数字设计第4版答案DigitalDesignsolutionbyMORRISMANO

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SOLUTIONS MANUAL

DIGITAL DESIGN

FOURTH EDITION

M. MORRIS MANO

California State University, Los Angeles

MICHAEL D. CILETTI

University of Colorado, Colorado Springs

rev 01/21/2007

from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording,

or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

= 11011

Integer Fraction Coefficient

.315 x 2 = 0 + .630 a

-1

= 0

.630 x 2 = 1 + .26 a

-2

= 1

.26 x 2 = 0 + .52 a

-3

= 0

.52 x 2 = 1 + .04 a

-4

= 1

.315

# .0101

= .25 + .0625 = .3125

27.315 # 11011.0101

(b) 2/3 # .6666666667

Integer Fraction Coefficient

.6666_6666_67 x 2 = 1 + .3333_3333_34 a

-1

= 1

.3333333334 x 2 = 0 + .6666666668 a

-2

= 0

.6666666668 x 2 = 1 + .3333333336 a

-3

= 1

.3333333336 x 2 = 0 + .6666666672 a

-4

= 0

.6666666672 x 2 = 1 + .3333333344 a

-5

= 1

.3333333344 x 2 = 0 + .6666666688 a

-6

= 0

.6666666688 x 2 = 1 + .3333333376 a

-7

= 1

.3333333376 x 2 = 0 + .6666666752 a

-8

= 0

.6666666667

# .10101010

= .5 + .125 + .0313 + ..0078 = .6641

.101010102 = .1010_1010

= .AA

= 10/16 + 10/256 = .6641

(Same as (b)).

1.14 (a) 1000_0000 (b) 0000_0000 (c) 1101_1010

1s comp: 0111_1111 1s comp: 1111_1111 1s comp: 0010_0101

2s comp: 1000_0000 2s comp: 0000_0000 2s comp: 0010_0110

(d) 0111_0110 (e) 1000_0101 (f) 1111_1111

1s comp: 1000_1001 1s comp: 0111_1010 1s comp: 0000_0000

2s comp: 1000_1010 2s comp: 0111_1011 2s comp: 0000_0001

1.15 (a) 52,784,630 (b) 63,325,600

9s comp: 47,215,369 9s comp: 36,674,399

10s comp: 47,215,370 10s comp: 36,674,400

9s comp: 74,999,999 9s comp: 99,999,999

10s comp: 75,000,000 10s comp: 00,000,000

1.16 B2FA B2FA: 1011_0010_1111_1010

15s comp: 4D05 1s comp: 0100_1101_0000_0101

16s comp: 4D06 2s comp: 0100_1101_0000_0110 = 4D06

1.17 (a) 3409 o 03409 o96590 (9s comp) o 96591 (10s comp)

06428 – 03409 = 06428 + 96591 = 03019

(b) 1800 o 01800 o 98199 (9s comp) o 98200 (10 comp)

125 – 1800 = 00125 + 98200 = 98325 (negative)

Magnitude: 1675

Result: 125 – 1800 = 1675

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or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

2043 – 6152 = 02043 + 93848 = 95891 (Negative)

Magnitude: 4109

Result: 2043 – 6152 = -4109

(d) 745 o 00745 o 99254 (9s comp) o 99255 (10s comp)

1631 -745 = 01631 + 99255 = 0886 (Positive)

Result: 1631 – 745 = 886

1.18 Note: Consider sign extension with 2s complement arithmetic.

(a) 10001 (b) 100011

1s comp: 01110 1s comp: 1011100 with sign extension

2s comp: 01111 2s comp: 1011101

10011

0100010

Diff: 00010 1111111 sign bit indicates that the result is negative

0000001 2s complement

-000001 result

1s comp: 1010111 1s comp: 1101010 with sign extension

2s comp: 1011000 2s comp: 1101011

001001

110000

Diff: 1100001 (negative) 0011011 sign bit indicates that the result is positive

0011111 (2s comp) Check: 48 -21 = 27

-011111 (diff is -31)

1.19 +9286 o 009286; +801 o 000801; -9286 o 990714; -801 o 999199

(a) (+9286) + (_801) = 009286 + 000801 = 010087

(b) (+9286) + (-801) = 009286 + 999199 = 008485

(d) (-9286) + (-801) = 990714 + 999199 = 989913

1.20 +49 o 0_110001 (Needs leading zero indicate + value); +29 o 0_011101 (Leading 0 indicates + value)

-49 o 1_001111; -29 o 1_100011

(a) (+29) + (-49) = 0_011101 + 1_001111 = 1_101100 (1 indicates negative value.)

Magnitude = 0_010100; Result (+29) + (-49) = -20

(b) (-29) + (+49) = 1_100011 + 0_110001 = 0_010100 (0 indicates positive value)

(-29) + (+49) = +20

(-29) + (-49) = 11_100011 + 11_001111 = 10_110010 (1 indicates negative result)

Magnitude: 1_001110 = 78

Result: (-29) + (-49) = -78

from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording,

or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

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