This document discusses encoders and multiplexers. It begins with defining an encoder as a combinational circuit that performs the reverse operation of a decoder, taking in 2n inputs and outputting n bits. An example of a simple 2n to n binary encoder is provided. The key differences between encoders and decoders are outlined. Circuit diagrams and truth tables are shown for an octal-to-binary encoder. The document then defines a multiplexer as a circuit that selects one of several input signals to route to a single output. An example of implementing a Boolean function using an 8:1 multiplexer is given. Finally, some common applications of multiplexers in communication systems, telephone networks, computer memory, and satellite transmission