CENG 241 Digital Design 1 Lecture 9

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CENG 241Digital Design 1Lecture 9

• Amirali Baniasadi
• amirali_at_ece.uvic.ca

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This Lecture

• Chapter 4 Decoders, Multiplexers

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Decoders

• A decoder converts binary information from n
  input lines to a maximum of 2n output lines
• Also known as n-to-m line decoders where mlt 2n
• Example 3-to-8 decoders.

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Decoders Truth Table

• X Y Z D0 D1 D2
  D3 D4 D5 D6 D7
• 0 0 0 1 0 0
  0 0 0 0 0
• 0 0 1 0 1 0
  0 0 0 0 0
• 0 1 0 0 0 1
  0 0 0 0 0
• 0 1 1 0 0 0
  1 0 0 0 0
• 1 0 0 0 0 0
  0 1 0 0 0
• 1 0 1 0 0 0
  0 0 1 0 0
• 1 1 0 0 0 0
  0 0 0 1 0
• 1 1 1 0 0 0
  0 0 0 0 1

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Decoders AND implementation
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How to build bigger decoders?
We can combine two 3-to-8 decoders to build a
4-to-16 decoder.
Generates from 0000 to 0111
Generates from 1000 to 1111
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Combinational Logic implementation

• A decoder provides the 2n minterms of n input
  variables.
• Any function is can be expressed in sum of
  minterms.
• Use a decoder to make the minterms and an
  external OR gate to make the sum.
• Example consider a full adder.
• S(x,y,z) S(1,2,4,7)
• C(x,y,z) S (3,5,6,7)

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Combinational Logic implementation
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Multiplexers

• Multiplexer selects one binary input from many
  selections
• example 2-to-1 MUX

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4-to-1 MUX
Directs 1 of the 4 inputs to the output
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Multi-bit selection logic

• Multiplexers can be combined with common
  selection inputs to support multi-bit selection
  logic

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Implementing Boolean functions w/ MUX

• General rules for implementing any Boolean
  function with n variables
• Use a multiplexer with n-1 selection inputs and 2
  n-1 data inputs
• List the truth table
• Apply the first n-1 variables to the selection
  inputs of multiplexer
• For each combination evaluate the output as a
  function of the last variable.
• The function can be 0, 1 the variable or the
  complement of the variable.

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Implementing Boolean functions w/ MUX
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Implementing Boolean functions w/ MUX
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Decoder as Demultiplexer

• A decoder with enable can function as a
  demultiplexer
• A demultiplexer is a circuit that receives
  information from a single line and directs it to
  one of the 2n possible output lines.
• E has a path to each of the four outputs. Ex. If
  AB10 then D2E

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Summary

• Reading up to page 156
• HW 4 4-25,4-26,4-31,4-32,4-35
• Due Thursday June 14th.