To solve this problem the exponent is stored as an unsigned value which is suitable for comparison, and when being interpreted it is converted into an exponent within a signed range by subtracting the bias.
The purpose of this is to enable high speed comparisons between floating-point numbers using fixed-point hardware.
[2] Therefore, the possible integer values that the biased exponent can express lie in the range
bits in the exponent, the possible unsigned integers lie in the range
However, the strings containing all zeros and all ones are reserved for special values, so the expressible integers lie in the range
It follows that: When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent.
The floating-point format of the IBM 704 introduced the use of a biased exponent in 1954.