Exponent bias

The floating point format of the IBM 704 introduced the use of a biased exponent in 1954.

In IEEE 754 floating point numbers, the exponent is biased 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.

To calculate the bias for an arbitrarily sized floating point number apply the formula 2^k−1 − 1 where k is the number of bits in the exponent.

When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent.

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