Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 12 - Section 12.4 - Minimization of Circuits - Exercises - Page 842: 19

Answer

Defining rows and columns of a 4 × 16 map for Boolean functions in six variables using the Gray codes 1111, 1110, 1010, 1011, 1001, 1000, 0000, 0001, 0011, 0010, 0110, 0111, 0101, 0100, 1100, 1101 to label the columns and 11, 10, 00, 01 to label the rows need to be considered adjacent so that cells that represent minterms that differ in exactly one literal are considered adjacent

Work Step by Step

--Rows 1 and 4 are considered adjacent. --The pairs of columns considered adjacent are: - columns 1 and 4, - 1 and 12, - 1 and 16, -2 and 11, - 2 and 15, -3 and 6, - 3 and 10, -4 and 9, -5 and 8, - 5 and 16, -6 and 15, - 7 and 10, -7 and 14, -8 and 13, - 9 and 12, - 11 and 14, - 13 and 16.
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