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The IEEE 754 standard [9] specifies a binary16 as having the following format: Sign bit: 1 bit; Exponent width: 5 bits; Significand precision: 11 bits (10 explicitly stored) The format is laid out as follows: The format is assumed to have an implicit lead bit with value 1 unless the exponent field is stored with all zeros.
Single precision is termed REAL in Fortran; [1] SINGLE-FLOAT in Common Lisp; [2] float in C, C++, C# and Java; [3] Float in Haskell [4] and Swift; [5] and Single in Object Pascal , Visual Basic, and MATLAB. However, float in Python, Ruby, PHP, and OCaml and single in versions of Octave before 3.2 refer to double-precision numbers.
A Boolean type, typically denoted bool or boolean, is typically a logical type that can have either the value true or the value false. Although only one bit is necessary to accommodate the value set true and false, programming languages typically implement Boolean types as one or more bytes.
In computer science, type conversion, [1] [2] type casting, [1] [3] type coercion, [3] and type juggling [4] [5] are different ways of changing an expression from one data type to another. An example would be the conversion of an integer value into a floating point value or its textual representation as a string, and vice versa.
This means that numbers that appear to be short and exact when written in decimal format may need to be approximated when converted to binary floating-point. For example, the decimal number 0.1 is not representable in binary floating-point of any finite precision; the exact binary representation would have a "1100" sequence continuing endlessly:
The decimal number 0.15625 10 represented in binary is 0.00101 2 (that is, 1/8 + 1/32). (Subscripts indicate the number base .) Analogous to scientific notation , where numbers are written to have a single non-zero digit to the left of the decimal point, we rewrite this number so it has a single 1 bit to the left of the "binary point".
A floating-point format is specified by a base (also called radix) b, which is either 2 (binary) or 10 (decimal) in IEEE 754; a precision p; an exponent range from emin to emax, with emin = 1 − emax, or equivalently emin = − (emax − 1), for all IEEE 754 formats. A format comprises
The standard type hierarchy of Python 3. In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. [1]