What is the difference between signed and unsigned int

Question

What is the difference between signed and unsigned int?

Answer 1

As you are probably aware, ints are stored internally in binary. Typically an int contains 32 bits, but in some environments might contain 16 or 64 bits (or even a different number, usually but not necessarily a power of two).

But for this example, let's look at 4-bit integers. Tiny, but useful for illustration purposes.

Since there are four bits in such an integer, it can assume one of 16 values; 16 is two to the fourth power, or 2 times 2 times 2 times 2. What are those values? The answer depends on whether this integer is a signed int or an unsigned int. With an unsigned int, the value is never negative; there is no sign associated with the value. Here are the 16 possible values of a four-bit unsigned int:

bits  value
0000    0
0001    1
0010    2
0011    3
0100    4
0101    5
0110    6
0111    7
1000    8
1001    9
1010   10
1011   11
1100   12
1101   13
1110   14
1111   15

... and Here are the 16 possible values of a four-bit signed int:

bits  value
0000    0
0001    1
0010    2
0011    3
0100    4
0101    5
0110    6
0111    7
1000   -8
1001   -7
1010   -6
1011   -5
1100   -4
1101   -3
1110   -2
1111   -1

As you can see, for signed ints the most significant bit is 1 if and only if the number is negative. That is why, for signed ints, this bit is known as the "sign bit".