Two's complement representation in ARM Architecture - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to represent the negative number -5 in 8-bit two's complement.

ARM Architecture

binary = "[1]"  # 8-bit two's complement of -5

Drag options to blanks, or click blank then click option'

A00000101

B11111011

C11110101

D00001011

Attempts:

3 left

💡 Hint

Common Mistakes

Using the positive binary representation instead of two's complement.

Forgetting to add 1 after inverting bits.

The 8-bit two's complement of -5 is 11111011. This is found by inverting the bits of 5 (00000101) and adding 1.

2fill in blank

medium

Complete the code to calculate the decimal value of the 8-bit two's complement binary '11110110'.

ARM Architecture

decimal_value = [1]  # decimal value of 11110110

Drag options to blanks, or click blank then click option'

A-10

B246

C10

D-6

Attempts:

3 left

💡 Hint

Common Mistakes

Interpreting the binary as unsigned and getting 246.

Confusing the sign bit and magnitude.

The binary 11110110 in 8-bit two's complement represents -10. The leading 1 means it's negative. Invert bits and add 1 to find magnitude.

3fill in blank

hard

Fix the error in the code that converts a negative decimal number to its 8-bit two's complement binary string.

ARM Architecture

def to_twos_complement(n):
    if n >= 0:
        return format(n, '08b')
    else:
        return format([1], '08b')  # fix this line

Drag options to blanks, or click blank then click option'

A(256 + n)

B(n - 256)

C(128 + n)

D(-n)

Attempts:

3 left

💡 Hint

Common Mistakes

Adding 128 instead of 256.

Using negative of n without adjustment.

For negative numbers, adding 256 (2^8) to n gives the correct 8-bit two's complement representation.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps numbers to their 8-bit two's complement binary strings only if the number is negative.

ARM Architecture

twos_complement_map = {num: format([1], '08b') for num in numbers if num [2] 0}

Drag options to blanks, or click blank then click option'

A256 + num

B>

C<

Dnum

Attempts:

3 left

💡 Hint

Common Mistakes

Using '>' instead of '<' in the condition.

Not adding 256 to negative numbers.

The comprehension adds 256 to negative numbers to get their two's complement binary. The condition filters numbers less than zero.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps numbers to their 8-bit two's complement binary strings, handling both positive and negative numbers.

ARM Architecture

twos_complement = {n: format([1], '08b') for n in nums}

# where [2] = n if n >= 0 else [3]

Drag options to blanks, or click blank then click option'

An

B256 + n

Cn if n >= 0 else 256 + n

Dn - 256

Attempts:

3 left

💡 Hint

Common Mistakes

Not using a conditional expression for negative numbers.

Using incorrect arithmetic for two's complement.

The comprehension uses a conditional expression: if n is non-negative, use n; otherwise, add 256 to get two's complement.

Practice

1. What is the main purpose of using two's complement in ARM architecture?

easy

A. To represent both positive and negative integers in binary

B. To store only positive numbers efficiently

C. To convert decimal numbers to hexadecimal

D. To encrypt data for security

Solution

1. Step 1: Understand number representation in computers

   Computers use binary to represent numbers, but need a way to show both positive and negative values.

2. Step 2: Role of two's complement

   Two's complement allows representing negative numbers by inverting bits and adding one, enabling simple arithmetic.

3. Final Answer:

   To represent both positive and negative integers in binary -> Option A

4. Quick Check:

   Two's complement = Signed integer representation [OK]

Hint: Two's complement = signed numbers in binary [OK]

Common Mistakes:

• Thinking it only stores positive numbers
• Confusing with encryption or encoding
• Assuming it converts decimal to hex

2. Which of the following is the correct 4-bit two's complement representation of -3?

easy

A. 1101

B. 0011

C. 1011

D. 1110

Solution

1. Step 1: Find binary of positive 3 in 4 bits

   3 in binary is 0011.

2. Step 2: Calculate two's complement for -3

   Invert bits: 1100, then add 1: 1101.

3. Final Answer:

   1101 -> Option A

4. Quick Check:

   -3 in 4-bit two's complement = 1101 [OK]

Hint: Invert bits and add 1 for negative numbers [OK]

Common Mistakes:

• Using positive binary without complement
• Adding instead of inverting bits first
• Confusing bit length or dropping bits

3. Given an 8-bit two's complement number 11111010, what decimal value does it represent?

medium

A. 22

B. -22

C. 250

D. -6

Solution

1. Step 1: Identify if number is negative

   Most significant bit is 1, so number is negative.

2. Step 2: Find magnitude by two's complement

   Invert bits: 00000101, add 1: 00000110 (6 decimal).

3. Final Answer:

   -22 -> Option B

4. Quick Check:

   11111010 two's complement = -22 [OK]

Hint: If MSB=1, invert bits +1 to find negative value [OK]

Common Mistakes:

• Reading as unsigned binary (250)
• Ignoring two's complement rules
• Mistaking bit inversion step

4. A programmer wrote this 4-bit two's complement number: 1001. They claim it equals +9. What is the error?

medium

A. 1001 equals +9 correctly

B. 1001 is invalid in two's complement

C. 1001 represents -7, not +9

D. Two's complement cannot represent 4-bit numbers

Solution

1. Step 1: Check sign from MSB

   MSB is 1, so number is negative in two's complement.

2. Step 2: Calculate decimal value

   Invert bits: 0110, add 1: 0111 (7 decimal), so value is -7.

3. Final Answer:

   1001 represents -7, not +9 -> Option C

4. Quick Check:

   1001 two's complement = -7, not +9 [OK]

Hint: MSB 1 means negative, check two's complement value [OK]

Common Mistakes:

• Assuming binary is always positive
• Ignoring sign bit meaning
• Confusing two's complement with unsigned

5. In ARM 8-bit two's complement, what is the result of adding 00010110 (+22) and 11101010 (-22)?

hard

A. 00011100 (28)

B. 11111111 (-1)

C. Overflow error

D. 00000000 (0)

Solution

1. Step 1: Understand the numbers

   00010110 is +22, 11101010 is -22 in two's complement.

2. Step 2: Add the binary numbers

   00010110 + 11101010 = 00000000 (ignoring carry out), which is 0.

3. Final Answer:

   00000000 (0) -> Option D

4. Quick Check:

   +22 + (-22) = 0 [OK]

Hint: Adding number and its negative gives zero [OK]

Common Mistakes:

• Expecting overflow when adding opposites
• Misreading negative number value
• Ignoring carry out in two's complement addition