Integers and floats can overflow is you try to use more bits than you have available.
Integer Overflow
Suppose 3 bits that allow us to count to 7 (000). If we try to count to 8 (1000) but only have 3 bits, then we will end up with 1000, or just 0. This is integer overflow.
Examples of integer overflow:
The y2k problem (storing last 2 digits of any year back when memory was expensive)
The next y2k problem: in 2038, the number representing the seconds since jan 1st 1970 overflow past 32-bits and the date will reset to 1901
Solution? Kick the can further, add more bits.
Boeing airplane needing to be rebooted after 208 days until a software patch was made.