The term arithmetic overflow or simply overflow has the following meanings. In a computer, the condition that occurs when a calculation produces a result that is greater in magnitude than that which a given register or storage location can store or represent. In a computer, the amount by which a calculated value is greater in magnitude than that which a given register or storage location can store or represent. Note that the overflow may be placed at another location.
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Arithmetic underflow
The term arithmetic underflow (or "floating point underflow", or just "underflow") is a condition in a computer program where the result of a calculation is a smaller number than what the computer can actually store in memory. Arithmetic underflow can occur when the true result of a floating point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating point number in the target datatype.
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Arbitrary-precision arithmetic
In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers which digits of precision are limited only by the available memory of the host system. This contrasts with the faster fixed-precision arithmetic found in most arithmetic logic unit (ALU) hardware, which typically offers between 16 and 64 bits of precision.
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Floating point
In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16.
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Multiplication
Multiplication (often denoted by the cross symbol "×") is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic.
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Central processing unit
The central processing unit (CPU, occasionally central processor unit) is the hardware within a computer system which carries out the instructions of a computer program by performing the basic arithmetical, logical, and input/output operations of the system. The CPU plays a role somewhat analogous to the brain in the computer. The term has been in use in the computer industry at least since the early 1960s.
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