Binary Arithmetic : Binary Overflow

In Binary Arithmetic operations have a potential to run into a condition known as overflow. Overflow occurs with respect to the size of the data type that must accommodate the result. Overflow indicates that the result was too large or too small to fit in the original data type. For example, Lets 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 example of an 8-bit overflow occurs in the binary sum (11111111)2 + (1)2

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.

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).

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