Signed formats — sign-magnitude on 8 bits Express the decimal number −37 using 8-bit sign-magnitude representation (MSB is the sign).

Introduction / Context:Several binary signed-number schemes exist: sign-magnitude, one's complement, and two's complement. In sign-magnitude, the most significant bit (MSB) encodes the sign (0 = positive, 1 = negative), and the remaining bits encode the magnitude as an ordinary unsigned number. This question asks for −37 in 8-bit sign-magnitude form.

Given Data / Assumptions:

• Total width: 8 bits.
• Sign-magnitude convention: MSB is sign; 0 = positive, 1 = negative.
• Magnitude to encode: 37 in decimal.

Concept / Approach:

First convert the magnitude to binary using as many lower bits as needed (here 7 magnitude bits). Then set the MSB to 1 to indicate a negative number. No inversion or addition is performed in sign-magnitude (contrast with two's complement).

Step-by-Step Solution:

Verification / Alternative check:

Check that the magnitude portion equals 00100101 when viewed as 8 bits with MSB cleared, and that the sign bit is 1. No complements are involved in sign-magnitude.

Why Other Options Are Wrong:

00100101: sign bit 0 → +37, not −37.

11011000 or 11010001: these patterns do not represent −37 in sign-magnitude; they resemble unrelated bit patterns and, if interpreted as two's complement, would encode different values.

Common Pitfalls:

Confusing sign-magnitude with two's complement (which requires inverting and adding 1), or forgetting that only the MSB encodes the sign while the magnitude stays uninverted.

Final Answer:

10100101