Float vs Double Patching -->
|
||||
<rect x="40" y="550" width="540" height="230" rx="8" class="pnl"/>
|
||||
<text x="310" y="588" text-anchor="middle" class="sub">Float Patch</text>
|
||||
|
||||
<text x="60" y="628" class="txt">Words changed:</text>
|
||||
<text x="300" y="628" class="grn">1</text>
|
||||
<text x="60" y="663" class="txt">r2 (low):</text>
|
||||
<text x="260" y="663" class="dim">stays 0x0</text>
|
||||
<text x="60" y="698" class="txt">r3 (high):</text>
|
||||
<text x="280" y="698" class="amb">patched</text>
|
||||
<text x="60" y="733" class="dim">Easier to patch</text>
|
||||
|
||||
<rect x="620" y="550" width="540" height="230" rx="8" class="pnl"/>
|
||||
<text x="890" y="588" text-anchor="middle" class="sub">Double Patch</text>
|
||||
|
||||
<text x="640" y="628" class="txt">Words changed:</text>
|
||||
<text x="880" y="628" class="red">2</text>
|
||||
<text x="640" y="663" class="txt">r2 (low):</text>
|
||||
<text x="840" y="663" class="amb">patched</text>
|
||||
<text x="640" y="698" class="txt">r3 (high):</text>
|
||||
<text x="860" y="698" class="amb">patched</text>
|
||||
<text x="640" y="733" class="dim">Both words must change</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 3.9 KiB |
@@ -0,0 +1,101 @@
|
||||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 1200 800">
|
||||
<style>
|
||||
.bg{fill:#0a0a0f}.pnl{fill:#12121a;stroke:#1a1a2e}.hdr{fill:#12121a}
|
||||
.title{font:bold 42px 'Courier New',monospace;fill:#00ff41}
|
||||
.sub{font:bold 28px 'Courier New',monospace;fill:#00d4ff}
|
||||
.txt{font:24px 'Courier New',monospace;fill:#c0c0c0}
|
||||
.dim{font:20px 'Courier New',monospace;fill:#888}
|
||||
.grn{font:bold 24px 'Courier New',monospace;fill:#00ff41}
|
||||
.red{font:bold 24px 'Courier New',monospace;fill:#ff0040}
|
||||
.cyn{font:bold 24px 'Courier New',monospace;fill:#00d4ff}
|
||||
.amb{font:bold 24px 'Courier New',monospace;fill:#ffaa00}
|
||||
.badge{stroke:#00ff41;rx:14}
|
||||
</style>
|
||||
<rect class="bg" width="1200" height="800"/>
|
||||
|
||||
<!-- Title -->
|
||||
<text x="600" y="52" text-anchor="middle" class="title">IEEE 754 & Data Types</text>
|
||||
<text x="600" y="88" text-anchor="middle" class="dim">Data Types and IEEE 754 Reference</text>
|
||||
|
||||
<!-- Reference Table -->
|
||||
<rect x="40" y="110" width="1120" height="330" rx="8" class="pnl"/>
|
||||
<text x="600" y="148" text-anchor="middle" class="sub">IEEE 754 Hex Values</text>
|
||||
|
||||
<!-- Table Header -->
|
||||
<text x="60" y="188" class="cyn">Value</text>
|
||||
<text x="260" y="188" class="cyn">Float (32b)</text>
|
||||
<text x="560" y="188" class="cyn">Double (64b)</text>
|
||||
|
||||
<line x1="60" y1="198" x2="1140" y2="198" stroke="#1a1a2e" stroke-width="1"/>
|
||||
|
||||
<!-- Row 1 -->
|
||||
<text x="60" y="228" class="txt">42.0</text>
|
||||
<text x="260" y="228" class="grn">0x42280000</text>
|
||||
<text x="560" y="228" class="grn">0x4045000000000000</text>
|
||||
|
||||
<!-- Row 2 -->
|
||||
<text x="60" y="258" class="txt">42.5</text>
|
||||
<text x="260" y="258" class="grn">0x422A0000</text>
|
||||
<text x="560" y="258" class="grn">0x4045400000000000</text>
|
||||
|
||||
<!-- Row 3 -->
|
||||
<text x="60" y="288" class="txt">99.0</text>
|
||||
<text x="260" y="288" class="amb">0x42C60000</text>
|
||||
<text x="560" y="288" class="amb">0x4058C00000000000</text>
|
||||
|
||||
<!-- Row 4 -->
|
||||
<text x="60" y="318" class="txt">99.99</text>
|
||||
<text x="260" y="318" class="amb">0x42C7F5C3</text>
|
||||
<text x="560" y="318" class="amb">0x4058FF5C28F5C28F</text>
|
||||
|
||||
<!-- Row 5 -->
|
||||
<text x="60" y="348" class="txt">3.14</text>
|
||||
<text x="260" y="348" class="red">0x4048F5C3</text>
|
||||
<text x="560" y="348" class="red">0x40091EB851EB851F</text>
|
||||
|
||||
<!-- Row 6 -->
|
||||
<text x="60" y="378" class="txt">100.0</text>
|
||||
<text x="260" y="378" class="red">0x42C80000</text>
|
||||
<text x="560" y="378" class="red">0x4059000000000000</text>
|
||||
|
||||
<text x="60" y="418" class="dim">Tip: float low word often 0x0; double low word usually non-zero</text>
|
||||
|
||||
<!-- Patching Workflow -->
|
||||
<rect x="40" y="460" width="1120" height="155" rx="8" class="pnl"/>
|
||||
<text x="600" y="498" text-anchor="middle" class="sub">Patching Workflow</text>
|
||||
|
||||
<rect x="60" y="518" width="200" height="70" rx="6" fill="#0a0a0f" stroke="#00d4ff" stroke-width="1"/>
|
||||
<text x="160" y="548" text-anchor="middle" class="cyn">1. Identify</text>
|
||||
<text x="160" y="570" text-anchor="middle" class="dim">float / double</text>
|
||||
|
||||
<rect x="280" y="518" width="200" height="70" rx="6" fill="#0a0a0f" stroke="#ffaa00" stroke-width="1"/>
|
||||
<text x="380" y="548" text-anchor="middle" class="amb">2. Check r2</text>
|
||||
<text x="380" y="570" text-anchor="middle" class="dim">zero = float</text>
|
||||
|
||||
<rect x="500" y="518" width="200" height="70" rx="6" fill="#0a0a0f" stroke="#ff0040" stroke-width="1"/>
|
||||
<text x="600" y="548" text-anchor="middle" class="red">3. Calculate</text>
|
||||
<text x="600" y="570" text-anchor="middle" class="dim">new hex value</text>
|
||||
|
||||
<rect x="720" y="518" width="200" height="70" rx="6" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="820" y="548" text-anchor="middle" class="grn">4. Patch</text>
|
||||
<text x="820" y="570" text-anchor="middle" class="dim">in byte editor</text>
|
||||
|
||||
<rect x="940" y="518" width="200" height="70" rx="6" fill="#0a0a0f" stroke="#00ff41" stroke-width="1"/>
|
||||
<text x="1040" y="548" text-anchor="middle" class="grn">5. Export</text>
|
||||
<text x="1040" y="570" text-anchor="middle" class="dim">UF2 + test</text>
|
||||
|
||||
<!-- Key Takeaways -->
|
||||
<rect x="40" y="635" width="540" height="145" rx="8" class="pnl"/>
|
||||
<text x="310" y="670" text-anchor="middle" class="sub">Integer Types</text>
|
||||
|
||||
<text x="60" y="705" class="txt">uint8_t: 0-255</text>
|
||||
<text x="60" y="735" class="txt">int8_t: -128 to 127</text>
|
||||
<text x="60" y="765" class="dim">Two's complement for signed</text>
|
||||
|
||||
<rect x="620" y="635" width="540" height="145" rx="8" class="pnl"/>
|
||||
<text x="890" y="670" text-anchor="middle" class="sub">Key Insight</text>
|
||||
|
||||
<text x="640" y="705" class="txt">Float: patch 1 word</text>
|
||||
<text x="640" y="735" class="txt">Double: patch 2 words</text>
|
||||
<text x="640" y="765" class="dim">Check r2 to detect type</text>
|
||||
</svg>
|
||||
|
After Width: | Height: | Size: 4.5 KiB |
Reference in New Issue
Block a user