Nonweighted, unit-distance identification — which of the following is a nonweighted binary code that also changes only one bit between successive values (a unit-distance code)?

Introduction / Context:Binary codes are often categorized by whether they are weighted (each position has a fixed weight) or nonweighted (no simple positional weights). In applications like position encoders and certain counters, a “unit-distance” property—successive code words differ by one bit—is highly desirable to minimize transition errors.

Given Data / Assumptions:

• We need a code that is nonweighted.
• We also need only a single-bit change between successive values.
• Codes under consideration include Gray and Excess-3.

Concept / Approach:Gray code (reflected binary) is both nonweighted and unit-distance. It is constructed recursively to ensure that adjacent code words differ by exactly one bit, which reduces decoding ambiguity during changes. Excess-3, while nonweighted and self-complementing, does not guarantee single-bit transitions between successive decimal digits and is designed for decimal arithmetic, not transition robustness. Weighted codes like 8421 BCD explicitly use positional weights and are therefore not nonweighted.

Step-by-Step Solution:

Verification / Alternative check:Construct a short Gray sequence (3-bit): 000, 001, 011, 010, 110, 111, 101, 100 — observe one-bit transitions throughout. Compare to Excess-3 of decimal digits and note multiple-bit changes frequently occur.

Why Other Options Are Wrong:

Common Pitfalls:Equating “nonweighted” with “unit-distance”; they are independent properties. Gray happens to possess both, which is why it is common in encoders.

Final Answer:Gray code (reflected binary)