What are decoders and encoders in digital circuits?

A decoder converts n input lines to 2^n output lines, activating exactly one output for each input combination. Common examples are 2-to-4, 3-to-8 decoders used in memory address decoding and seven-segment displays. An encoder performs the reverse operation, converting 2^n input lines to n output lines. Priority encoders handle multiple active inputs by encoding the highest priority one. Both are essential in data conversion and address decoding applications.