Gray to Binary Conversion (The Hard Direction)
Hardware receivers use Gray to binary converters to decode rotary encoder states and clock domain crossing signals back into standard arithmetic formats.
The system under analysis receives a 4-bit Gray code word G[3:0], where G3 is the most significant bit. The output is a 4-bit binary word B[3:0].
Trace the logic required to generate each binary bit from the Gray code input. Identify the structural difference between encoding and decoding this sequence. Determine the correct binary values and routing topology for the conversion.
Constraints
- Input
G[3:0]is a standard reflected Gray code. - Output
B[3:0]is a standard unsigned binary integer. G3andB3represent the most significant bits of their respective buses.- Assume all logic gates have a uniform propagation delay.
Topics
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