Redirected
edited by
1,760 views

2 Answers

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.

 

selected by
8 votes
8 votes

@arvin already showed a nice way. Still I am answering as what I understands... 

201 = (11001001)

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 

Related questions

0 votes
0 votes
0 answers
1
Balaji Jegan asked Jan 28, 2019
1,425 views
What is the minimum difference between two successive real numbers representable in this system?
4 votes
4 votes
2 answers
2
2 votes
2 votes
1 answer
3
Hitoshi asked Dec 19, 2017
4,826 views
If the decimal number is 3.248 x 104 ,then its equivalent floating number in IEEE 754 standard is ?