Discrete Mathematics and Its Applications, Seventh Edition

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

Chapter 4 - Section 4.2 - Integer Representations and Algorithms - Exercises - Page 255: 22

Answer

a) Sum of (112)x_{y}3 = 35 product of (210)x_{y}3 = 294 35 into base 3 =(1022)x_{y}3 294 into base 3=(101220)x_{y}3

Work Step by Step

(112)x_{y}3 =1\times 3x^{y}2+1\times3x^{y}1+2\times3x^{y}0 =14 (210)x_{y}3 =2\times3x^{y}2+1\times3x^{y}1+0\times3x^{y}0 =21 sum=(112)x_{y}3+(210)x_{y}3 =35 product=(112)x_{y}3\times(210x_{y}3)=294 35 into base 3: 35 =3\times11+2 11 =3\times3+2 3 =3\times1+0 1 =3\times0+1 Base is (1022)x_{y}3 294 into base 3 294 =3\times98+0 98 =3\times32+2 32 =3\times10+2 10 =3\times3+1 3 =3\times1+0 1 =3\times0+1 Base is (101220)x_{y}3
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