Normal number (computing)In computing, a normal number is a non-zero number in a floating-point representation which is within the balanced range supported by a given floating-point format: it is a floating point number that can be represented without leading zeros in its significand.
Floating-point arithmeticComputer approximation for real numbersAn early electromechanical programmable computer, the Z3, included floating-point arithmetic (replica on display at Deutsches Museum in Munich).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.SignificandThe significand (also coefficient, sometimes argument, or more ambiguously mantissa, fraction, or characteristic) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. For negative numbers, it does not include the initial minus sign.
Exponent biasIn IEEE 754floating-point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias, also called a biased exponent. Biasing is done because exponents have to be signed values in order to be able to represent both tiny and huge values, but two's complement, the usual representation for signed values, would make comparison harder.
Arithmetic underflowThe term arithmetic underflow (also floating-point underflow, or just underflow) is a condition in a computer program where the result of a calculation is a number of more precise absolute value than the computer can actually represent in memory on its central processing unit (CPU).Leading zeroA leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation. For example, James Bond's famous identifier, 007, has two leading zeros. Any zeros appearing to the left of the first non-zero digit before the decimal point do not affect its value, and can be omitted (or replaced with blanks) with no loss of information.IEEE 754-1985IEEE 754-1985 is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. During its 23 years, it was the most widely used format for floating-point computation. It was implemented in software, in the form of floating-point libraries, and in hardware, in the instructions of many CPUs and FPUs.
Sign (mathematics)In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign. In some contexts, it makes sense to distinguish between a positive and a negative zero.
RadixNumber of digits of a numeral system In a positional numeral system, the radix (pl. radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, in decimal systems (the most common systems in use today) the radix is ten. In any standard positional numeral system, a number is conventionally written as (x)y with x as the string of digits and y as its base.Significant figuresSignificant figures, also referred to as significant digits, are specific digits within a number that is written in positional notation that carry both reliability and necessity in conveying a particular quantity.
Computer scienceStudy of computationFundamental areas of computer scienceProgramming language theoryComputer architectureArtificial intelligenceComputational complexity theoryComputer science is the study of computation, information, and automation, together with their associated phenomena.
IEEE 754-2008 revisionIEEE 754-2008 (previously known as IEEE 754r) is a revision of the IEEE 754 standard for floating-point arithmetic. It was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 standard.IEEE 754The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard.
Floating-point arithmeticComputer approximation for real numbersAn early electromechanical programmable computer, the Z3, included floating-point arithmetic (replica on display at Deutsches Museum in Munich).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.SignificandThe significand (also coefficient, sometimes argument, or more ambiguously mantissa, fraction, or characteristic) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. For negative numbers, it does not include the initial minus sign.Exponent biasIn IEEE 754floating-point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias, also called a biased exponent. Biasing is done because exponents have to be signed values in order to be able to represent both tiny and huge values, but two's complement, the usual representation for signed values, would make comparison harder.Arithmetic underflowThe term arithmetic underflow (also floating-point underflow, or just underflow) is a condition in a computer program where the result of a calculation is a number of more precise absolute value than the computer can actually represent in memory on its central processing unit (CPU).Leading zeroA leading zero is any 0 digit that comes before the first nonzero digit in a number string in positional notation. For example, James Bond's famous identifier, 007, has two leading zeros. Any zeros appearing to the left of the first non-zero digit before the decimal point do not affect its value, and can be omitted (or replaced with blanks) with no loss of information.IEEE 754-1985IEEE 754-1985 is a historic industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. During its 23 years, it was the most widely used format for floating-point computation. It was implemented in software, in the form of floating-point libraries, and in hardware, in the instructions of many CPUs and FPUs.Sign (mathematics)In mathematics, the sign of a real number is its property of being either positive, negative, or 0. Depending on local conventions, zero may be considered as having its own unique sign, having no sign, or having both positive and negative sign. In some contexts, it makes sense to distinguish between a positive and a negative zero.RadixNumber of digits of a numeral system In a positional numeral system, the radix (pl. radices) or base is the number of unique digits, including the digit zero, used to represent numbers. For example, in decimal systems (the most common systems in use today) the radix is ten. In any standard positional numeral system, a number is conventionally written as (x)y with x as the string of digits and y as its base.Significant figuresSignificant figures, also referred to as significant digits, are specific digits within a number that is written in positional notation that carry both reliability and necessity in conveying a particular quantity.Computer scienceStudy of computationFundamental areas of computer scienceProgramming language theoryComputer architectureArtificial intelligenceComputational complexity theoryComputer science is the study of computation, information, and automation, together with their associated phenomena.IEEE 754-2008 revisionIEEE 754-2008 (previously known as IEEE 754r) is a revision of the IEEE 754 standard for floating-point arithmetic. It was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 standard.IEEE 754The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard.*As an Amazon Associate I earn from qualifying purchases.