Value of NSUInteger and NaN?

Question

Why is the value of NSUInteger 2^32 - 1 instead of 2^32? Is there a relationship between this fact and the need of a nan value? This is so confusing.

Answer 1

Count to 10 on your fingers. Really :)

The standard way to count to 10 is 1,2,3,..10 (the ordinality of each finger is counted). However, what about "0 fingers"?

Normally that might represent that by putting your hands behind our back, but that adds another piece of information to the system: are your hands in front (present) or behind (missing)?

In this case, putting hands behind your back would equivalent to assigning nil to an NSNumber variable. However, NSUInteger represents a native integer type which does not have this extra state and must still encode 0 to be useful.

The key to encode the value 0 on your fingers is to simply count 0,1,2..9 instead. The same number of fingers (or bits of information) are available, but now the useful 0 can be accounted for .. at the expense of not having a 10 value (there are still 10 fingers, but the 10th finger only represents the value 9). This is the same reason why unsigned integers have a maximum value of 2^n-1 and not 2^n: it allows 0 to be encoded with maximum efficiency.

Now, NaN is not a typical integer value, but rather comes from floating point encodings - think of float or CGFloat. One such common encoding is IEEE 754:

In computing, NaN, standing for not a number, is a numeric data type value representing an undefined or unrepresentable value, especially in floating-point calculations ..

Answer 2

2^32-1 because counting starts from 0 for bits. If it's easier think of it as 2^32 - 2^0.

Answer 3

It is the largest value a 32-bit unsigned integer variable can hold. Add one to that, and it will wrap around to zero.

The reason for that is that the smallest unsigned number is zero, not one. Think of it: the largest number you can fit into four decimal places is 9999, not 10000. That's 10^4-1.

Answer 4

You cannot store 2^32 in 4 bytes, but if you subtract one then it fits (result is 0xffffffff)

Answer 5

Exactly the same reason why the odometer in your car shows a maximum of 999999 mi/km (assuming 6 digits) - while there are 10^6 possible values it can't show 10^6 itself but 0 through 10^6-1.