1 for the normalized floating point system 2557 a what is...

'1. For the normalized floating point system (2,5,~5,7) A. What is the rounding unit? Estimate the absolute error A(z)| and relative error error by chopping and rounding (use the results in the Theorem) . C. Use the result in Part B to estimate the errors of the floating point representation o = = 105.'

Transcript

00:01 In this question it is given that for the normalized floating point system, floating point system is 2 .5 comma minus 5 .7.

00:12 This is given to us.

00:13 We have to find the rounding unit in the first part.

00:16 In the first part, we have to find the rounded unit.

00:18 We have the value of x that is equals to 105.

00:21 So a number representation system, it is given by 2 power 5 multiplied by b0, plus v1 divided by 2 plus b1 divided by 4.

00:30 This is given by this so we have where b note is equivalent to 1 and 0 it is less than equals to b1 and b2 is less than equals to 1 so here this will be the value so we have minus 5 this is less than e and this is less than 7 so what we are having we having x equals to 105 here so x here can be written as 2 power 5 and this can be written as b0 that is 1 plus 0 0 divided by this is 2 plus 1 divided by 2 squared plus 1 divided by 2 cube plus 1 divided by 2 q this can be written as 0 divided by 2 power 4 plus 1 divided by 2 power 5 so from here we can write this value as so we get the floating point representation f x as 2 power 5 this is 1 plus 1 1 divided by 2 power 5 solving this it is 1 .01 multiplied by 2 power 5 so solving this out we get this value as 1 .01 divided multiplied by 2 power 5 so what is the rounding value so here the rounding value of f x that is equivalent to what this is 1 .1 multiplied by 2 power 5 this will be the rounding and this will be the required answer for this particular given question of the a part now we will solve the b part in which we have to calculate the absolute error absolute error now this is given by x minus f of x x is 105 so this is equals to 105 minus f of x is this is 32 .32...

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