What is an integer overflow error?

When you store an integer in memory, the computer stores it as a series of bytes. These can be represented as a series of ones and zeros.

For example, zero will be represented as 00000000 (8 bit integers), and often, 127 will be represented as 01111111. If you add one to 127, this would "flip" the bits, and swap it to 10000000, but in a standard two's compliment representation, this is actually used to represent -128. This "overflows" the value.

With unsigned numbers, the same thing happens: 255 (11111111) plus 1 would become 100000000, but since there are only 8 "bits", this ends up as 00000000, which is 0.

You can avoid this by doing proper range checking for your correct integer size, or using a language that does proper exception handling for you.

Integer overflow occurs when you try to express a number that is larger than the largest number the integer type can handle.

If you try to express the number 300 in one byte, you have an integer overflow (maximum is 255). 100,000 in two bytes is also an integer overflow (65,535 is the maximum).

You need to care about it because mathematical operations won't behave as you expect. A + B doesn't actually equal the sum of A and B if you have an integer overflow.

You avoid it by not creating the condition in the first place (usually either by choosing your integer type to be large enough that you won't overflow, or by limiting user input so that an overflow doesn't occur).

The easiest way to explain it is with a trivial example. Imagine we have a 4 bit unsigned integer. 0 would be 0000 and 1111 would be 15. So if you increment 15 instead of getting 16 you'll circle back around to 0000 as 16 is actually 10000 and we can not represent that with less than 5 bits. Ergo overflow...

In practice the numbers are much bigger and it circles to a large negative number on overflow if the int is signed but the above is basically what happens.

Another way of looking at it is to consider it as largely the same thing that happens when the odometer in your car rolls over to zero again after hitting 999999 km/mi.