Comment Re:It's not that big of deal (Score 1) 334
No, there is one way to represent every number.
The mantissa doesn't state a "number", it is the decimal part of 1.xxxxx.
Say we have a 2 bit mantissa. The mantissa would thus describe the following numbers:
00 -> 1.00
01 -> 1.25
10 -> 1.5
11 -> 1.75
When we reach 2 we just increase the exponent instead, This gives the double representation a bigger range.
For very small numbers there is also a "subnormal" representation in the IEEE standard. This is when the exponent reaches the "smallest" possible value. At this point the mantissa bits represents numbers from "2" to "0" with the smallest exponent.
If i'm not off my hat right now this is why setting all the bits of a float or double will actually produce a 0, lowest exponent, -> subnormals = actual 0 and no sign(irrelevant in the case of floating point numbers though)