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+18 votes
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What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding?

$(113. + -111.) + 7.51$

$113. + (-111. + 7.51)$

  1. $9.51$ and $10.0$ respectively

  2. $10.0$ and $9.51$ respectively

  3. $9.51$ and $9.51$ respectively

  4. $10.0$ and $10.0$ respectively

asked in Digital Logic by Veteran (59.6k points)
edited by | 3k views
+2

Rewrite the smaller number such that its exponent matches with the exponent of the larger number.

4 Answers

+36 votes
Best answer

$(113. + -111.) = 1.13 \times 10^2 + -1.11 \times 10^2 = 0.02 \times 10^2 = 2.0 \times 10^0$

$2.0 \times 10^0 + 7.51 \times 10^0 = 9.51 \times 10^0 $

$(-111. + 7.51) = -1.11 \times 10^2 + 7.51 \times 10^0 = -1.1 \times 10^2 + 0.08 \times 10^2 = -1.03 \times 10^2 $

$113. + -1.03 \times 10^2 = 1.13 \times 10^2 + -1.03 \times 10^2 = 0.1 \times 10^2 = 10.0$

Reference: https://www.doc.ic.ac.uk/~eedwards/compsys/float/ 

answered by Veteran (359k points)
edited by
0
sir Is it not same thing as i had posted ?
+1
yes, I just gave an intermediate step :)
0
0
@Mithilesh I had told you not to edit others answer. Everyone won't be thinking like you.
0
there is difference in the answers rt?
+3

@Arjun sir Your ref. link is as always amazing.

0
+7.51∗10^0

why 7.51 is not rounded of to 8.00 in first part addition?
+2
Why it should be rounded? Rounding happens only when it is really required (as we loose precision) or when explicitly told. Also, this question is regarding fixed point arithmetic which is in GATE syllabus but not well covered in most books.
0

@Arjun Sir,

Here in the following step:
(−111.+7.51) = −1.11∗102+7.51∗100 = −1.1∗102+0.08∗102
The rule is to convert the exponent of smaller number as same as of the larger. But, here lager number is 7.51, whose exponent is zero. But, here you have converted the exponent of larger number to that of smaller's (i.e., exponent of 7.51 (larger) to that of -1.11 (smaller))?

Can you please explain it?

0
So floating point additions are not associative right?
0
Thanks for the link @Arjun sir thanks a lot ...really it was life saving ...
0
@Arjun sir link is wonderful
0
Thank you for explaination.
+11 votes
3 digit floating point arithmetic is used..
(113.+-111.)+7.51 = 2.00 + 7.51 = 9.51
113.+(-111.+7.51) = 113. + (-111. + 8.00) //rounding off to make compatible 7.51 and 111. with respect  3 digit floating point arithmetic
113. - 103. = 10.0
answered by Veteran (55.4k points)
0
First one is 9.51
Second evaluates to 10.49(let 10.4 as per 3digit )
As per option ..select A coz 10.4 can be rounded to 10 not to 9.51
0

10.51 ???
is it three-digit floating point arithmetic ???

+1

As it is  three-digit floating point arithmetic with rounding   

so Rounding off should be done on (111.+7.51) ie, 103.49 to 103. 

Though ans will remain same..But approach should be this,in my view.103.103.49 is rounded to 103.0

+2
to apply operation ur operand should be THREE FLOATING POINT ARITHMATIC ..
+1

Please explain the meaning "three-digit floating point arithmetic with rounding"

+2 votes
–2 votes

2nd part:  113. + (-111. + 7.51)

(-111. + 7.51) = - .111 x 10+ .751 x 10

= 10( - .111 x 102 + .751)

= 10(-11.1 + .751)

= 10(- 10.349)

= - 103.49

now, 113. + (- 103.49) = .113 x 103 - .10349 x 103 

= 103(.113 - .103)  // ignor 49 bcz  three-digit floating point arithmetic with rounding

= 103 x .010

= 10

answered by Active (1.1k points)


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