Gray code advantage for rotary position encoding Why is Gray code preferred for encoding the angular position of a rotating shaft in encoders and position sensors?

Introduction / Context:
Rotary encoders and absolute position sensors often use Gray code rather than straight binary to minimize reading errors during transitions. Mechanical contacts, optical sensors, and sampling circuits rarely change all bits at exactly the same instant. Gray code reduces ambiguity when the shaft moves between adjacent positions while being read.

Given Data / Assumptions:

• We compare properties of Gray code vs straight binary.
• Adjacent codewords in Gray code differ by a Hamming distance of 1.
• Sampling may occur during a code transition due to mechanical or timing skew.

Concept / Approach:
The key Gray code property is that consecutive counts change only one bit. If a sensor or reader samples during the change, at most a single bit may be ambiguous, limiting the interpreted error to at most one adjacent code rather than a large jump that could occur with multi-bit changes in binary code.

Step-by-Step Reasoning:

Verification / Alternative check:
Plot Hamming distance between successive Gray codewords: it is uniformly 1. In contrast, binary’s worst-case transition changes many bits, which is problematic for asynchronous sampling and mechanical bounce.

Why Other Options Are Wrong:

• All digits or two digits change: contradicts Gray code definition.
• Weighted code with parity: Gray is non-weighted and does not inherently include parity.
• Fewer bits: both Gray and binary use the same number of bits for the same range.

Common Pitfalls:

• Assuming Gray code simplifies arithmetic; it is mainly for transition robustness, not computation.

Final Answer:
Only one digit changes between counts.