Nature of Gray code: Is Gray code an “octal (base-8) number system,” or is it a binary code in which only one bit changes between successive values to reduce transition errors?

Introduction / Context:
Gray code is widely used in position encoders, communication protocols, and state machines to minimize errors during transitions. This question checks whether Gray code is an octal (base-8) number system or a binary code with a special ordering property where adjacent values differ by exactly one bit.

Given Data / Assumptions:

• Gray code symbols are binary bit patterns.
• The sequence is arranged so that consecutive codes have Hamming distance 1.
• The base (radix) refers to the number of allowed symbols per digit position.

Concept / Approach:
Gray code is not a different radix system like octal or decimal; it is an ordering of binary patterns. Because only one bit flips at a time, sampling during transitions is less likely to capture multiple simultaneous bit changes, reducing the chance of misread values in mechanical or asynchronous environments. Grouping bits by three to form octal digits is a notation convenience for pure binary, not a change to Gray code’s nature.

Step-by-Step Solution:

Verification / Alternative check:
Compare binary-reflected Gray sequence to standard binary count; both use binary symbols, but ordering differs. No octal digits or base-8 arithmetic are involved.

Why Other Options Are Wrong:
Calling it octal confuses notation with radix; restricting it to analog encoders ignores digital uses; “decimal with parity” is unrelated.

Common Pitfalls:
Assuming that grouping bits (like 3-bit octal groupings) changes the underlying code’s base; conflating Gray ordering with numerical base systems.

Final Answer:
Incorrect