Half precision conversion

问题

How comes that 0 11110 1111111111 is equal to the half precision format 1.1111111111 * 2^15? Both should be 65504.

The sign bit here is a 0. The exponent would be 11101 and the fractional part 1111111111. But that doesn't look like 1.1111111111 * 2^15 at all.

Can someone explain that to me?

回答1:

Here is the layout of your half-precision number:

The exponent's value is 11110₂, which is 30₁₀. Half-precision numbers have exponent bias of 15₁₀, so we need to subtract 15₁₀ from 30₁₀ to get the actual exponent of 15₁₀.

There is an implicit 1₂ pre-pended to the fraction, so the actual fraction has one extra 1 in front of it. The binary fraction point is located immediately after that implicit 1, making the number look like this:

1.1111111111

In order to apply the binary exponent of 15₁₀, we need to move the fraction point fifteen positions to the right. This produces the number 1111111111100000₂, which is equal to 65504₁₀ after the conversion.

来源：https://stackoverflow.com/questions/33461757/half-precision-conversion