Line Decoders

• General n-to-m-line decoders
  • Decode n inputs to 2^n (or fewer) minterm outputs.
  • 2 to 4 decoder with enable
  • 3 to 8 decoder - from scratch and from two 2 to 4 decoders
  • Active high outputs and active low outputs.
  • Special purpose decoders: hex to 7-segment

• 2^n inputs lines, n control lines, 1 output
  • "Switch" model of multiplexer
  • 4 to 1 multiplexer
    • Block diagram
    • Truth table
    • Circuit
    • Equation for output
  • 4 to 1 multiplexer with enable
  • 8 to 1 multiplexer from 4 to 1 multiplexers (Hierarchical design)
  • Other sizes for multiplexers
    • 2^N to 1: 16 to 1, 32 to 1, etc.
    • M-bit 2^N to 1 - example: Quad 2 to 1 multiplexer
• Implementing fuctions with multiplexers
  • N variable functions with N control signals - inputs correspond to function truth table.
  • N variable functions with N-1 control signals - inputs are 0, 1, excess variable or it's compliment.
    • Attach N most significant variables to control signals.
    • Divide truth table into sections, 2 rows per section.
    • Find function of the extra variable for each section.
    • Attach the functions to the inputs of the multiplexor.
  • N variable functions with less than N-1 control signals - external gates are required.

Demultiplexors - used to switch a single input to one of many outputs