INTRO.TO COMPUTING SYSTEMS >INTL.ED.<
INTRO.TO COMPUTING SYSTEMS >INTL.ED.<
3rd Edition
ISBN: 9781260565911
Author: PATT
Publisher: MCG
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Chapter 3, Problem 36E

a.

Explanation of Solution

Truth table for 1-bit comparator:

Given:

G=1 if A>B, "0" otherwiseE=1 if A==B, "0" otheriwseL=1 if A<B, "0" otherwise

The truth table for 1-bit comparator is as follows,

ABGEL
00010
01001
10100
11010

b.

Explanation of Solution

Implementation of “G”, “E”, and “L”:

Implementation of “G”:

  • “G” can be implemented by taking the Boolean expression from the truth table where “G” has the output “1”.
  • The Boolean expression for “G” is “G=A.B¯”.
  • The implementation of “G” is as follows,

Implementation of “E”:

  • “E” can be implemented by taking the Boolean expression from the truth table where “E” has the output “1”.
  • The Boolean expression for “E” is “E=A¯

c.

Explanation of Solution

Four-bit equality checker:

  • To build four-bit equality checker, four 1-bit comparators are used.
  • The four-bit equality comparator is constructed as follows,

  • The output line “E” of every 1-bit comparator is connected with the input line of AND gate, because it produces the output EQUAL “1”, when “4” inputs of “A” and “B” are equal.
  • The output EQUAL produces “0” for the rebuking inputs of “A” and “B”.
  • Example:
    • Consider the four-bit numbers “1011” and “1011” and are given to the above circuit.
    • 1-bit from both “A” and “B” are taken by each comparator and the output is generated as follows,
      • A0” is the first bit from “A” and its value is “1”. “B0” is the first bit from “B” and its value is “1”. Both bits are equal and the output of “E” for the first comparator is “1”.
      • A1” is the second bit from “A” and its value is “1”

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INTRO.TO COMPUTING SYSTEMS >INTL.ED.<

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