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
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
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
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