2 ms·
I see what you're saying, but if you take the 111011 as representing 1/2 1/4 1/8 etc. then it does equal 0.921875. I'm presuming that this value is added onto 1
by MikeDucker 14y ago
I see what you're saying, but if you take the 111011 as representing 1/2 1/4 1/8 etc. then it does equal 0.921875. I'm presuming that this value is added onto 1 (fiddling with the tick boxes confirms this) to be used as the mantissa.
I'm not doubting what you know about floating points, but I think that this calculator is still trying to say (whether that be right or wrong based on IEEE) 6 ^ 1.921875
- acqq 14y agoYou didn't get the different FP representation, what's important are the bits, they are what they are, not how you decide to translate them to the decimal system. The only thing being processed are the bits. Concentrating on the decimal interpretation (which is just that, the number is processed as the base 2 IEEE 754 FP) you missed that 123 has an absolutely exact binary representation.
- Tuna-Fish 14y agoWell, it is, but it's still exact. Think of it a while, in base-10 (if it makes it easier for you). Let's say you save numbers in format a * 10^b. B has enough range to not to be a problem, but a can only hold 3 digits. What integers can you represent exactly? 1 = 1.00 * 10^0. 2 = 2.00 * 10^1, trough to 999 = 9.99*10^2. Or in other words, so long as mantissa has less bits than the number you are converting, it can be represented perfectly in floating point. So, 4 is always 4, not some number very close to 4. If it ends up as something else, you're the one who has messed it up.