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# Show that the octal expansion of a positive integer can be ISBN: 9780073383095 37

## Solution for problem 15E Chapter 4.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 15E

Show that the octal expansion of a positive integer can be obtained from its binary expansion by grouping together blocks of three binary digits, adding initial zeros if necessary, and translating each block of three binary digits into a single octal digit.

Step-by-Step Solution:

Solution Step 1To Show that the octal expansion of a positive integer can be obtained by first converting positive integer into its binary equivalent and then grouping binary digits into a group of 3 from the least significant bit( LSB).Step 2 Consider a positive integer 56, first we need to obtain its binary equivalent.The binary equivalent of 56 can be obtained as shown below remainder = 0 remainder = 0 remainder = 0 remainder = 1 remainder = 1 remainder = 1.Step 3 The Binary Equivalent of 56 would be the remainders from bottom of Step-2 56 = ( 111000)2Step 4 Now Converting Binary Expansion to it’s equivalent Octal expansion. Given Binary Expansion = (111000)2Step 5 From the Least Significant Bit (LSB) that corresponds to the Last Bit, 3 bits are Grouped, Grouping 3 bits as shown below. 111 000

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##### ISBN: 9780073383095

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