Embedded-Hacking/WEEKS/WEEK05/QUIZ05.md

Week 5 Quiz: Integers, Floats, Doubles, and IEEE 754

Instructions

Choose the best answer for each question. There is only one correct answer per question.

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Questions

Question 1

What is the valid value range of int8_t (a signed 8-bit integer)?

A) 0 to 255
B) 0 to 127
C) -128 to 127
D) -256 to 255

📖 Reference: Week 5, Part 1 – "Signed vs Unsigned Integers" (table: int8_t range is -128 to 127)

Correct Answer: C

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Question 2

How is the value -42 stored in a single byte using two's complement?

A) 0x2A — the sign is tracked separately by the CPU
B) 0xD6 — the CPU flips all bits of 42 (0x2A) and adds 1
C) 0xAA — negative values always have the pattern 1010... in binary
D) 0x42 — the value is stored identically to positive 42

📖 Reference: Week 5, Part 1 – "The Integer Variables" (two's complement: flip bits of 0x2A and add 1 = 0xD6)

Correct Answer: B

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Question 3

In IEEE 754 single-precision (32-bit float), how are the 32 bits divided among sign, exponent, and mantissa?

A) 1 sign bit, 11 exponent bits, 20 mantissa bits
B) 1 sign bit, 8 exponent bits, 23 mantissa bits
C) 2 sign bits, 8 exponent bits, 22 mantissa bits
D) 1 sign bit, 10 exponent bits, 21 mantissa bits

📖 Reference: Week 5, Part 2 – "What is a Float?" (IEEE 754 Single-Precision diagram: 1 sign, 8 exponent, 23 mantissa)

Correct Answer: B

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Question 4

Why does printf receive a 64-bit double even when the source code declares a float variable?

A) The Pico 2's ARM Cortex-M33 does not have a floating-point unit
B) Ghidra automatically converts floats to doubles during analysis
C) The C standard requires float arguments to variadic functions like printf to be promoted to double
D) The %f format specifier forces the compiler to use 64-bit precision

📖 Reference: Week 5, Part 2.7, Step 14 – "Understand the Float Encoding" (C standard requires float arguments to variadic functions are promoted to double)

Correct Answer: C

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Question 5

What is the exponent bias for IEEE 754 double-precision, and why is it 1023?

A) 127 — because the exponent field is 8 bits and (2^8 / 2) - 1 = 127
B) 1023 — because the exponent field is 11 bits and (2^{11} / 2) - 1 = 1023
C) 1024 — because 2^{10} = 1024 and the exponent uses 10 bits
D) 2047 — because 2^{11} - 1 = 2047 is the maximum 11-bit value

📖 Reference: Week 5, Part 2.7, Step 15 – "Why 1023?" callout (exponent is 11 bits, 2^{11} = 2048, midpoint = (2048 / 2) - 1 = 1023)

Correct Answer: B

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Question 6

On the ARM Cortex-M33, how is a 64-bit double passed to a function like printf?

A) In a single 64-bit register r0
B) On the stack as an 8-byte value
C) In two 32-bit registers: r2 (low 32 bits) and r3 (high 32 bits)
D) In the floating-point register d0

📖 Reference: Week 5, Part 2.7, Step 14 – "A 64-bit double is passed in two 32-bit registers" (table: r2 = low, r3 = high)

Correct Answer: C

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Question 7

What does the mcrr p0, #4, r4, r5, c0 instruction do on the RP2350?

A) It reads the current GPIO pin state into registers r4 and r5
B) It writes to the GPIO coprocessor to set a pin's output value (r4 = pin, r5 = value)
C) It configures the GPIO function select register for SIO mode
D) It copies data between two ARM general-purpose registers

📖 Reference: Week 5, Part 1 – "The Blink Loop with Inline Assembly" (coprocessor register c0 controls output value, r5 = 1 drives HIGH, r5 = 0 drives LOW)

Correct Answer: B

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Question 8

When configuring a GPIO pin with inline assembly, what value is written to the FUNCSEL field to select SIO (Single-cycle I/O) mode?

A) 0 — default reset value
B) 3 — UART function
C) 5 — SIO function
D) 31 — null function (disabled)

📖 Reference: Week 5, Part 1 – "GPIO Initialization with Inline Assembly" (Step 2: clears FUNCSEL bits and sets to 5 for SIO)

Correct Answer: C

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Question 9

What is the key difference between a float (32-bit) and a double (64-bit) in terms of decimal precision?

A) A float has ~15 digits precision; a double has ~7 digits precision
B) A float has ~7 digits precision; a double has ~15 digits precision
C) Both have the same precision; doubles just have a larger range
D) A float has exact precision; a double introduces rounding errors

📖 Reference: Week 5, Part 3 – "Float vs Double - Key Differences" (table: float ~7 decimal digits, double ~15 decimal digits)

Correct Answer: B

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Question 10

When patching the double 42.5 to 99.0 in Ghidra, only the high word (r3) needed to change. When patching 42.52525 to 99.99, both words needed to change. Why?

A) The value 99.99 is larger than 99.0, so it needs more bits to store
B) The value 99.0 has a clean fractional part (.0) so the low word is all zeros, but 99.99 has a repeating binary fraction that requires non-zero bits in the low 32 bits
C) Ghidra encodes doubles differently depending on the number of decimal places
D) The compiler uses a different instruction format for values with more decimal digits

📖 Reference: Week 5, Part 3.95 – "Key takeaway" (clean values like 42.5 only need one patch; messy fractions like 42.52525 need two)

Correct Answer: B

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Answer Key

1. C - int8_t is a signed 8-bit integer with range -128 to 127
2. B - Two's complement: flip all bits of 0x2A (42) and add 1 → 0xD6
3. B - IEEE 754 single-precision: 1 sign bit, 8 exponent bits, 23 mantissa bits
4. C - The C standard requires float arguments to variadic functions (printf) to be promoted to double
5. B - The 11-bit exponent gives 2048 values; the midpoint (2^{11} / 2) - 1 = 1023 is the bias
6. C - 64-bit doubles are split across r2 (low 32 bits) and r3 (high 32 bits) on ARM Cortex-M33
7. B - mcrr p0, #4, r4, r5, c0 writes to the GPIO coprocessor's output register (c0), setting pin r4 to value r5
8. C - FUNCSEL = 5 selects SIO mode for software-controlled GPIO
9. B - Float has ~7 decimal digits precision; double has ~15 decimal digits precision
10. B - Clean fractions (like .0) produce a zero low word; repeating binary fractions (like .99) need all 52 mantissa bits, making both words non-zero

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Scoring Guide

• 10 correct: Excellent! You have a strong grasp of Week 5 concepts
• 8-9 correct: Very good! Review the topics you missed
• 6-7 correct: Good start. Go back and review the key concepts
• 5 or fewer: Review the Week 5 material again and try the practice exercises

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Topics Covered

This quiz tests your understanding of:

• Signed vs unsigned integers: uint8_t and int8_t ranges
• Two's complement encoding of negative numbers
• IEEE 754 single-precision (32-bit) field layout
• Float-to-double promotion in C variadic functions
• IEEE 754 double-precision exponent bias (1023) and its derivation
• ARM Cortex-M33 register pairs (r2:r3) for 64-bit doubles
• GPIO coprocessor instruction mcrr for pin output control
• FUNCSEL field and SIO mode selection
• Float vs double precision differences
• Patching strategy: clean fractions (one word) vs repeating fractions (two words)