Originally Posted by
cyberfish
It's like scientific notation. in 3.94*10^9, the mantissa is 3.94, which is always normalized to the range [1, 2), the exponent is 9, and the sign bit is 0 (for positive). The decimal point is always after the first significant figure (a non-zero).
Floating point numbers work in the exact same way, except it's in base 2 (so the binary point is always before the first 1 bit in mantissa).
[edit]I think I made a mistake. The binary point is to the left of the most significant 1 in the mantissa, since a leading 1 is assumed). Corrected above.[/edit]