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

\[ 45_{10} = 101101_2
45_{16} = 69_{10} \Rightarrow 69 = 1000101_2 \Rightarrow 45 - 69 = -24 \] Now: \[ -24_{10} = 2\text{’s complement of } 011000 = 101000\ (\text{in 6-bit}) \]