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CS 230 (51)
Lecture

# CS 230 tutorial3_solutions.pdf

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School
Department
Computer Science
Course
CS 230
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Semester
Fall

Description
CS230 Fall 2012 - Tutorial 3 Solutions Monday, Oct 1, 2012 1 Floating Point Representation Steps skipped in later sections can be veriﬁed at http://babbage:cs:qc:cun y:edu/IEEE-754/ for converting to/from IEEE-754, and http://www:exp loringbinary:com/binary-converter/ for working with binary num- bers with fractional parts. 1. (a) 41.3267 41 / 2 = 20 R 1 20 / 2 = 10 R 0 10 / 2 = 5 R 0 5 / 2 = 2 R 1 2 / 2 = 1 R 0 1 / 2 = 0 R 1 ! 41 = 1010012 0.3267 ▯ 2 = 0.6534 0.6534 ▯ 2 = 1.3068 0.3068 ▯ 2 = 0.6136 0.6136 ▯ 2 = 1.2272 0.2272 ▯ 2 = 0.4544 0.4544 ▯ 2 = 0.9088 0.9088 ▯ 2 = 1.8176 0.8176 ▯ 2 = 1.6352 0.6352 ▯ 2 = 1.2704 0.2704 ▯ 2 = 0.5408 0.5408 ▯ 2 = 1.0816 0.0816 ▯ 2 = 0.1632 0.1632 ▯ 2 = 0.3264 0.3264 ▯ 2 = 0.6528 0.6528 ▯ 2 = 1.3056 1 0.3056 ▯ 2 = 0.6112 0.6112 ▯ 2 = 1.2224 0.2224 ▯ 2 = 0.4448 ! .3267 = .010100111010001010... 2 41.3267 = 101001.010100111010001010 5 = 1.01001010100111010001010 ▯ 2 Sign = 0 (+) Exponent = 5 + bias = 5 + 127 = 132 = 10000100 Signiﬁcand = 01001010100111010001010 41.3267 = 0 10000100 01001010100111010001010 (b) -987.2 987 / 2 = 493 R 1 493 / 2 = 246 R 1 246 / 2 = 123 R 0 123 / 2 = 61 R 1 61 / 2 = 30 R 1 30 / 2 = 15 R 0 15 / 2 = 7 R 1 7 / 2 = 3 R 1 3 / 2 = 1 R 1 1 / 2 = 0 R 1 ! 987 = 1111011011 2 0.200000 ▯ 2 = 0.400000 0.400000 ▯ 2 = 0.800000 0.800000 ▯ 2 = 1.600000 0.600000 ▯ 2 = 1.200000 0.200000 ▯ 2 = 0.400000 ... repeats ... ! 0.2 = 0.0011 0011 0011 .2. 987.2 = 1111011011.00110011001100 9 = 1.11101101100110011001100 ▯ 2 Sign = 1 (-) Exponent = 9 + bias = 9 + 127 = 136 = 10001000 Signiﬁcand = 11101101100110011001100 -987.2 = 1 10001000 11101101100110011001100 (c) 6 2 6 / 2 = 3 R 0 3 / 2 = 1 R 1 1 / 2 = 0 R 1 ! 6 = 1102 0.0 ! 0.0 = 0.02 2 6.0 = 110.0 = 1.100 ▯ 2 Sign = 0 (+) Exponent = 2 + bias = 2 + 127 = 129 = 10000001 Signiﬁcand = 10000000000000000000000 6.0 = 0 10000001 10000000000000000000000 (d) 0.0000048 0 = 02 0.0000048 ▯ 2 = 0.0000096 0.0000096 ▯ 2 = 0.0000192 0.0000192 ▯ 2 = 0.0000384 0.0000384 ▯ 2 = 0.0000768 0.0000768 ▯ 2 = 0.0001536 0.0001536 ▯ 2 = 0.0003072 0.0003072 ▯ 2 = 0.0006144 0.0006144 ▯ 2 = 0.0012288 0.0012288 ▯ 2 = 0.0024576 0.0024576 ▯ 2 = 0.0049152 0.0049152 ▯ 2 = 0.0098304 0.0098304 ▯ 2 = 0.0196608 0.0196608 ▯ 2 = 0.0393216 0.0393216 ▯ 2 = 0.0786432 0.0786432 ▯ 2 = 0.1572864 0.1572864 ▯ 2 = 0.3145728 0.3145728 ▯ 2 = 0.6291456 0.6291456 ▯ 2 = 1.2582912 0.2582912 ▯ 2 = 0.5165824 0.5165824 ▯ 2 = 1.0331648 0.0331648 ▯ 2 = 0.0663296 0.0663296 ▯ 2 = 0.1326592 0.1326592 ▯ 2 = 0.2653184 3 0.2653184 ▯ 2 = 0.5306368 0.5306368 ▯ 2 = 1.0612736 0.0612736 ▯ 2 = 0.1225472 0.1225472 ▯ 2 = 0.2450944 0.2450944 ▯ 2 = 0.4901888 0.4901888 ▯ 2 = 0.9803776 0.9803776 ▯ 2 = 1.9607552 0.9607552 ▯ 2 = 1.9215104 0.9215104 ▯ 2 = 1.8430208 0.8430208 ▯ 2 = 1.6860416 0.6860416 ▯ 2 = 1.3720832 0.3720832 ▯ 2 = 0.7441664 0.7441664 ▯ 2 = 1.4883328 0.4883328 ▯ 2 = 0.9766656 0.9766656 ▯ 2 = 1.9533312 0.9533312 ▯ 2 = 1.9066624 0.9066624 ▯ 2 = 1.8133248 0.8133248 ▯ 2 = 1.6266496 ! 0.0000048 = 0.00000000000000000101000010000111110101111 2 ▯18 = 1.01000010000111110101111 ▯ 2 Sign = 0 (+) Exponent = -18 + bias = -18 + 127 = 109 = 01101101
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