What is the difference between signed and unsigned int

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".

In laymen's terms an unsigned int is an integer that can not be negative and thus has a higher range of positive values that it can assume. A signed int is an integer that can be negative but has a lower positive range in exchange for more negative values it can assume.