Signed and unsigned integers in ARM Architecture - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main difference between signed and unsigned integers?

Signed integers can represent both positive and negative numbers, while unsigned integers represent only non-negative numbers (zero and positive).

intermediate

How does ARM architecture typically represent signed integers internally?

ARM architecture uses two's complement representation to store signed integers, allowing easy arithmetic with positive and negative values.

beginner

What is the range of an 8-bit unsigned integer?

An 8-bit unsigned integer ranges from 0 to 255 because it uses all bits to represent positive values only.

beginner

What is the range of an 8-bit signed integer in two's complement?

An 8-bit signed integer ranges from -128 to 127, using two's complement representation.

intermediate

Why is two's complement preferred for signed integers in ARM and many other architectures?

Two's complement simplifies hardware design because addition and subtraction work the same way for signed and unsigned numbers, avoiding separate circuits for sign handling.

Which of the following can an unsigned integer NOT represent?

A Large positive numbers

B Negative numbers

C Positive numbers

D Zero

Unsigned integers only represent zero and positive numbers, so they cannot represent negative numbers.

In ARM architecture, what method is used to represent signed integers?

A Two's complement

B Sign-magnitude

C One's complement

D Floating point

ARM uses two's complement to represent signed integers for efficient arithmetic operations.

What is the maximum value of a 16-bit unsigned integer?

A 65536

B 32767

C 65535

D 32768

A 16-bit unsigned integer ranges from 0 to 65535 (2^16 - 1).

What is the minimum value of an 8-bit signed integer in two's complement?

A -128

B -127

C 0

D -256

The minimum value for an 8-bit signed integer in two's complement is -128.

Why does two's complement simplify arithmetic operations in hardware?

A Because it stores sign separately

B Because it uses fewer bits

C Because it avoids negative numbers

D Because addition and subtraction use the same circuits for signed and unsigned numbers

Two's complement allows the same hardware circuits to handle addition and subtraction for both signed and unsigned numbers.

Explain the difference between signed and unsigned integers and give an example of their value ranges for 8-bit numbers.

Think about how many values can be represented and how the sign affects the range.

Describe why ARM architecture uses two's complement for signed integers and how it benefits arithmetic operations.

Consider how hardware performs math with signed numbers.

Practice

1.

What is the main difference between signed and unsigned integers in ARM architecture?

easy

A. Signed integers use more memory than unsigned integers.

B. Signed integers can represent negative and positive numbers, unsigned only non-negative.

C. Unsigned integers can represent negative numbers, signed cannot.

D. Signed integers are faster to process than unsigned integers.

Solution

1. Step 1: Understand signed integers

   Signed integers use two's complement to represent both negative and positive numbers.

2. Step 2: Understand unsigned integers

   Unsigned integers represent only zero and positive numbers, allowing a larger positive range.

3. Final Answer:

   Signed integers can represent negative and positive numbers, unsigned only non-negative. -> Option B

4. Quick Check:

   Signed = negative and positive, Unsigned = only positive [OK]

Hint: Signed = negatives allowed, unsigned = only zero or positive [OK]

Common Mistakes:

• Thinking unsigned can represent negative numbers
• Assuming signed uses more memory
• Believing signed is always faster

2.

Which of the following is the correct way to declare an unsigned 8-bit integer in ARM assembly?

easy

A. mov r0, #255 (assuming r0 is unsigned 8-bit)

B. movs r0, #255

C. mov r0, #-1

D. mov r0, #256

Solution

1. Step 1: Understand unsigned 8-bit range

   Unsigned 8-bit integers range from 0 to 255, so 255 is valid.

2. Step 2: Check instructions

   mov r0, #255 moves the immediate value 255 into register r0 correctly.

3. Final Answer:

   mov r0, #255 (assuming r0 is unsigned 8-bit) -> Option A

4. Quick Check:

   Unsigned 8-bit max = 255, mov loads immediate [OK]

Hint: Unsigned 8-bit max is 255, use mov with that value [OK]

Common Mistakes:

• Using movs which sets flags unnecessarily
• Trying to move negative values to unsigned
• Using values above 255 for 8-bit

3.

Consider a 4-bit signed integer using two's complement. What decimal value does the binary 1101 represent?

medium

A. -3

B. 13

C. -5

D. 5

Solution

1. Step 1: Identify two's complement sign

   In 4-bit two's complement, if the leftmost bit is 1, the number is negative.

2. Step 2: Calculate decimal value

   Binary 1101: invert bits -> 0010, add 1 -> 0011 (3 decimal), so value is -3. But careful: 1101 is -3 or -5? Let's check carefully:
   1101 binary = (1x-8) + (1x4) + (0x2) + (1x1) = -8 + 4 + 0 + 1 = -3

3. Final Answer:

   -3 -> Option A

4. Quick Check:

   Two's complement 1101 = -3 decimal [OK]

Hint: If MSB is 1, subtract 2^bits from value [OK]

Common Mistakes:

• Treating binary as unsigned
• Forgetting two's complement negative calculation
• Mixing bit positions

4.

In ARM assembly, a programmer tries to store the value -1 in an unsigned 8-bit register. What is the likely result?

medium

A. The program crashes at runtime.

B. Syntax error occurs during assembly.

C. The register stores 0.

D. The register stores 255 due to wrap-around.

Solution

1. Step 1: Understand unsigned storage

   Unsigned 8-bit registers store values 0 to 255. Negative values wrap around using modulo 256.

2. Step 2: Calculate wrap-around for -1

   -1 modulo 256 equals 255, so the register stores 255.

3. Final Answer:

   The register stores 255 due to wrap-around. -> Option D

4. Quick Check:

   Unsigned wrap-around: -1 = 255 [OK]

Hint: Negative to unsigned wraps modulo max+1 [OK]

Common Mistakes:

• Expecting syntax error for negative immediate
• Assuming register stores zero
• Thinking program crashes

5.

You have a 16-bit unsigned integer register holding the value 65535. You subtract 1 from it. What is the result stored in the register?

hard

A. 65536

B. -1

C. 65534

D. 0

Solution

1. Step 1: Understand 16-bit unsigned range

   16-bit unsigned integers range from 0 to 65535.

2. Step 2: Perform subtraction

   65535 - 1 = 65534, which fits in 16 bits without wrap-around.

3. Final Answer:

   65534 -> Option C

4. Quick Check:

   65535 - 1 = 65534 within unsigned 16-bit [OK]

Hint: Subtract within range stays positive, no wrap [OK]

Common Mistakes:

• Thinking result becomes negative
• Assuming overflow to zero
• Confusing unsigned with signed behavior