duobt

Question

please explain me this calculation part  bold part

In implicit form largest digit will be = 1.111...11∗2¹⁰²⁴=(2−2¹¹)∗2¹⁰²⁴

Second largest will be = 1.111...10∗2¹⁰²⁴=(2−2¹⁰)∗2¹⁰²⁴

Hence sum will be (2−2¹¹)∗2¹⁰²⁴   +    (2−2¹⁰)∗2¹⁰²⁴

2¹⁰²⁵−2¹⁰¹³+2¹⁰²⁵−2¹⁰¹⁴=2¹⁰²⁶−2¹⁰¹³(1+2)=2¹⁰²⁶−3∗2¹⁰¹³

Comments

It should be $(2-2^{-11})*2^{1024} + (2-2^{-10})*2^{1024}$

Answer 1

mohit u have made a mistake i think....here should be neagative  power....

let talk about this...

1.111...11(let there is 11 times 1's after decimal point)

 ...we can write is like this...1*2⁰+.111111(11 times) ....1+(1-2^-11)  or (2-2^-11)....

....example:- 

0.11  ....decimal equivalent is....(1-1/4)

Comments

see ashwin ans :

https://gateoverflow.in/190206/ieee-754?show=190206#q190206

means instead of 2-2¹¹        it should be 2-2^{-11    right?}

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ya i think soo....