Chapter 2, Problem 5E

Explanation of Solution

To represent “7” using “5” bits:

• Using “5” bits, one can mean “$2^5$”, which means “32” unique integers.
• If those integers are numbers from “0” to “31, then one can mean the digits from “0” to “4” with bits.
• The “32” possible bit configurations is as follows,

16	8	4	2	1	Integer
0	0	0	0	0	0
0	0	0	0	1	1
0	0	0	1	0	2
0	0	0	1	1	3
0	0	1	0	0	4
0	0	1	0	1	5
0	0	1	1	0	6
0	0	1	1	1	7
0	1	0	0	0	8
0	1	0	0	1	9
0	1	0	1	0	10
0	1	0	1	1	11
0	1	1	0	0	12
0	1	1	0	1	13
0	1	1	1	0	14
0	1	1	1	1	15
1	0	0	0	0	16
1	0	0	0	1	17
1	0	0	1	0	18
1	0	0	1	1	19
1	0	1	0	0	20
1	0	1	0	1	21
1	0	1	1	0	22
1	0	1	1	1	23
1	1	0	0	0	24
1	1	0	0	1	25
1	1	0	1	0	26
1	1	0	1	1	27
1	1	1	0	0	28
1	1	1	0	1	29
1	1	1	1	0	30
1	1	1	1	1	31

• From the above table, the configuration of “5” bits that represent “7” is “00111”