ace test series

Question

The largest value that can be represented by IEEE 754 double precision floating point format (for implicit number) is (approximately)___

A)2^1022

B)2^1023

C)2^1024

D)2^1021

Comments

Ans B)?

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I am getting C .. :/

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how?

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1.111.....1_{52 times} x 2^2043-1023 =(1 + (1-2^-52)) x 2¹⁰²³ = (2-2^-52)x2¹⁰²³

It is approx 2*2¹⁰²³ (by neglecting 2^-52)

So 2¹⁰²⁴

Answer 1

(-1)⁰ x 1.1111111111111111111111111111111111111111111111111111 (52 times) x 2^2046-1023

= 1.1111111111111111111111111111111111111111111111111111 (52 times) x 2¹⁰²³

= 11111111111111111111111111111111111111111111111111111 (53 times) x 2⁹⁷¹

= (2⁵⁴-1)x 2⁹⁷¹

= 2¹⁰²⁵-2⁹⁷¹

Among the options option C) i.e 2¹⁰²⁴ is the closest.

Comments

Nice sakharam