| > Thats not the right way of thinking about it. Sure, the first non-zero digit of any binary number is 1, but who is to say that the number has a bit that isn't 0? Couldn't the number be zero? When I was taught scientific notation in middle school, high school, and at college, it was always explicitly stated that: 1. You can have only one digit before the decimal point. 2. That digit cannot be 0 (unless your number is 0, of course). So 0.3 * 10^5 is not scientific notation. This is no different. The "twist" is that there is only one possible non-zero bit, whereas in decimal it could be [1-9]. I think this explanation is neat. However, the "usual" formulation is just scientific notation, with the optimization that one bit is redundant. Personally, I prefer the alternative notation: M * 2^(exponent-precision+1), with M being a p-bit integer. It's easier to work with when you know that M is always an integer, and you don't need to deal with fractions in base 2. In fact, FP made a lot more sense when I took this formulation in decimal, and worked with that. |