What is Gray code and why is it important in digital systems?

Gray code is a binary code where adjacent values differ by only one bit. This property eliminates multi-bit transition errors in position encoders (no ambiguous intermediate states), reduces errors in asynchronous clock domain crossing (single-bit changes are safely synchronized), and minimizes switching noise. Conversion: Binary to Gray: G[n]=B[n], G[i]=B[i+1] XOR B[i]. Gray to Binary: B[n]=G[n], B[i]=B[i+1] XOR G[i]. Applications include rotary encoders, ADC design, and FIFO pointer synchronization.