Express -15 as a 6-bit signed binary number.

Concept: In the sign-magnitude scheme for representing signed binary integers, the leftmost (most significant) bit is a dedicated sign bit — 0 for positive, 1 for negative — and the remaining bits store the number's magnitude in ordinary binary.

1. With 6 bits total and 1 bit reserved for the sign, the magnitude of 15 is written in the remaining 5 bits: 15 = 01111.

2. Because the number is negative, the sign bit is set to 1.

3. Concatenating the sign bit with the magnitude gives 1 followed by 01111, i.e. 101111.

Cross-check: Reading 101111 back — the leading 1 marks it negative, and the remaining 01111 equals 15 in magnitude — reproduces -15, confirming the encoding. Note: an unqualified "signed binary" can in principle also mean one's or two's complement; sign-magnitude is used here because it is the simplest signed scheme (the conventional default when no other scheme is named), and — consistent with that — neither two's complement of -15 (110001) nor one's complement (110000) appears among the four options offered.

Hence, -15 as a 6-bit signed binary number (sign-magnitude) is 101111.