Gradual lower and denormalized number in IEEE

Question

I read about floating point representation and overflow / overflow, and I realized something interesting - gradual overflow. Since I understand that gradual overflow means that the result of, for example, subtracting xy is so small that it can be reset to 0, but the floating point system produces a number less than the UFL. Wherever I read that this is done, losing some precession, it means that some bits of the mantissa go to the exponent, so can we have a smaller exponent?

Answer 1

The answer is yes, the mantissa bit goes to exponentially. They are called abnormal (AKA denormal) numbers. For example, with IEEE double precision, the smallest power of two exponents for a normal number is a number with a full 53 bit precision - 2 ^-1022 . But two degrees can be represented up to ^2-1074 which are determined by the location of the first 1 bit in an abnormal value. Thus, an indicator ^2-1023 has 52 bits of accuracy, ^2-1024 has 51 bits of precision, ..., ^2-1074 has 1 bit of accuracy.

(See my article, What powers of two look inside a computer to visualize this better.)