MTH510-Assignment1 - MTH 501/510 Assignment 1 Fall 2011...

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Unformatted text preview: MTH 501/510 Assignment # 1 Fall 2011 DUE (at the beginning of your Lab): the week of October 3 1. Recall that a floating-point number can be expressed as (- 1) s (1 + f ) 2 e where s , f and e are binary numbers. Recall that s is the sign indicator, f the mantissa (or fractional part), and e the exponent. In single-precision, the sign is 1 bit long, the mantissa is 23 bits long, and the exponent has 8 bits. What is the largest positive number in single-precision? 2. Express the decimal number 92 . 953125 as a binary fraction. 3. (a) Consider the function f ( x ) = x 4- 8 . 86 x. Use 3-digit rounding to compute f (2 . 76). What is the true percent relative error of your answer? (b) Find three 3-digit numbers such that x ( y + z ) 6 = xy + xz in 3-digit chopping. 4. (a) Find the MacLaurin series for e 2 x , and use it to estimate e . 1 with at least 4 signifi- cant figures (by hand). As part of your answer, add terms one at a time until an appropriate stopping criterion gives you an estimate of the desired accuracy.stopping criterion gives you an estimate of the desired accuracy....
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