Assignment 7

Zhiyong YangCS 10051Instructor: Dean Zeller

Q.1

00011001 = 2511111101 = 25311010101 = 21300111010 = 58001010011000 = 664111011101110 = 3822

Diagram:

2048 1024 512 256 128 64 32 16 8 4 2 1

1 1 1 0 1 1 1 0 1 1 1 0

= 1x2048 + 1x1024 + 1x512 + 1x128 + 1x64 + 1x32 + 1x8 + 1x4 + 1x2= 3822

Q.2

29 = 0001110178 = 01001110250 = 11111010315 = 0001001110111000 = 0011111010002049 = 100000000001

Diagram:

2049/2 = 1024 R = 11024/2 = 512 R = 0512/2 = 256 R = 0256/2 = 128 R = 0128/2 = 64 R = 064/2 = 32 R = 032/2 = 16 R = 016/2 = 8 R = 08/2 = 4 R = 04/2 = 2 R = 02/2 = 1 R = 01/2 = 0 R = 1

Thus2049 = 1000000000001

Q.3 10101100+ 1001010 11110010

10111011+ 1110010100101101

10101000+ 1010111 11111111

11000000+ 1111111100111111

100010001010+ 1111011100110001100110

100111001000+ 101101000101 1010100001101

Q.4

10111011- 1001001 01110010

10110110- 1011001 01011101

10101000- 1011111 01001001

11101011- 11011110 00001101

101110101010- 1111011100 11111001110

111111001000- 101111000101 010000000011

Q.500001101x 11101011011

00011010x 1101101010010

00101001x 101011101011101

00100010x 100101001100100

00101011x 1110110011011111

10100011x 111111001110111101

Example:

00011010x 1101 11010 00000 11010+11010101010010

Assignment 8

Zhiyong YangCS 10051Instructor: Dean Zeller

Q.1

01101100010)110110000 10 10 10 11 10 10 10 0 R = 0

001001110)110110

R = 0

001101100100)110110000

R = 0

00100001101) 10101001

R = 100

0001101001000)110110000

R = 0

00001101110000)110110000

R = 0

00010110111)10011011

R = 1

000101011010)11010110

R = 100

Q.2

0.01101000 = 0.40625

0.00000001 = 0.00390625

0.10000100 = 0.515625

0.10101010 = 0.6640625

0.11111111 = 0.99609375

0.10000100 = 0.515625

0.00000011 = 0.01171875

0.01010100 = 0.328125

½ ¼ 1/8 1/16 1/32 1/64 1/128 1/256. 0 1 0 1 0 1 0 1

= ¼ + 1/16 + 1/64 + 1/256= 0.33203125

Q.3

1/5 = 0.00111/7 = 0.0011/10 = 0.000111/20 = 0.0000113/8 = 0.0111/14 = 0.00014/11 = 0.01011101003/16 = 0.00113/32 = 0.000013/64 = 0.0000015/16 = 0.010161/64 = 0.1111010.2 = 0.00110.3 = 0.010010.7125 = 0.101101100.796875 = 0.1100110.00390625 = 0.00000001

0.00390625 x 2 = 0.00781250 R = 00.00781250 x 2 = 0.01562500 R = 00.01562500 x 2 = 0.03125000 R = 00.03125000 x 2 = 0.06250000 R = 00.06250000 x 2 = 0.12500000 R = 00.12500000 x 2 = 0.25000000 R = 00.25000000 x 2 = 0.50000000 R = 00.50000000 x 2 = 1.00000000 R = 10.00000000 x 2 = 0 R = 0

Thus 0.00390625 = 0.00000001

Q.4

0.0525 = 0.000011010111000010100011

0.995 x 2 = 1.990 R = 10.990 x 2 = 1.980 R = 10.980 x 2 = 1.960 R = 10.960 x 2 = 1.920 R = 10.920 x 2 = 1.840 R = 10.840 x 2 = 1.680 R = 10.680 x 2 = 1.360 R = 10.360 x 2 = 0.720 R = 00.720 x 2 = 1.440 R = 10.440 x 2 = 0.880 R = 00.880 x 2 = 1.760 R = 10.760 x 2 = 1.520 R = 10.520 x 2 = 1.040 R = 10.040 x 2 = 0.080 R = 00.080 x 2 = 0.160 R = 00.160 x 2 = 0.320 R = 00.320 x 2 = 0.640 R = 00.640 x 2 = 1.280 R = 10.280 x 2 = 0.560 R = 0

0.560 x 2 = 1.120 R = 10.120 x 2 = 0.240 R = 00.240 x 2 = 0.480 R = 00.480 x 2 = 0.960 R = 00.960

0.995 = 0.11111110101110000101000

Q.5

0.53 = 0.10000111

0.42 = 0.01101011

0.10 = 0.00011001

0.75 = 0.11000000

0.73 = 0.10111010

0.25 = 0.10000000

0.99 = 0.11111101

0.01 = 0.00000010

0.51 = 0.10000001

0.24 = 0.00111101

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~ Example:

0.53 x 2 = 1.06 R = 10.06 x 2 = 0.12 R = 00.12 x 2 = 0.24 R = 00.24 x 2 = 0.48 R = 00.48 x 2 = 0.96 R = 00.96 x 2 = 1.92 R = 10.92 x 2 = 1.84 R = 10.84 x 2 = 1.68 R = 1