2 votes 2 votes Let A and B are the largest and second largest numbers respectively in IEEE Double precision format as shown below(Implicit Normalization). 1(sign) 11(exponent) 52(mantissa) Then A-B= ______ CO and Architecture co-and-architecture + – gari asked Jan 9, 2018 gari 772 views answer comment Share Follow See all 10 Comments See all 10 10 Comments reply joshi_nitish commented Jan 9, 2018 reply Follow Share it will be, $2^{971}$ 0 votes 0 votes gari commented Jan 9, 2018 reply Follow Share yes it's correct can u please explain the format. 0 votes 0 votes Ashwin Kulkarni commented Jan 9, 2018 i edited by Ashwin Kulkarni Jan 9, 2018 reply Follow Share HIghest number = $1.111...111 * 2^{1023}$ 2nd Highrst number = $1.111...110 * 2^{1023}$ Difference = $(0.0000...001) * 2^{1023}$ = $2^{-52} * 2^{1023}$ = $2^{971}$ 1 votes 1 votes joshi_nitish commented Jan 9, 2018 reply Follow Share maximum no. in double precision is when, exponent, E = 11111111110 and mantissa, M = 1111.....11111 so max no., A = 1.111....1111*21023 .......................................................................................................................................................... second max no. in double precision is when, exponent, E = 11111111110 and mantissa, M = 1111.....11110 so second max no., B = 1.111.....1110*21023 A-B = 1.1111.....1111*21023 - 1.1111.....1110*21023 A-B = 0.000...00001*21023 = 2971 1 votes 1 votes gari commented Jan 9, 2018 reply Follow Share i feel i got my answer.. please see. exponent is 11 bits . Largest no has exponent as 1111111110. mantissa as 111111....1111 so exponent is 2046 Second largest no has exponent as 11111111110 and mantissa as 11111...1110 Bias =1023 on solving we get 2971 I was getting confused that what should be the exponent. 0 votes 0 votes joshi_nitish commented Jan 9, 2018 reply Follow Share @gari, yes you got it :) 1 votes 1 votes Anu007 commented Jan 9, 2018 reply Follow Share Biased exponant = 1023 now max number = 1.11111...1( 52 times 1) = 1.111111 $\times $ 22046-1023 2046 = expoanant = 11111111110 , here if we take 11 1;s then NAN so second max = 1.11111...0( 51 times 1 and 0 at last) = 1.111110 $\times $ 22046-1023 so difference = 1.111111 $\times $ 22046-1023 - 1.111110 $\times $ 22046-1023 = 1.000000...1$\times $ 21023 0.000000...1$\times $ 21023 = 2-52$\times $ 21023 = 2971 0 votes 0 votes srestha commented Jan 9, 2018 reply Follow Share Can u plz tell me in double precision number of bits in mantissa=54 no of bits in exponent=11 and sign bit 1 means total 66 bits. or it should be 65 bit? 0 votes 0 votes Anu007 commented Jan 9, 2018 reply Follow Share 64 = 52(mantissa) + 11(exponant)+ 1(sign) 2 votes 2 votes rdfan19 commented Jan 21, 2018 reply Follow Share @joshi_nitish why can't we take all bits 1 in exponent? 0 votes 0 votes Please log in or register to add a comment.