8 votes 8 votes The difference between 201 and next larger double precision number is 2$^P$. If IEEE double precision format is used then the value of P is ______________________ Digital Logic ieee-representation digital-logic floating-point-representation co-and-architecture + – Magma asked Aug 13, 2018 edited Jan 5, 2019 by Shaik Masthan Magma 1.8k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 8 votes 8 votes A Double precision(64bits) format means it has 1bit for sign 11bits for exponent and 52bits for significand. The binary floating point representation of 201 is (1.1001001)2 × 2 7 . so the gap between this number and the next larger double precision floating point number is (1.1001001+2−52 )× 2 7 = 2−45 -45 is the answer. arvin answered Aug 13, 2018 selected Jan 5, 2019 by Shaik Masthan arvin comment Share Follow See all 4 Comments See all 4 4 Comments reply pankaj_vir commented Aug 13, 2018 reply Follow Share Correct approach 1 votes 1 votes Magma commented Aug 13, 2018 reply Follow Share thanks arvin ..but i didn,t understand the term next larger double precision ...what's that mean ???? 0 votes 0 votes arvin commented Aug 13, 2018 reply Follow Share @pankaj thanku :) . @magma : its just like next number to (1.10000)2 is (1.10001)2 ==> (1.10001)2=(1.10000* 2-5)2 2 votes 2 votes amitqy commented Feb 27, 2019 reply Follow Share the next larger double precision floating point number is (1.1001001+2^-52 )× 2^7 please explain this line. how + is used? 0 votes 0 votes Please log in or register to add a comment.
8 votes 8 votes @arvin already showed a nice way. Still I am answering as what I understands... 201 = (11001001)2 so can be represented in IEEE 754 standard double precision (Excess 1023) (https://en.wikipedia.org/wiki/Double-precision_floating-point_format) as 1.1001001000...0 * 21030 So next number in sequence is to add 1 to above number i.e. 52th bit is 1 in mantissa. So difference will be 0.0000...1 * 21030 = 1* 2978 So a number 1 * 2978 of double precision (Excess 1023) can be represented in decimal as 1 * 2978-1023 = 1 * 2-45 So answer is -45 Abbas answered Aug 13, 2018 Abbas comment Share Follow See all 0 reply Please log in or register to add a comment.