Madeeasy_Subject_Test_digitalLogic

Question

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 ______________________

Answer 1

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.

 

Comments

Correct approach

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

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@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

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the next larger double precision floating point number is (1.1001001+2^-52 )× 2^7

please explain this line. how + is used?

 

Answer 2

@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 * 2^978-1023 = 1 * 2^-45

So answer is -45