Code: The Hidden Language of Computer Hardware and Software

by Petzold Charles

Notice that I haven’t mentioned any way to express a very common number that we seem to have forgotten about, namely 0. That’s one of the special cases, which are these: If e equals 0, and f equals 0, the number is 0. Generally, all 32 bits are set to 0 to signify 0. But the sign bit can be 1, in which case the number is interpreted as a negative 0. A negative 0 can indicate a very small number that can’t be represented with the available digits and exponents in single-precision format but which is still less than 0. If e equals 0 and f doesn’t equal 0, the number is valid, but it’s not normalized. The number equals (–1)s x 0.f x 2-127 Notice that the significand has a 0 to the left of the binary point. If e equals 255 and f equals 0, the number is positive or negative infinity, depending on the sign s. If e equals 255 and f doesn’t equal 0, the value is considered to be not a number, which is abbreviated NaN. A NaN could indicate an unknown number or the result of an invalid operation.