Binary is just a number base, the same as decimal - apart from it works in powers of two rather than powers of 10.
If by full detail you actually mean how binary numbers are used to represent positive / negative decimal numbers in real life rather than just integers, then you're looking to research the IEEE754 standard. There's two versions, 1985 and (I think) 2008 - but the 1985 spec will be more than enough if you have a proper look at that.
I don't usually recommend wikipedia, but in this instance the article on it
is actually quite good for looking at how it all works.