IEEE smallest difference

Question

What is the minimum difference between two successive real numbers representable in this system?

Comments

minimum= $2^{-40}$

maximum= $2^{22}$

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Nope. Maximum = 2^22

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https://gateoverflow.in/934/gate2003-43

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ohh sry i wrongly checked i though there are 5 bits in exponent. Now check minimum will be same but i corrected maximum.

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@Shubhgupta how minimum is 2^-40?

I am getting this

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First small- $(1+000000000*2^{-9})*2^{0-31}= 1*2^{-31}= 2^{-31}$

Second small- $(1+000000001*2^{-9})*2^{0-31}= 1*2^{-31}+ 1*2^{-9}*2^{-31}= 2^{-31}+2^{-40}$

Difference - $2^{-40}$

If IEEE 754 is mentioned then for minimum we can't take E = 000..0 as E = 0 is reserved for special number.

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https://docs.google.com/document/d/1y32_pAsYZ49fJM4Aim_qKjx4pCM-Lb-B9jZTyVDx1vg/edit

 

please check 36th question’s solution in this link

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there no explicit form is mentioned like in this question.

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Correct solution is given