Read e-book online Computer organization, design, and architecture PDF

By Sajjan G Shiva

ISBN-10: 0849304164

ISBN-13: 9780849304163

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Example text

6 FLOATING-POINT NUMBERS Fixed-point representation is convenient for representing numbers with bounded orders of magnitude. For instance, in a digital computer that uses 32 bits to represent numbers, the range of integers that can be used is limited to ± (231À1), which is approximately ±1012. In scientific computing environments, a wider range of numbers may be needed, and floating-point representation may be used. 56) 3 106 The last three forms are valid floating-point representations. Among them, the first two forms are preferred; however, since with these forms there is no need to represent the integer portion of the mantissa, which is 0.

Because the 10s complement system displays the same characteristics as the 2s complement system, it will not be discussed here. 32 (a) The 2s complement of (01010)2 is 25 À (01010) ¼ 100000 À 01010 ¼ 10110: Here, n ¼ 5 and r ¼ 2. 0010)2 is 21 À (0:0010) ¼ 10:0000 À 0:0010 ¼ 1:1110: Here, n ¼ 1 and r ¼ 2. (c) The 10s complement of (4887)10 is 102 À 4887 ¼ 5113: Here, n ¼ 4 and r ¼ 10. 87)10 is 102 À 48:87 ¼ 51:13: Here, n ¼ 2 and r ¼ 10. 32, there are two other methods for radix complement of a number.

Are digits such that 0 an is the most significant digit (MSD) aÀm is the least significant digit (LSD) ß 2007 by Taylor & Francis Group, LLC. 1 Number Systems Decimal r 5 10 Binary r52 Ternary r53 Quaternary r54 Octal r58 Hexadecimal r 5 16 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 10001 10010 10011 10100 0 1 2 10 11 12 20 21 22 100 101 102 110 111 112 120 121 122 200 201 202 0 1 2 3 10 11 12 13 20 21 22 23 30 31 32 33 100 101 102 103 110 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 22 23 24 0 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 The polynomial representation of the earlier number is N¼ n X ai r i : (2:2) i¼Àm There are n þ 1 integer digits and m fraction digits in the number shown earlier.

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Computer organization, design, and architecture by Sajjan G Shiva


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