Express −15 as a 6-bit signed binary number (sign-magnitude representation).

Concept

In sign-magnitude representation, an n-bit number splits into two parts: the most-significant bit is the sign bit (0 = positive, 1 = negative), and the remaining n−1 bits store the plain magnitude of the value. The magnitude bits are identical for +x and −x; only the sign bit differs.

Application

1. Take the magnitude: |−15| = 15.

2. Write 15 in the remaining 5 magnitude bits: 15 = 8 + 4 + 2 + 1 = 01111.

3. The value is negative, so set the sign bit (MSB) to 1.

4. Concatenate sign bit and magnitude: 1 | 01111 = 101111.

Cross-check / Contrast

Read it back: MSB 1 → negative; magnitude 01111 = 15 → the value is −15. Correct.

• 001111 has sign bit 0, so it is +15, not −15.

• Magnitude 01110 = 14, so any option with that magnitude encodes ±14, not ±15.

Note on conventions: in two's-complement representation −15 would instead be 110001 (invert 001111 to 110000, then add 1). That form is not offered here because the question asks for the sign-magnitude representation.