lab7 - State University of New York at Stony Brook...

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State University of New York at Stony Brook Department of Electrical and Computer Engineering ESE 218 Digital Systems Design Spring 2009 L ab 7 . Design with multiplexers 1. Objective Implementation of Boolean function s with multiplexers. Design of the magnitude comparator of two 2-bit binary numbers using only multiplexers and inverters. 2. Introduction In general, a multiplexer is a switch that directs binary information from the selected data input to one output. Selection of the particular data input is performed with a binary code applied to the special control (select) inputs. In computer systems it is often necessary to choose data from one of several possible sources. Assume Arithmetic and Logic Unit (ALU) of some m icroprocessor has to select input data from one of 16 registers to perform certain operation. This selection can be performed with a 16 –to-1 multiplexer. Multiplexers can be used for implementation of Boolean functions. The simplest multiplexer ( 2-to-1 ) is shown in Figure 1. One can see that Y = I 0 when S 0 = 0 and Y = I 1 when S 0 = 1. The multiplexers can be used in a more general way to implement logic functions. Suppose we need to implement NOR function: F = (A + B)’ = A’B’. Figure 1. The possible circuit diagram can be derived from the truth table. One of the input variables will go to control input S 0, let it be A. One can see from the table that F = B’ if A = 0 and F = 0 if A = 1. The circuit diagram is shown on the right of Figure 2. S 0 Y 0 I 0 1 I 1 Y = S 0 I 1 + S 0 ’I 0 I 0 I 1 S 0 Y control input data inputs
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2 Figure 2. With a 4-to-1 multiplexer one can implement a ny binary function of three variables with no additional logic gates (possibly an inveter may be needed for one of the variables). Any t wo input variables can be applied to control (select) inputs and used to select one of the four data inputs. The third variable (or its
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This note was uploaded on 04/12/2009 for the course ESE 218 taught by Professor Donetsky during the Spring '08 term at SUNY Stony Brook.

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lab7 - State University of New York at Stony Brook...

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