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.
thanks arvin ..but i didn,t understand the term next larger double precision ...what's that mean ????
@pankaj thanku :)
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@magma : its just like next number to (1.10000)2 is (1.10001)2
==> (1.10001)2=(1.10000* 2-5)2
the next larger double precision floating point number is (1.1001001+2^-52 )× 2^7
please explain this line. how + is used?
@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