How do I convert a hexadecimal number in IEEE 754 double precision (64bit) format to a decimal number?

Question

My task is to convert a hexadecimal number in double precision format (IEEE 754) on a paper. I've converted a hexadecimal number: 0x40790A0000000000 to a binary 64bit format so far and now I have: 0 10000000111 1001000010100000000000000000000000000000000000000000

For the next step I am not totally sure what to do. I have to convert it into a decimal number and I've tried out several ways, but never got the right result. Hope you can help me and thank you.

Answer 1

Going from https://en.wikipedia.org/wiki/Double-precision_floating-point_format ,

4    0    7    9    0    A    0    0    0    0    0    0    0    0    0    0
0100 0000 0111 1001 0000 1010 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000
0 - Sign bit (this is a positive number)
 100 0000 0111 - Exponent
               1001 0000 1010 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 - Fraction

The exponent's value is 1031. Because it's nonzero the fractional part is given by the expression 1 + sum from i = 1 to 52 bit_(52-i) * 2^(-i).

The fraction's value is therefore 1 + 1/2 + 0/4 + 0/8 + 1/16 + ... ~= 1.56

From there you should be able to figure the rest out.

(Not solving this completely because this looks like homework.)