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# Show that the hexadecimal expansion of a positive integer ISBN: 9780073383095 37

## Solution for problem 13E Chapter 4.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 13E

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

Step-by-Step Solution:
Step 1 of 3

Step-1: To Show that the Hexadecimal Expansion of a positive integer can be Obtained by first

Obtaining its Binary Equivalent and grouping the obtained Binary Equivalent to

Group of 4 bits, then obtaining the hexadecimal equivalent of each group.

Step-2:  Consider a positive Integer 56, first we need to obtain its binary equivalent. The Binary

Equivalent of 56 is 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)2

Step-4: Now Converting Binary Expansion to it’s equivalent Hexadecimal expansion.

Given Binary Expansion = (111000)2

Step-5:  From the Least Significant Bit (LSB) that corresponds to the Last Bit, 4 bits are

Grouped, Grouping 4 bits as shown below.

11 1000

Step-6:  In the Grouping, the first group  as only 1 bit and hence add...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383095

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