Computer organization, design, and architecture - download pdf or read online

By Sajjan G Shiva

ISBN-10: 0849304164

ISBN-13: 9780849304163

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The largest finite positive and smallest finite negative numbers (represented by the value with 254 in the Exp field and all 1s in the fraction field) are Æ(2128 À 2104 ) % Æ3:4028235 Â 1038 : ß 2007 by Taylor & Francis Group, LLC. 625 using the IEEE 754 system: 1. ’’ 2. 101. 3. 110110101 3 26. This is a normalized floating-point number. The mantissa is the part at the right of the radix point, filled with 0s on the right to make it 23 bits. That is 11011010100000000000000. 4. The exponent is 6, the bias is 127 and hence the exponent field will be 6 þ 127 ¼ 133.

19 1011 ϫ 1100 Multiplicand Multiplier Multiplier bits (1011) ϫ 0 0000 0000 1011 1011 (1011) ϫ 0 (1011) ϫ 1 (1011) ϫ 1 10000100 PRODUCT In general, the product of two n-bit numbers is 2n bits long. 19, there are two nonzero bits in the multiplier, one in position 2 corresponding to 22 and the other in position 3 corresponding to 23. These 2 bits yield partial products whose values are simply that of the multiplicand shifted left 2 and 3 bits, respectively. The 0 bits in the multiplier contribute partial products with 0 values.

Let us now concentrate on the representation of floating-point numbers. The radix is implied by the number system used and hence is not shown explicitly in the representation. The mantissa and the exponent can be either positive or negative. Hence, the floating-point representation consists of the four components ß 2007 by Taylor & Francis Group, LLC. E, F, SE, and SF, where SE and SF are signs of the exponent and mantissa, respectively. The F is represented in the normalized form. True binary form is used in the representation of F (rather than any of the complement forms), and 1 bit is used to represent SF (0 for positive, 1 for negative).

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Computer organization, design, and architecture by Sajjan G Shiva

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