MSI%20Combinational%20logic%20circuits

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MSI Combinational logic circuits
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Outline

• Decoders
• Multiplexers

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Decoders/Demultiplexers

• A decoder is a combinational circuit that
  converts binary information from n inputs to a
  maximum of unique 2n output lines. If n bit
  decoded information has unused or don't care
  combination, the decoder output will have less
  than 2n outputs.

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Decoders/Demultiplexers

• 12 Decoder

A D0 D1
0 1 0
1 0 1
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Decoders/Demultiplexers

• 24 Decoder

A B D0 D1 D2 D3
0 0 1 0 0 0
0 1 0 1 0 0
1 0 0 0 1 0
1 1 0 0 0 1
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Example

• Design a 2-input, 4-output combinational logic
  circuit to decode the 2-bit output of the
  following function table

Input Input Output Output Output Output
X Y A S M D
0 0 1 0 0 0
0 1 0 1 0 0
1 0 0 0 1 0
1 1 0 0 0 1
Function Code Code
Add 1 00
Sub 0 01
Mul 0 10
Div 0 11
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Example

• Full adder
• S(A,B,C) ?m(1,2,4,7)
• Cin(A,B,C) ?m(1,2,4,7)

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Decoder with Enable

• A decoder with an enable can function as a
  demultiplexer. A demultiplexer is a circuit that
  receives information on a single line and
  transmits this information on one of possible 2n
  lines. The selection of a specific output line
  is controlled by the bit values of n selection
  lines.

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Standard MSI Decoders
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Example

• Realize Boolean function f A'B' AB with a 24
  decoder 74139.

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38 Decoder
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416 Decoder
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Cascading decoders

• Build a 416 decoder using two 74138 decoders.

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Encoders

• An encoder is a digital circuit that performs the
  inverse operation of a decoder. An encoder has
  2n (or fewer) input lines and n output lines.
  The output lines generate the binary code
  corresponding to the input value.

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Example

• A calculator has four function keys (add,
  subtract, multiply, divide). Only one of the
  function keys can be pressed at a time. When a
  particular key is pressed, that key is encoded
  according to the following function tab
• X A'S'
• Y A'M'

Input Input Input Input Output Output
Line A S M D X Y
1 1 0 0 0 0 0
2 0 1 0 0 0 1
3 0 0 1 0 1 0
4 0 0 0 1 1 1
Function Code Code
Add 1 00
Sub 0 01
Mul 0 10
Div 0 11
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Example

• X A'S'
• Y A'M'

Input Input Input Input Output Output
Line A S M D X Y
1 1 0 0 0 0 0
2 0 1 0 0 0 1
3 0 0 1 0 1 0
4 0 0 0 1 1 1
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Multiplexers/selectors

• Multiplexing means transmitting a large number of
  information units over a smaller number of
  channels or lines. A digital multiplexer is a
  combination circuit that selects binary
  information from one of many input lines and
  directs it to a single output line. The
  selection of a particular input line is
  controlled by a set of selection lines.
  Normally, there are 2 input lines and selection
  lines whose bit combinations determine which
  input is selected.

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2?1 Multiplexers
s0 z
0 I0
1 I1
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2?1 Multiplexers

• Z s0 I0 s1 I1

I1 I0 s0 Z
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
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4?1 Multiplexers

• Z s1 s0I0 s1s0 I1 s1s0 I2 s1s0 I3

s1 s0 Z
0 0 I0
0 1 I1
1 0 I2
1 1 I3
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8?1 Multiplexers
s2 s1 s0 Z
0 0 0 I0
0 0 1 I1
0 1 0 I2
0 1 1 I3
1 0 0 I4
1 0 1 I5
1 1 0 I6
1 1 1 I7

• Z s2s1s0I0 s2s1s0 I1 s2s1s0 I2 s2s1s0 I3
  s2s1s0I4 s2s1s0 I5 s2s1s0 I6 s2s1s0 I7

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Alternative Implementation

• The following diagrams show how to construct a 8
  ? 1 multiplexer using either 4 ? 1 multiplexers
  or
• 2 ? 1 multiplexers.

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Example

• F(A,B,C) ?m(0,2,6,7)

A B C F
0 0 0 1
0 0 1 0
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 1
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Example
A B C F
0 0 0 1 C'
0 0 1 0 C'
0 1 0 1 C'
0 1 1 0 C'
1 0 0 0 0
1 0 1 0 0
1 1 0 1 1
1 1 1 1 1
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Examples

• Implement a 2 ? 1 multiplexer to
• F(A,B,C) ?m(1,3,5,6)
• Implement a 4 ? 1 multiplexer to
• F(A,B,C,D) ?m(0,1,3,4,8,9.15)

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Multiplexer devices

• There are multiplexers devices in 7400 series,
• 74150 16-to-1 multiplexer (24 pins)
• 74151 8-to-1 multiplexer (16 pins)
• 74153 4-to-1 multiplexer
• 74157 2-to-1 multiplexer

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Multiplexer devices
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Exercises

• p.319 4.3, 4.4, 4.5, 4.9, 4.15, 4.16, 4.18, 4.19,
  4.20, 4.21, 4.23, 4.25