Question

The result of \( 45_{10} - 45_{16} \), expressed in 6-bit 2's complement, is:

• A. 011000
• B. 100111
• C. 101000
• D. 101001

Hint:

In 2's complement: Negative numbers = Invert + 1 on positive binary.

Answer 1

The Correct Option is C

To solve the problem, we need to find the result of \(45_{10} - 45_{16}\) and express it in 6-bit 2's complement.

1. Convert \(45_{16}\) to decimal:

\(45_{16} = 4 \times 16^1 + 5 \times 16^0 = 64 + 5 = 69_{10}\)

2. Perform the subtraction \(45_{10} - 69_{10}\):

\(45 - 69 = -24\)

3. Convert \(-24\) to binary using 6-bit 2's complement:

a. Find the 6-bit binary representation of \(24\):

\(24_{10} = 011000_2\)

b. Invert the digits to get the 1's complement:

\(100111_2\)

c. Add 1 to get the 2's complement:

\(100111_2 + 1 = 101000_2\)

The result expressed in 6-bit 2's complement is \(101000_2\).