Negative Numbers in 32 bit Floating Point IEEE Numbers So I understand the logic behind converting positive decimal numbers to IEEE 32 bit floating numbers but I'm not completely sure behind the negative one's. If for example we have a decimal number say -15.5, do we have to do two's complement first then convert it to the floating point representation or we directly do it for 15.5 and at the sign bit we do 1.
Thank you in advance.
Contrary to two's complement representation of negative integers, the negative numbers in IEEE floating-point are represented with only a sign bit change, as shown in there.
For example, $0\cdot01111100\cdot01000000000000000000000$ is the representation of $0.15625$, and $1\cdot01111100\cdot01000000000000000000000$ is the representation of $-0.15625$.
In particular, there are two representations of zero (the positive one and the negative one).