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⭐ Core Definition: Floating-point representation

In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a significand (a signed sequence of a fixed number of digits in some base) multiplied by an integer power of that base.Numbers of this form are called floating-point numbers.

For example, the number 2469/200 is a floating-point number in base ten with five digits: $2469/200=12.345=\!\underbrace {12345} _{\text{significand}}\!\times \!\underbrace {10} _{\text{base}}\!\!\!\!\!\!\!\overbrace {{}^{-3}} ^{\text{exponent}}$ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits.The nearest floating-point number with only five digits is 12.346.And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits.In practice, most floating-point systems use base two, though base ten (decimal floating point) is also common.

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👉 Floating-point representation in the context of Fixed-point arithmetic

In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representing the cents (1/100 of a dollar). More generally, the term may refer to representing fractional values as integer multiples of some fixed small unit, e.g., a fractional amount of hours as an integer multiple of ten-minute intervals. Fixed-point number representation is often contrasted to the more complicated and computationally demanding floating-point representation.

In the fixed-point representation, the fraction is often expressed in the same number base as the integer part, but using negative powers of the base b. The most common variants are decimal (base 10) and binary (base 2). The latter is commonly known also as binary scaling. Thus, if n fraction digits are stored, the value will always be an integer multiple of b. Fixed-point representation can also be used to omit the low-order digits of integer values, for instance, when representing large dollar values as multiples of $1000 ($1K).

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Floating-point representation in the context of "Fixed-point arithmetic"

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⭐ Core Definition: Floating-point representation

👉 Floating-point representation in the context of Fixed-point arithmetic