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Assignment 7 Zhiyong Yang CS 10051 Instructor: Dean Zeller

Assignment 7 Zhiyong Yang CS 10051 Instructor: Dean Zeller. Q.1 00011001 = 25 11111101 = 253 11010101 = 213 00111010 = 58 001010011000 = 664 111011101110 = 3822. Diagram: 2048 1024 512 256 128 64 32 16 8 4 2 1 1 1 0 1 1 1 0 1 1 1 0

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Assignment 7 Zhiyong Yang CS 10051 Instructor: Dean Zeller

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  1. Assignment 7 Zhiyong Yang CS 10051 Instructor: Dean Zeller Q.1 00011001 = 25 11111101 = 253 11010101 = 213 00111010 = 58 001010011000 = 664 111011101110 = 3822 • Diagram: • 2048 1024 512 256 128 64 32 16 8 4 2 1 • 1 1 0 1 1 1 0 1 1 1 0 • = 1x2048 + 1x1024 + 1x512 + • 1x128 + 1x64 + 1x32 + • 1x8 + 1x4 + 1x2 • = 3822

  2. Q.2 29 = 00011101 78 = 01001110 250 = 11111010 315 = 000100111011 1000 = 001111101000 2049 = 100000000001 Diagram: 2049/2 = 1024 R = 1 1024/2 = 512 R = 0 512/2 = 256 R = 0 256/2 = 128 R = 0 128/2 = 64 R = 0 64/2 = 32 R = 0 32/2 = 16 R = 0 16/2 = 8 R = 0 8/2 = 4 R = 0 4/2 = 2 R = 0 2/2 = 1 R = 0 1/2 = 0 R = 1 Thus 2049 = 1000000000001

  3. Q.3 10101100 + 1001010 11110010 10111011 + 1110010 100101101 10101000 + 1010111 11111111 11000000 + 1111111 100111111 100010001010 + 1111011100 110001100110 100111001000 + 101101000101 1010100001101 Q.4 10101000 - 1011111 01001001 10111011 - 1001001 01110010 10110110 - 1011001 01011101 111111001000 - 101111000101 010000000011 11101011 - 11011110 00001101 101110101010 - 1111011100 11111001110

  4. Q.5 00001101 x 111 01011011 00011010 x 1101 101010010 Example: 00011010 x 1101 11010 00000 11010 +11010 101010010 00100010 x 10010 1001100100 00101011 x 11101 10011011111 00101001 x 10101 1101011101 10100011 x 11111 1001110111101

  5. Assignment 8 Zhiyong Yang CS 10051 Instructor: Dean Zeller 001001 110)110110 R = 0 001101100 100)110110000 R = 0 Q.1 000110100 1000)110110000 R = 0 00100001 101) 10101001 R = 100 011011000 10)110110000 10 10 10 11 10 10 10 0 R = 0 00010110 111)10011011 R = 1 000011011 10000)110110000 R = 0 00010101 1010)11010110 R = 100

  6. Q.2 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 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

  7. Q.3 0.00390625 x 2 = 0.00781250 R = 0 0.00781250 x 2 = 0.01562500 R = 0 0.01562500 x 2 = 0.03125000 R = 0 0.03125000 x 2 = 0.06250000 R = 0 0.06250000 x 2 = 0.12500000 R = 0 0.12500000 x 2 = 0.25000000 R = 0 0.25000000 x 2 = 0.50000000 R = 0 0.50000000 x 2 = 1.00000000 R = 1 0.00000000 x 2 = 0 R = 0 Thus 0.00390625 = 0.00000001 1/5 = 0.0011 1/7 = 0.001 1/10 = 0.00011 1/20 = 0.000011 3/8 = 0.011 1/14 = 0.0001 4/11 = 0.0101110100 3/16 = 0.0011 3/32 = 0.00001 3/64 = 0.000001 5/16 = 0.0101 61/64 = 0.111101 0.2 = 0.0011 0.3 = 0.01001 0.7125 = 0.10110110 0.796875 = 0.110011 0.00390625 = 0.00000001

  8. Q.4 0.0525 = 0.000011010111000010100011 0.995 x 2 = 1.990 R = 1 0.990 x 2 = 1.980 R = 1 0.980 x 2 = 1.960 R = 1 0.960 x 2 = 1.920 R = 1 0.920 x 2 = 1.840 R = 1 0.840 x 2 = 1.680 R = 1 0.680 x 2 = 1.360 R = 1 0.360 x 2 = 0.720 R = 0 0.720 x 2 = 1.440 R = 1 0.440 x 2 = 0.880 R = 0 0.880 x 2 = 1.760 R = 1 0.760 x 2 = 1.520 R = 1 0.520 x 2 = 1.040 R = 1 0.040 x 2 = 0.080 R = 0 0.080 x 2 = 0.160 R = 0 0.160 x 2 = 0.320 R = 0 0.320 x 2 = 0.640 R = 0 0.640 x 2 = 1.280 R = 1 0.280 x 2 = 0.560 R = 0 0.560 x 2 = 1.120 R = 1 0.120 x 2 = 0.240 R = 0 0.240 x 2 = 0.480 R = 0 0.480 x 2 = 0.960 R = 0 0.960 0.995 = 0.11111110101110000101000

  9. 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 Example: 0.53 x 2 = 1.06 R = 1 0.06 x 2 = 0.12 R = 0 0.12 x 2 = 0.24 R = 0 0.24 x 2 = 0.48 R = 0 0.48 x 2 = 0.96 R = 0 0.96 x 2 = 1.92 R = 1 0.92 x 2 = 1.84 R = 1 0.84 x 2 = 1.68 R = 1 ~ ~ ~ ~ ~ ~ ~

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