Signed and unsigned integers in ARM Architecture - Step-by-Step Execution

Concept Flow - Signed and unsigned integers

Start with binary bits

↓

Interpret bits as unsigned integer

↓

Interpret bits as signed integer (two's complement)

↓

Compare values

↓

Use depends on context: arithmetic or memory

↓

End

The same binary bits can be read as unsigned or signed integers depending on interpretation, affecting their value and use.

Execution Sample

ARM Architecture

Bits: 10000001
Unsigned: 129
Signed (two's complement): -127

Shows how the same 8 bits represent different values when interpreted as unsigned or signed integers.

Analysis Table

Step	Bits	Interpretation	Value	Explanation
1	10000001	Unsigned	129	Calculate as 1*2^7 + 0 + 0 + 0 + 0 + 0 + 0 + 1*2^0 = 128 + 1
2	10000001	Signed (two's complement)	-127	Most significant bit is sign bit (1 means negative), value = -(2^7) + 1 = -128 + 1
3	01111111	Unsigned	127	All bits except sign bit set, value = 127
4	01111111	Signed (two's complement)	127	Positive number, same as unsigned
5	11111111	Unsigned	255	All bits set, max unsigned 8-bit value
6	11111111	Signed (two's complement)	-1	Negative one in two's complement
7	00000000	Unsigned	0	All bits zero
8	00000000	Signed (two's complement)	0	Zero is same in both
9				End of examples

💡 All examples show how the same bits have different values depending on signed or unsigned interpretation.

State Tracker

Bits	Unsigned Value	Signed Value
10000001	129	-127
01111111	127	127
11111111	255	-1
00000000	0	0

Key Insights - 3 Insights

Why does the bit pattern 10000001 represent 129 as unsigned but -127 as signed?

Because unsigned integers treat all bits as magnitude, while signed integers use the most significant bit as a sign indicator with two's complement encoding, changing the value (see execution_table rows 1 and 2).

Why is 11111111 equal to 255 unsigned but -1 signed?

In unsigned, all bits set means maximum value (255). In signed two's complement, all bits set represents -1 (see execution_table rows 5 and 6).

Is zero represented the same way in signed and unsigned integers?

Yes, zero is all bits zero in both signed and unsigned, so the value is the same (see execution_table rows 7 and 8).

Visual Quiz - 3 Questions

Look at the execution_table row 2. What is the signed value of bits 10000001?

A 129

B -1

C -127

D 127

💡 Hint

Check the 'Signed (two's complement)' interpretation in row 2 of execution_table.

At which step does the bit pattern represent -1 as signed integer?

A Step 3

B Step 6

C Step 4

D Step 1

💡 Hint

Look for 'Signed (two's complement)' with value -1 in execution_table.

If the bits 01111111 are interpreted as unsigned, what value do they represent?

A 127

B 255

C -127

D -1

💡 Hint

See execution_table row 3 for unsigned interpretation of 01111111.

Concept Snapshot

Signed and unsigned integers use the same bits but differ in interpretation.
Unsigned integers treat all bits as positive magnitude.
Signed integers use two's complement: MSB is sign bit.
Two's complement allows negative numbers by inverting and adding one.
Same bits can represent different values depending on signedness.
Understanding this is key in ARM and other architectures.

Full Transcript

This visual execution shows how the same binary bits can represent different numbers depending on whether they are interpreted as signed or unsigned integers. For example, the bits 10000001 equal 129 if unsigned, but -127 if signed using two's complement. The most significant bit acts as a sign bit in signed integers. The table traces several examples, showing values for both interpretations. Key moments clarify common confusions about sign bit usage and zero representation. The quiz tests understanding by asking about specific steps and values. This knowledge is essential for working with ARM architecture and understanding how computers handle 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