Computer Organization EECE 6278
University of Memphis
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This 1 page Class Notes was uploaded by Denis Gulgowski on Friday October 23, 2015. The Class Notes belongs to EECE 6278 at University of Memphis taught by Staff in Fall. Since its upload, it has received 23 views. For similar materials see /class/228458/eece-6278-university-of-memphis in ELECTRICAL AND COMPUTER ENGINEERING at University of Memphis.
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Date Created: 10/23/15
EECE 62784278 Handout2 Spring 03 Floating Point Numbers Intro du ction are cover a to separate number its precision In order to accomplish this point uses scientific notation number mantissa lOAexponent 8 1234000 1234 X 10A6 005 5 X 10A3 The number of digits in the mantissa re ects the precision and the size of exponent controls the range IEEE Floating Point Standard Originally computer manufacturers had their own standard but now most adhere to the IEEE standard which was released in the 198039s I Three formats for numbers I Single precision 32 bits I Double precision 64 bits I Extended precision 80 bits Number is divided into the following three parts I Sign bit for overall number 0 for positive and l for negative I Exponent I Single Precision 8 bits using excess 127 notation I Double Precision 11 bits using excess 1023 notation I Fraction Uses base 2 and normalized to lie between 1 and slightly less than 2 The leading l and the quotbinaryquot point are implied I Single Precision 23 bits I Double Precision 52 bits Denormalized numbers are used to represent small numbers ie the range 0 to 1 These numbers have an exponent of 0 and an implied 0 for the fraction piece Numeric Ranges I Single Precision approx lOA38 to 10A38 lOA45 for denormalized I Double Precision approx lOA308 to 10M308 GOA324 for denormalized Special Values I Zero There are two zeros positive and negative I Infinity exponent of all 139s and and a fraction of 0 I NAN Not a number produced by dividing 0 by 0 or infinity by infinity exponent of all 139s and any nonzero fraction Conversion Examples Converting from decimal to IEEE oating point