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+6 votes

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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.

0

thanks arvin ..but i didn,t understand the term next larger double precision ...what's that mean ????

+6 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 * 2

^{1030}

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 * 2

^{1030}= 1* 2^{978 }

So a number 1 * 2^{978 }of double precision (Excess 1023) can be represented in decimal as

1 * 2

^{978-1023 }= 1 * 2^{-45}

So answer is **-45**

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