MSI Combinational logic circuits CS 3402 Digital Logic

MSI Combinational logic circuits CS 3402 --Digital Logic MSI Devices

Outline • Decoders • Multiplexers CS 3402 --Digital Logic MSI Devices 2

Decoders/Demultiplexers A decoder is a combinational circuit that converts binary information from n inputs to a maximum of unique 2 n output lines. If n bit decoded information has unused or don't care combination, the decoder output will have less than 2 n outputs. CS 3402 --Digital Logic MSI Devices 3

Decoders/Demultiplexers 1: 2 Decoder CS 3402 --Digital Logic MSI Devices A D 0 D 1 0 1 0 1 4

Decoders/Demultiplexers 2: 4 Decoder CS 3402 --Digital Logic A B D 0 D 1 D 2 D 3 0 0 1 0 0 1 0 0 0 1 MSI Devices 5

Example Design a 2 -input, 4 -output combinational logic circuit to decode the 2 -bit output of the following function table: Function Code Input Output Add 1 00 X Y A S M D Sub 0 01 0 0 0 Mul 0 10 0 1 0 0 Div 0 11 1 0 0 0 1 CS 3402 --Digital Logic MSI Devices 6

Example Full adder S(A, B, C) = m(1, 2, 4, 7) Cin(A, B, C) = m(1, 2, 4, 7) CS 3402 --Digital Logic MSI Devices 7

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 2 n lines. The selection of a specific output line is controlled by the bit values of n selection lines. CS 3402 --Digital Logic MSI Devices 8

CS 3402 --Digital Logic MSI Devices 9

Standard MSI Decoders CS 3402 --Digital Logic MSI Devices 10

Example Realize Boolean function f = A'B' + AB with a 2: 4 decoder 74139. CS 3402 --Digital Logic MSI Devices 11

3: 8 Decoder CS 3402 --Digital Logic MSI Devices 12

4: 16 Decoder CS 3402 --Digital Logic MSI Devices 13

Cascading decoders Build a 4: 16 decoder using two 74138 decoders. CS 3402 --Digital Logic MSI Devices 14

Encoders An encoder is a digital circuit that performs the inverse operation of a decoder. An encoder has 2 n (or fewer) input lines and n output lines. The output lines generate the binary code corresponding to the input value. CS 3402 --Digital Logic MSI Devices 15

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 Function Input Code Output Add 1 00 Line A S M D X Y Sub 0 01 1 1 0 0 0 Mul 0 10 2 0 1 0 0 0 1 Div 0 11 3 0 0 1 0 4 0 0 0 1 1 1 X = A'S' Y = A'M' CS 3402 --Digital Logic MSI Devices 16

Example X = A'S' Y = A'M' Input Output Line A S M D X Y 1 1 0 0 0 2 0 1 0 0 0 1 3 0 0 1 0 4 0 0 0 1 1 1 CS 3402 --Digital Logic MSI Devices 17

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. CS 3402 --Digital Logic MSI Devices 18

2 1 Multiplexers CS 3402 --Digital Logic MSI Devices s 0 z 0 I 0 1 I 1 19

2 1 Multiplexers I 1 I 0 s 0 Z 0 0 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 Z = s 0 I 0 + s 1 I 1 CS 3402 --Digital Logic MSI Devices 20

4 1 Multiplexers s 1 s 0 Z 0 0 I 0 0 1 I 1 1 0 I 2 1 1 I 3 Z = s 1 s 0 I 0 + s 1 s 0 I 1 + s 1 s 0 I 2 + s 1 s 0 I 3 CS 3402 --Digital Logic MSI Devices 21

8 1 Multiplexers s 2 s 1 s 0 Z 0 0 0 I 0 0 0 1 I 1 0 I 2 0 1 1 I 3 1 0 0 I 4 1 0 1 I 5 1 1 0 I 6 1 1 1 I 7 Z = s 2 s 1 s 0 I 0 + s 2 s 1 s 0 I 1 + s 2 s 1 s 0 I 2 + s 2 s 1 s 0 I 3+ s 2 s 1 s 0 I 4 + s 2 s 1 s 0 I 5 + s 2 s 1 s 0 I 6 + s 2 s 1 s 0 I 7 CS 3402 --Digital Logic MSI Devices 22

Alternative Implementation The following diagrams show to construct a 8 1 multiplexer using either 4 1 multiplexers or 2 1 multiplexers. CS 3402 --Digital Logic MSI Devices 23

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Example F(A, B, C) = m(0, 2, 6, 7) A B C F 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 1 CS 3402 --Digital Logic MSI Devices 25

Example A B C F 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 1 CS 3402 --Digital Logic C' C' 0 1 MSI Devices 26

Examples 1) Implement a 2 1 multiplexer to F(A, B, C) = m(1, 3, 5, 6) 2) Implement a 4 1 multiplexer to F(A, B, C, D) = m(0, 1, 3, 4, 8, 9. 15) CS 3402 --Digital Logic MSI Devices 27

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 CS 3402 --Digital Logic MSI Devices 28

Multiplexer devices CS 3402 --Digital Logic MSI Devices 29

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 CS 3402 --Digital Logic MSI Devices 30