How to find machine infinity?

Question

Programming

For the format of the floating point number (FPZ) used, the number of bits allocated in this format for the mantissa (including the bit allocated under the sign) is 29, and the number of bits allocated in this format for the order (taking into account the bit allocated for the sign ), is equal to 14. Then the order of machine infinity when using this FF will be ...

For example: machine infinity is approximately 0.12 * 10^75

Answer: 75

I just can’t understand how to find machine infinity with different bit depths, on the Internet there is only code in which they find machine infinity for their bit depth by brute force.

Answer 1

Important question: is there an implicit unit and denormalized numbers?
We believe that it still exists, the order is unbiased, written in an additional code, the denormalized number is written 10 ... 00 in order. (Otherwise it happens, in our native float the order is shifted by 01 ... 11).
Then the maximum number that can be written is 1.1…111 ₂ ·2 ^{2^13−1} .
Well, infinity is approximately 2 2 ^{2^13−1} = 2 ^{2^13} .
Wolfram Alpha says it's 1.091 10 ²⁴⁶⁶ .