A CPU with a capacity of 8 bits has a capacity of up to 11111111 in binary. If one more bit was added there would be an overflow error.

An explanation of binary overflow errors

Example: 8-bit overflow

An example of an 8-bit overflow occurs in the binary sum 11111111 + 1 (denary: 255 + 1).

In binary, 11111111+00000001=100000000 but the leftmost 1 is an overflow number

The total is a number bigger than 8 digits, and when this happens the CPU drops the overflow digit because the computer cannot store it anywhere, and the computer thinks 255 + 1 = 0.

An overflow error causes a computer to think that 11111111+00000001=00000000

Overflow errors happen when the largest number that a register can hold is exceeded. The number of bits that it can handle is called the word size.

Most CPUs use a much bigger word size than 8 bits. Many PCs have a 64-bit CPU. A 64-bit CPU can handle numbers larger than 18 quintillion (18,446,744,073,709,551,615 to be precise).