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[Page 1245]

Answers to Self-Review Exercises

D.1

10, 2, 8, 16.

D.2

Fewer.

D.3

False. Hexadecimal does this.

D.4

Hexadecimal.

D.5

False. The highest digit in any base is one less than the base.

D.6

False. The lowest digit in any base is zero.

D.7

1 (the base raised to the zero power).

D.8

The base of the number system.

D.9

Fill in the missing values in this chart of positional values for the rightmost four positions in each of the indicated number systems:

decimal

1000

100

10

1

hexadecimal

4096

256

16

1

binary

8

4

2

1

octal

512

64

8

1


D.10

Octal 6530; Hexadecimal D58.

D.11

Binary 1111 1010 1100 1110.

D.12

Binary 111 011 001 110.

D.13

Binary 0 100 111 111 101 100; Octal 47754.

D.14

Decimal 2+4+8+32+64=110.

D.15

Decimal 7+1*8+3*64=7+8+192=207.

D.16

Decimal 4+13*16+15*256+14*4096=61396.

D.17

Decimal 177

to binary:

256 128 64 32 16 8 4 2 1
128 64 32 16 8 4 2 1
(1*128)+(0*64)+(1*32)+(1*16)+(0*8)+(0*4)+(0*2)+(1*1)
10110001

to octal:

512 64 8 1
64 8 1
(2*64)+(6*8)+(1*1)
261

to hexadecimal:

256 16 1
16 1
(11*16)+(1*1)
(B*16)+(1*1)
B1

D.18

Binary:


[Page 1246]
512 256 128 64 32 16 8 4 2 1 256 128 64 32 16 8 4 2 1 (1*256)+(1*128)+(0*64)+(1*32)+(0*16)+(0*8)+(0*4)+(0*2)+(1*1) 110100001

One's complement: 001011110

Two's complement: 001011111

Check: Original binary number + its two's complement

110100001
001011111
---------
000000000

D.19

Zero.


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