# Two-Level Combinational Logic - University of Houston

MSI Combinational logic circuits 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 2n output lines. If n bit decoded information has unused or don't care combination, the decoder output will have less than 2n outputs. CS 3402--Digital Logic MSI Devices 3 Decoders/Demultiplexers 1:2 Decoder CS 3402--Digital Logic MSI Devices

A D0 D1 0 1 0 1 0 1 4 Decoders/Demultiplexers 2:4 Decoder CS 3402--Digital Logic 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 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 1

0 0 0 Mul 0 10 0 1 0 1 0 0 Div 0 11 1 0

0 0 1 0 1 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 2n 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 2n (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

0 0 Mul 0 10 2 0 1 0 0 0 1 Div 0 11 3 0

0 1 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 0

0 2 0 1 0 0 0 1 3 0 0 1 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

21 Multiplexers CS 3402--Digital Logic MSI Devices s0 z 0 I0 1 I1 19 21 Multiplexers 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 Z = s0 I0 + s1 I1 CS 3402--Digital Logic MSI Devices

20 41 Multiplexers s1 s0 Z 0 0 I0 0 1 I1 1 0 I2 1 1 I3

Z = s1 s0I0 + s1s0 I1 + s1s0 I2 + s1s0 I3 CS 3402--Digital Logic MSI Devices 21 81 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 CS 3402--Digital Logic MSI Devices 22 Alternative Implementation The following diagrams show how to construct a 8 1 multiplexer using either 4 1 multiplexers or 2 1 multiplexers. CS 3402--Digital Logic MSI Devices 23

CS 3402--Digital Logic MSI Devices 24 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 CS 3402--Digital Logic MSI Devices 25 Example 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 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

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