Digital Design – Solution Manual. M. Mano. M.D. Ciletti, Copyright 2007, All rights reserved.
4
27
10
= 11011
2
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
10
# .0101
2
= .25 + .0625 = .3125
27.315 # 11011.0101
2
(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
10
# .10101010
2
= .5 + .125 + .0313 + ..0078 = .6641
10
.101010102 = .1010_1010
2
= .AA
16
= 10/16 + 10/256 = .6641
10
(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
(c) 25,000,000 (d) 00,000,000
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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