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 $-6$?

To extend an $n$-bit 2's complement number to a higher bit-width, sign extension is performed, which copies the most significant bit (the sign bit) into all the new higher-order bit positions.

For the given 4-bit representation of $-6$:

The sign bit (MSB) is $1$.

• 8-bit representation: Replicate the sign bit ($1$) for the $4$ additional higher-order bits:

  $$1111\ 1010_2$$

  Hence, B is correct, while A is incorrect.

• 16-bit representation: Replicate the sign bit ($1$) for the $12$ additional higher-order bits:

  $$1111\ 1111\ 1111\ 1010_2$$

  Hence, D is correct, while C is incorrect.

Therefore, the correct options are B and D.