42 votes 42 votes What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding? $(113. + -111.) + 7.51$ $113. + (-111. + 7.51)$ $9.51$ and $10.0$ respectively $10.0$ and $9.51$ respectively $9.51$ and $9.51$ respectively $10.0$ and $10.0$ respectively Digital Logic gatecse-2004 digital-logic number-representation normal + – Kathleen asked Sep 18, 2014 • edited Jun 19, 2018 by Pooja Khatri Kathleen 16.5k views answer comment Share Follow See all 2 Comments See all 2 2 Comments reply amarVashishth commented Nov 16, 2015 i edited by amarVashishth Nov 17, 2015 reply Follow Share Rewrite the smaller number such that its exponent matches with the exponent of the larger number. 14 votes 14 votes Mayank0343 commented Feb 2, 2020 reply Follow Share @amarVashishth Do you mean smaller number in terms of magnitude without the sign ? As in the accepted answer −1.11×10^2+7.51×10^0 , -1.11 (also -111 < 7.51) is smaller than 7.51, but we are rewriting 7.51 's exponent to match with 1.11' s exponent 1 votes 1 votes Please log in or register to add a comment.
Best answer 88 votes 88 votes $(113. + -111.) = 1.13 \times 10^2 + -1.11 \times 10^2 = 0.02 \times 10^2 = 2.0 \times 10^0$ $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 = -1.11\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/ Correct Answer: $A$ Arjun answered Nov 16, 2015 • edited May 21, 2019 by Naveen Kumar 3 Arjun comment Share Follow See all 23 Comments See all 23 23 Comments reply Show 20 previous comments neel19 commented Jun 17, 2021 reply Follow Share @Arjun sir, In the link given it is said that the hidden bit is for binary floating-point numbers, but here the numbers are in decimal format. So why mantissa has only 2 digit? 0 votes 0 votes Abhrajyoti00 commented Jan 6, 2023 i edited by Abhrajyoti00 Jan 6, 2023 reply Follow Share @Arjun Sir, @Kabir5454, I have the same question as @jatinmittal199510. EDIT: Ok, Got it. The next examples on that page shows that we first need to normalize the numbers and then start doing the operations. 0 votes 0 votes thansen commented Jan 11 reply Follow Share three-digit floating point arithmetic with rounding what does this mean ? we have to take total three digit before and after the decimal ? 0 votes 0 votes Please log in or register to add a comment.
30 votes 30 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 Digvijay Pandey answered Apr 23, 2015 Digvijay Pandey comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments Digvijay Pandey commented Nov 16, 2015 reply Follow Share to apply operation ur operand should be THREE FLOATING POINT ARITHMATIC .. 2 votes 2 votes Ram Sharma1 commented Jul 19, 2016 reply Follow Share Please explain the meaning "three-digit floating point arithmetic with rounding" 3 votes 3 votes amitqy commented Feb 13, 2019 reply Follow Share In n-digit floating-point arithmetic, numbers are represented by a signed n-digit integer and an exponent 113. in floating point is represented as 1.11 x 10^2 0 votes 0 votes Please log in or register to add a comment.
8 votes 8 votes much better explanation http://math.stackexchange.com/questions/1531692/two-expressions-using-three-digit-floating-point-arithmetic-with-rounding ANKIT CHAUHAN 1 answered Nov 23, 2016 ANKIT CHAUHAN 1 comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes I have a doubt why .10349 is rounded off to .103 its should be .104 please help Kimimp answered Aug 27, 2019 Kimimp comment Share Follow See 1 comment See all 1 1 comment reply nitin-787 commented Nov 20, 2023 reply Follow Share because 0.103 is close to 0.10349… if it would have been 0.10351 then it would be 0.104 0 votes 0 votes Please log in or register to add a comment.