Sign representation basics: In common signed-number encodings (signed magnitude, one’s complement, two’s complement), what sign bit indicates a positive value?

Introduction / Context:Digital systems need consistent conventions for signed binary values. Several representations exist—signed magnitude, one’s complement, and two’s complement—but they agree on the meaning of the single sign bit: 0 for positive (and zero), 1 for negative. This question corrects a common misunderstanding about which sign-bit value indicates positivity.

Given Data / Assumptions:

• Single sign-bit formats are considered (no biased or excess-N encodings).
• Magnitude bits represent the absolute value in some form.
• We exclude floating-point encodings here.

Concept / Approach:Across the common signed integer encodings, the most significant bit (MSB) is designated the sign bit. Conventionally, sign = 0 indicates non-negative; sign = 1 indicates negative. The exact mapping of magnitude differs among formats, but the sign-bit meaning remains consistent, particularly for two’s complement, the dominant representation in modern processors.

Step-by-Step Solution:

Verification / Alternative check:Inspect two’s complement ranges: for 8-bit, 0x00..0x7F are non-negative (MSB=0), 0x80..0xFF are negative (MSB=1). Signed magnitude and one’s complement follow the same sign-bit convention even though zero handling differs.

Why Other Options Are Wrong:

Common Pitfalls:Confusing sign-bit meaning with bias encodings (e.g., excess-127 in floating point) or with sign extension behavior on shifts.

Final Answer:Incorrect — the sign bit 0 denotes positive; sign bit 1 denotes negative