# PS2 - Department of Electrical and Computer Engineering...

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Department of Electrical and Computer Engineering McGill University ECSE-322 Computer Engineering Fall 2010 Problem Set 2 1. Floating point representation: (a) Show the IEEE-754 binary representation of the number –0.75 (i.e.- ¾ in base 10) using the single precision format. (b) What floating point number (in IEEE-754 format) is represented by the following: 00110000001000000000000000000000 (c) Represent 0.125 x 16 5 and -0.125 x 16 -5 in USASI. (d) Identify how infinity, not a number, and 0 are represented in IEEE-754 and USASI. 2. Determine the maximum relative error and minimum and maximum values of a real number stored using the following floating point formats: (a) IEEE 754 (single precision), (b) USASI. We define the relative error in terms of the difference between the number and its representation as follows: Let rep(n) be the representation of n. The relative error is err(n) = |rep(n) – n| / |n|, where |n| represents the absolute value of n. (Note: This question is intended to be particularly challenging.)

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## This note was uploaded on 11/22/2010 for the course ECSE ECSE 322 taught by Professor Lowther during the Winter '04 term at McGill.

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PS2 - Department of Electrical and Computer Engineering...

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