Kinda off-topic for here but whatever...
Assuming 64-bit double, it has a mantissa of 52 bits and an exponent of
11 bits. If the mantissa is all-ones, that will give a significant of
2-2^(-52). The exponent cannot be all-ones (an all-ones exponent means
infinity or NaN), so the largest exponent is 2^11-2 = 2046, minus bias
(1023), it gives a maximum effective exponent of 1023, so that would
give a value of (2-2^(-52))*2^(1023) = 2^1024 - 2^971, roughly 10^308.
What do you mean by "precision"?
Firas