# 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.

• What is a decimal number? I have intuitions about number, decimal representation of a number, and "IEEE format" number representations that work for me. – greybeard Apr 1 at 17:41

For example, $$0\cdot01111100\cdot01000000000000000000000$$ is the representation of $$0.15625$$, and $$1\cdot01111100\cdot01000000000000000000000$$ is the representation of $$-0.15625$$.
IEEE floating point numbers have a sign bit. The representation of $$-x$$ is generally the same as that of $$x$$, with the sign bit flipped. This has the unfortunate consequence of having two different zeroes.