C Bitwise Operators Example
given the following function:
int boof(int n) {
return n + ~n + 1;
}
What does this function return? I'm having trouble understanding exactly what is being passed in to it. If I called boof(10), would it convert 10 to base 2, and then do the bitwise operations on the binary number?
This was a question I had on a quiz recently, and I think the answer is supposed to be 0, but I'm not sure how to prove it.
note: I know how each bitwise operator works, I'm more confused on how the input is processed.
Thanks!
Bitwise operations will not change the underlying representation of the number to base 2 - all math on the CPU is done using binary operations regardless.
What this function does is take n and then add it to the two's complement negative representation of itself. This essentially negates the input. Anything you put in will equal 0.
Let me explain with 8 bit numbers as this is easier to visualize.
10 is represented in binary as 00001010.
Negative numbers are stored in two's complement (NOTing the number and adding 1)
So the (~n + 1) portion for 10 looks like so:
11110101 + 1 = 11110110
So if we take n + ~n+1:
00001010 + 11110110 = 0
Notice if we add these numbers together we get a left carry which will set the overflow flag, resulting in a 0. (Adding a negative and positive number together never means the overflow indicates an exception!)
See this The CARRY and OVERFLOW flag in Binary Arithmetic
When n is an int, n + ~n will always result in an int` that has all bits set.
Strictly speaking, the behavior of adding 1 to such an int will depend on the representation of signed numbers on the platform. The C standard support 3 representations for signed int :
for Two's Complement machines (the vast majority of systems in use today), the result will be 0 since an int with all bits set is -1.
on a One's Complement machine (which are pretty rare today, I believe), the result will be 1 since an int with all bits set is 0 or -0 (negative zero) or undefined behavior.
a Signed-magnitude machine (are there really any of these still in use?), an int with all bits set is a negative number with the maximum magnitude (so the actual value will depend on the size of an int ). In this case adding 1 to it will result in a negative number (the exact value, again depends on the number of bits that are used to represent an int ).
Note that the above ignores that it might be possible for some implementations to trap with various bit configurations that might be possible with n + ~n .
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