Question

The number \(-6\) can be represented as \(1010\) in 4-bit 2’s complement representation. Which of the following is/are CORRECT 2’s complement representation(s) of \(-6\)?

• A. \(1000 \, 1010\) in 8-bits
• B. \(1111 \, 1010\) in 8-bits
• C. \(1000 \, 0000 \, 0000 \, 1010\) in 16-bits
• D. \(1111 \, 1111 \, 1111 \, 1010\) in 16-bits

Hint:

When representing negative numbers in 2's complement, always extend the most significant bit (MSB) to the left when increasing the bit size. This ensures the number stays correctly represented.

Answer 1

The Correct Option is B, D

The 2’s complement representation of a negative number can be found by inverting the bits of the positive value and then adding 1.

For \( -6 \) in 4-bit 2’s complement:
1. The binary representation of \( 6 \) is \( 0110 \).
2. Invert the bits: \( 1001 \).
3. Add 1: \( 1010 \).

Now, let's consider the extended bit sizes:
- In 8-bits: The correct 2’s complement representation of \( -6 \) would be \( 1111 \, 1010 \). So, Option (B) is correct.
- In 16-bits: The correct 2’s complement representation of \( -6 \) would be \( 1111 \, 1111 \, 1111 \, 1010 \). So, Option (D) is correct.

Thus, the correct answers are \( \boxed{B} \) \& \( \boxed{D} \).