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When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent. For a half-precision number, the exponent is stored in the range 1 .. 30 (0 and 31 have special meanings), and is interpreted by subtracting the bias for an 5-bit exponent (15) to get an exponent value in the range −14 .. +15.
In computing, half precision (sometimes called FP16 or float16) is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. It is intended for storage of floating-point values in applications where higher precision is not essential, in particular image processing and neural networks .
Dalton's law, in chemistry and physics, states that the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture. Also called Dalton's law of partial pressure, and related to the ideal gas laws, this empirical law was observed by John Dalton in 1801.
The exponent field is biased by 16383, meaning that 16383 has to be subtracted from the value in the exponent field to compute the actual power of 2. [20] An exponent field value of 32767 (all fifteen bits 1 ) is reserved so as to enable the representation of special states such as infinity and Not a Number .
In single precision, the bias is 127, so in this example the biased exponent is 124; in double precision, the bias is 1023, so the biased exponent in this example is 1020. fraction = .01000… 2 . IEEE 754 adds a bias to the exponent so that numbers can in many cases be compared conveniently by the same hardware that compares signed 2's ...
Biased representations are now primarily used for the exponent of floating-point numbers. The IEEE 754 floating-point standard defines the exponent field of a single-precision (32-bit) number as an 8-bit excess-127 field. The double-precision (64-bit) exponent field is an 11-bit excess-1023 field; see exponent bias.
The exponent is usually shown as a superscript to the right of the base as b n or in computer code as b^n. This binary operation is often read as "b to the power n"; it may also be called "b raised to the nth power", "the nth power of b", [2] or most briefly "b to the n".
The number 123.45 can be represented as a decimal floating-point number with the integer 12345 as the significand and a 10 −2 power term, also called characteristics, [11] [12] [13] where −2 is the exponent (and 10 is the base). Its value is given by the following arithmetic: 123.45 = 12345 × 10 −2.