Correct : b,d

Correct Answer:
b and d (Multiple Select Question)

Explanation:
1. Concept of Sign Extension: In 2's complement representation, when you want to extend a signed integer from a smaller number of bits to a larger number of bits (e.g., from 4 bits to 8 bits or 16 bits), you perform an operation called sign extension.
• To do this, you simply look at the most significant bit (MSB), which is the leftmost sign bit.
• You replicate (copy) that sign bit into all the new higher-order positions to fill the extra space.

2. Analyze the Original Value:
• The original 4-bit representation of -6 is 1010.
• The sign bit (MSB) is 1 (indicating a negative value).

3. Convert to 8-bits:
• We need to add 4 extra bits to the left.
• Since the sign bit is 1, we extend it by adding four 1s: 1111.
• Combining them gives: 1111 1010.
• Therefore, Statement (b) is Correct and Statement (a) is Incorrect.

4. Convert to 16-bits:
• We need to add 12 extra bits to the left of the original 4 bits.
• Since the sign bit is 1, we copy it 12 times: 1111 1111 1111.
• Combining them gives: 1111 1111 1111 1010.
• Therefore, Statement (d) is Correct and Statement (c) is Incorrect.