Arithmetic is at the heart of the digital computer, and the majority of arithmetic performed by computers is binary arithmetic, that is, arithmetic on base two numbers.Decimal and floating-point numbers, also used in computer arithmetic, depend on binaryrepresentations, and an understanding of binary arithmetic is necessary in order tounderstand either one. Computers perform arithmetic on fixed-size numbers. The arithmetic of fixed- size numbers is called finite-precision arithmetic. The rules for finite-precisionarithmetic are different from the rules of ordinary arithmetic. The sizes of numbers which can be arithmetic operands are determined when the architecture of the computer is designed. Common sizes for integer arithmetic are eight,16, 32, and recently 64 bits. It is possible for the programmer to perform arithmetic onlarger numbers or on sizes which are not directly implemented in the architecture.However, this is usually so painful that the programmer picks the most appropriate sizeimplemented by the architecture. This puts a burden on the computer architect to selectappropriate sizes for integers, and on the programmer to be aware of the limitations of thesize he has chosen and on finite-precision arithmetic in general.

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