Gray Code Complete Sequence: Write All 4-Bit Values
Absolute rotary encoders use Gray code to prevent multi-bit transition errors during continuous physical rotation. The standard sequence is built using the reflect-and-prefix method: an N-bit sequence is formed by reflecting the (N-1)-bit sequence and prefixing 0 to the first half and 1 to the reversed second half.
A 4-bit Gray code sequence starts at 0000 and contains 16 unique values. Construct the complete 4-bit Gray code sequence using this reflective property. Analyze the bit transitions between adjacent values and evaluate the wrap-around boundary between the final and initial states.
Constraints
- All values must be evaluated as 4-bit binary strings.
- The sequence must be generated strictly using the reflective construction, not standard binary counting.
- Assume bit 3 is the most significant bit (MSB) and bit 0 is the least significant bit (LSB).
Topics
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