MSI Combinational logic circuits

Outline Decoders Multiplexers CS 3402--Digital Logic MSI Devices

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

Decoders/Demultiplexers A D0 D1 1 CS 3402--Digital Logic MSI Devices

Decoders/Demultiplexers A B D0 D1 D2 D3 1 CS 3402--Digital Logic MSI Devices

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

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

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

CS 3402--Digital Logic MSI Devices

Standard MSI Decoders CS 3402--Digital Logic MSI Devices

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

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

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

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

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

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

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

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

21 Multiplexers s0 z I0 1 I1 CS 3402--Digital Logic MSI Devices

21 Multiplexers Z = s0 I0 + s1 I1 I1 I0 s0 Z 1 CS 3402--Digital Logic 1 CS 3402--Digital Logic MSI Devices

41 Multiplexers Z = s1 s0I0 + s1s0 I1 + s1s0 I2 + s1s0 I3 s1 s0 Z I0 I0 1 I1 I2 I3 CS 3402--Digital Logic MSI Devices

81 Multiplexers s2 s1 s0 Z I0 1 I1 I2 I3 I4 I5 I6 I7 Z = s2s1s0I0 + s2s1s0 I1 + s2s1s0 I2 + s2s1s0 I3+ s2s1s0I4 + s2s1s0 I5 + s2s1s0 I6 + s2s1s0 I7 CS 3402--Digital Logic MSI Devices

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

CS 3402--Digital Logic MSI Devices

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

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

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) CS 3402--Digital Logic MSI Devices

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

Multiplexer devices CS 3402--Digital Logic MSI Devices

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