Decoders, Encoders, and Muxes, Oh My!

Tom Kelliher, CS 240

Feb. 15, 2012




Read 4.1-4.2. Review mostly; background for carry lookahead.

From Last Time

Combinational design example.


  1. Decoders

  2. Encoders

  3. Muxes

Coming Up

Lower bound for addition. Fast addition algorithms.


Block diagram (diagram a 3-8 decoder):


A circuit with $n$ inputs. The inputs are interpreted as a binary number and used to select one of $2^n$ output lines.

  1. Most common use: Address decoders for RAMs and register files.

  2. Decoder expansion example: design a 5-to-32 using 5 3-to-8 decoders.

  3. Example use: Design a BCD to seven segment decoder using a 4 to 16 decoder and OR gates.


Inverse of a decoder: $2^n$ inputs; $n$ outputs.

  1. What happens if multiple inputs are high?

  2. Most common uses: priority encoders for interrupt controllers; ``hit'' logic for caches.

  3. Design example: Four input priority encoder with a ``Valid'' output.


Used to select one of $2^n$ inputs. One way switch.

Block diagram (draw a 4-1 mux):


  1. Most common uses: RAM, register file data selection circuits; Boolean function generators.

  2. What's a quad 2-1 mux?

  3. Design example: Implement a three input Boolean function using an 8-1 mux. No additional logic.

    Four input Boolean function using an 8-1 mux and an inverter?

    Five input Boolean function?

Thomas P. Kelliher 2012-02-14
Tom Kelliher