Introduction / Context:
In many digital and electromechanical systems, transitioning between count values can cause momentary ambiguity if multiple bits change simultaneously. A code designed so that adjacent values differ in only one bit helps avoid hazards in sensors, rotary encoders, and asynchronous interfaces.
Given Data / Assumptions:
- We seek an unweighted code with a Hamming distance of 1 between consecutive code words.
- Code is used to reduce errors during transitions.
- Options include familiar weighted and character codes.
Concept / Approach:
Gray code (reflected binary code) is explicitly constructed so that adjacent values differ in exactly one bit, thereby minimizing glitches and decoding errors during transitions. It is unweighted (no fixed place-value weights), unlike BCD or Excess-3, and it is not a character set like ASCII.
Step-by-Step Solution:
Recognize that BCD and Excess-3 are weighted or digit-encoded decimal schemes.Recognize ASCII is an alphanumeric character code, not a numeric counting code.Identify Gray code as the one-bit-change code.
Verification / Alternative check:
Write a short sequence: 00, 01, 11, 10 (2-bit Gray). Each neighbor differs by one bit only.
Why Other Options Are Wrong:
BCD: Weighted decimal digit code; multiple bits may change between numbers.Excess-3: Decimal code offset by +3; not one-bit transition guaranteed.ASCII: Character encoding for text; not a numeric counting sequence.
Common Pitfalls:
Confusing Gray code with Johnson or ring counters; those are sequential circuits, not general-purpose codes.Assuming one-bit change applies to random transitions; property holds for adjacent Gray values.
Final Answer:
Gray
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