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The arithmetical difference between two consecutive representable floating-point numbers which have the same exponent is called a unit in the last place (ULP). For example, if there is no representable number lying between the representable numbers 1.45a70c22 hex and 1.45a70c24 hex , the ULP is 2×16 −8 , or 2 −31 .
In the floating-point case, a variable exponent would represent the power of ten to which the mantissa of the number is multiplied. Languages that support a rational data type usually allow the construction of such a value from two integers, instead of a base-2 floating-point number, due to the loss of exactness the latter would cause.
In 1946, Arthur Burks used the terms mantissa and characteristic to describe the two parts of a floating-point number (Burks [11] et al.) by analogy with the then-prevalent common logarithm tables: the characteristic is the integer part of the logarithm (i.e. the exponent), and the mantissa is the fractional part.
binary real values are represented in a binary format that includes the mantissa, the base (2, 8, or 16), and the exponent; the special values NaN, -INF, +INF , and negative zero are also supported Multiple valid types ( VisibleString, PrintableString, GeneralString, UniversalString, UTF8String )
The integer n is called the exponent and the real number m is called the significand or mantissa. [1] The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the fractional part of the common logarithm. If the number is negative then a minus sign precedes m, as in ordinary decimal notation.
Python supports normal floating point numbers, which are created when a dot is used in a literal (e.g. 1.1), when an integer and a floating point number are used in an expression, or as a result of some mathematical operations ("true division" via the / operator, or exponentiation with a negative exponent). Python also supports complex numbers ...
Of these, the subnormal numbers represent values which if normalized would have exponents below the smallest representable exponent (the exponent having a limited range). The significand (or mantissa) of an IEEE floating-point number is the part of a floating-point number that represents the significant digits .
A 2-bit float with 1-bit exponent and 1-bit mantissa would only have 0, 1, Inf, NaN values. If the mantissa is allowed to be 0-bit, a 1-bit float format would have a 1-bit exponent, and the only two values would be 0 and Inf. The exponent must be at least 1 bit or else it no longer makes sense as a float (it would just be a signed number).