Computer organization, design, and architecture by Sajjan G Shiva

By Sajjan G Shiva

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63 62 (52 bits) Mantissa . 52 51 (Bit index) . 0 NaNs and infinities are represented with exponent being all 1s (2047). For normalized numbers the exponent bias is þ1023 (so e is Exp À1023). For denormalized numbers the exponent is À1022 (the minimum exponent for a normalized number is not À1023 because normalized numbers have a leading 1 digit before the binary point and denormalized numbers do not). As earlier, both infinity and zero are signed. Note that 1. The smallest nonzero positive and largest nonzero negative numbers (represented by the denormalized value with all 0s in the Exp field and the binary value 1 in the fraction field) are Æ2À1074 % Æ5 Â 10À324 : 2.

How many megabytes are in a gigabyte memory? Express your answers as powers of 2. 9 Look up the details on the following popular benchmarks: Whetstone, Dhrystone, PERFECT, SLALOM. 10 What is a ‘‘Virtual Machine’’ architecture? ß 2007 by Taylor & Francis Group, LLC. CHAPTER 2 Number Systems and Codes As mentioned earlier, the elements in the discrete data representation correspond to discrete voltage levels or current magnitudes in the digital system hardware. If the digital system is required to manipulate only numeric data, for instance, it will be best to use 10 voltage levels, with each level corresponding to a decimal digit.

That is 11011010100000000000000. 4. The exponent is 6, the bias is 127 and hence the exponent field will be 6 þ 127 ¼ 133. In binary, this is 10000101. The representation is thus: Sign (8 bits) bit Exponent (23 bits) Mantissa 11000010111011010100000000000000 . 31 30 . 23 22 . 625 Some additional representations are shown below. 00000000000000000000001 ¼ 2(À149) (Smallest positive value) ß 2007 by Taylor & Francis Group, LLC. 2 Double Precision Double precision format is essentially the same except that the fields are wider: Sign bit (11 bits) Exponent .

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