Question

How is the decoder like the multiplexer. How is it different? Both at the circuit level, and in the logic behind them.

Answer 1

In decoder, if it take n (where n is number of variables) inputs then it produces 2^n outputs But the multiplexer is quite different as it takes 2^n inputs(where n is number of variables) with having n select lines and it product only one output as result.

If we talk about similarities Decoder is just similar to demultiplexer(which takes 1 input and having n select lines and produces 2^n output), You need change two things to make demultiplexer a decoder .

1. Make all n select lines as input for decoder and 2. Give 1(always true) to a single input of demultiplexer) we will get the decoder.