How can I subtract IEEE 754 numbers?

Question

I want to know how to subtract IEEE 754 numbers so I searched about this and found this answer: How to subtract IEEE 754 numbers? , and it works fine with all the examples I've tried, except when I substract one, the number 1 have a lot of 0's in the mantissa, so by this logic a number should stay the same when I substract 1 to it?

PS: It would be the same for any number - 2^something, the mantissa would be full of 0's.

Someone explain pls

Answer 1

When an IEEE 754 number is stored, it uses a very memory-efficient method.

All numbers except for very very small ones (so-called de-normalized numbers) can be written in the form:

sign * 1.mmmmmmmmmmmmmmmmm * 2^eeeee

When they are stored, only the seeeeeeeemmmmmmmmmmmmmmmmmmmmmmm bits are actually stored.

When storing 1.0000000 , the mmmmmmm bits are all zero, and the leading 1. is not stored, since that would be redundant. Therefore the mantissa in the stored bits is all-zeros. The mathematical value of the mantissa though is:

mantissa = 1 + 0.mmmmmmm

Actually, the exponent is also stored a little differently, to allow for both positive and negative exponents. But that's outside the scope of this question.

For more information, see the Wikipedia article on this subject .