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Boxing is the operation of converting a value of a value type into a value of a corresponding reference type. [15] Boxing in C# is implicit. Unboxing is the operation of converting a value of a reference type (previously boxed) into a value of a value type. [15] Unboxing in C# requires an explicit type cast. Example:
Implicit type conversion, also known as coercion or type juggling, is an automatic type conversion by the compiler. Some programming languages allow compilers to provide coercion; others require it. In a mixed-type expression, data of one or more subtypes can be converted to a supertype as needed at runtime so that the program will run correctly.
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
Conversion of the fractional part: Consider 0.375, the fractional part of 12.375. To convert it into a binary fraction, multiply the fraction by 2, take the integer part and repeat with the new fraction by 2 until a fraction of zero is found or until the precision limit is reached which is 23 fraction digits for IEEE 754 binary32 format.
In the IEEE standard the base is binary, i.e. =, and normalization is used.The IEEE standard stores the sign, exponent, and significand in separate fields of a floating point word, each of which has a fixed width (number of bits).
When a number is represented in some format (such as a character string) which is not a native floating-point representation supported in a computer implementation, then it will require a conversion before it can be used in that implementation. If the number can be represented exactly in the floating-point format then the conversion is exact.
Fast Half Float Conversions; Analog Devices variant (four-bit exponent) C source code to convert between IEEE double, single, and half precision can be found here; Java source code for half-precision floating-point conversion; Half precision floating point for one of the extended GCC features
The most common use case is the conversion between IEEE 754 binary32 and bfloat16. The following section describes the conversion process and its rounding scheme in the conversion. Note that there are other possible scenarios of format conversions to or from bfloat16. For example, int16 and bfloat16. From binary32 to bfloat16.