Gray code identification in digital systems Which binary coding scheme progresses so that only one bit changes between any two successive code words (minimizing transition errors at boundaries)?

Introduction / Context:
Digital encoding schemes are used to represent numbers, characters, and states. In applications like position encoders, asynchronous state transitions, and analog-to-digital interfaces, it is desirable to ensure that only one bit changes between successive values to avoid transient misreads. The code specifically designed for this purpose is the reflected Gray code.

Given Data / Assumptions:

• We compare common codes: 8421 (pure binary/BCD), Excess-3, nine's-complement, and Gray code.
• The target property: only one bit changes between successive code words.
• Successive means numerically adjacent values (e.g., 3 to 4).

Concept / Approach:

Gray code (reflected binary code) is constructed so adjacent integers differ by a Hamming distance of 1. This minimizes decoding ambiguity during transitions, a crucial advantage for mechanical and high-noise environments. Other codes do not guarantee single-bit adjacency across the entire counting sequence.

Step-by-Step Solution:

Verification / Alternative check:

Enumerate 3-bit Gray: 000, 001, 011, 010, 110, 111, 101, 100 → each step flips one bit. Compare with pure binary sequence and note multi-bit changes at boundaries such as 3→4.

Why Other Options Are Wrong:

Nine's-complement: used for decimal subtraction, not single-bit adjacency.

8421 code: standard binary/BCD; many transitions flip multiple bits.

Excess-3: decimal code offset by +3; does not enforce single-bit transitions.

Common Pitfalls:

Confusing Gray code with BCD variants; assuming any “special” decimal code has single-bit transitions—it does not.

Final Answer:

Gray code