Exponent bias
Encyclopedia
In IEEE 754 floating point
numbers, the exponent is bias
ed in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias.
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.
To solve this problem the exponent is biased before being stored, by adjusting its value to put it within an unsigned range suitable for comparison.
By arranging the fields so that the sign bit is in the most significant bit position, the biased exponent in the middle, then the mantissa in the least significant bits, the resulting value will be ordered properly, whether it's interpreted as a floating point or integer value. This allows high speed comparisons of floating point numbers using fixed point hardware.
When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent.
Floating point
In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...
numbers, the exponent is bias
Bias
Bias is an inclination to present or hold a partial perspective at the expense of alternatives. Bias can come in many forms.-In judgement and decision making:...
ed in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias.
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
Two's complement
The two's complement of a binary number is defined as the value obtained by subtracting the number from a large power of two...
, the usual representation for signed values, would make comparison harder.
To solve this problem the exponent is biased before being stored, by adjusting its value to put it within an unsigned range suitable for comparison.
By arranging the fields so that the sign bit is in the most significant bit position, the biased exponent in the middle, then the mantissa in the least significant bits, the resulting value will be ordered properly, whether it's interpreted as a floating point or integer value. This allows high speed comparisons of floating point numbers using fixed point hardware.
When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent.
- For a single-precision number, an exponent in the range −126 .. +127 is biased by adding 127 to get a value in the range 1 .. 254 (0 and 255 have special meanings).
- For a double-precisionDouble precisionIn computing, double precision is a computer number format that occupies two adjacent storage locations in computer memory. A double-precision number, sometimes simply called a double, may be defined to be an integer, fixed point, or floating point .Modern computers with 32-bit storage locations...
number, an exponent in the range −1022 .. +1023 is biased by adding 1023 to get a value in the range 1 .. 2046 (0 and 2047 have special meanings). - For a quad-precision number, an exponent in the range −16382 .. +16383 is biased by adding 16383 to get a value in the range 1 .. 32766 (0 and 32767 have special meanings).