Sign representation basics: In common signed-number encodings (signed magnitude, one’s complement, two’s complement), what sign bit indicates a positive value?
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AIncorrect — the sign bit 0 denotes positive; sign bit 1 denotes negative
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BCorrect — a positive number is represented by a 1 sign bit
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CDepends only on one’s complement; two’s complement is different
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DDepends only on signed magnitude; two’s complement uses 2 sign bits
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E
Answer
Correct Answer: Incorrect — the sign bit 0 denotes positive; sign bit 1 denotes negative
Explanation
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:
Identify the sign bit: the MSB in an n-bit word.Recall the convention: sign=0 → positive/zero; sign=1 → negative.Reject statements that invert this convention.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:
Positive is 1: Inverts the established convention.Depends on format: While magnitudes differ, sign-bit meaning does not.Two sign bits claim: Not true for standard binary integer encodings.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