How many bits of precision does a normalized double precision IEEE Floating Point number have?

Question

How many bits of precision does a normalized double precision IEEE Floating Point number have? Is there sort of formula

what I found was this but I feel like it is wrong:

• +2-1022 to (2-2-52) * 21023

Answer 1

Please read https://en.wikipedia.org/wiki/IEEE_754-1985

In particular, it reads

Precision is defined as the minimum difference between two successive mantissa representations; thus it is a function only in the mantissa;

A double-precision IEEE 754 value uses 52 bits for the mantissa. A normalized value has an implicit '1' bit:

The leading 1 bit is omitted since all numbers except zero start with a leading 1; the leading 1 is implicit and doesn't actually need to be stored which gives an extra bit of precision for "free."

Thus, there are 53 bits of precision in an IEEE 754 double-precision floating-point value.