Generating a bias.

  Problem: all zeros and all ones used to flag special conditions.

  Solution: shift (bias) representation of zero exponent up the number line.


Shift representation of exponent 0 to middle of range.
  Use formula 2^(n-1) - 1 where n is the size of the exponent.

  For our example using 7 bit exponent, calculate bias

    2^(7-1)-1 = 63 bias

Recall that we converted the original value to binary form of scientific
  notation.

  1.10 1110 0101 0110 00 * 2^-2
    So, our exponent is -2.

Biasing this exponent gives :
  * Add bias to exponent

  -2 + 63 = 61 = 011 1101 
                  (1x32+1x16+1x8+1*4+0*2+1*1)
                      48    +   12   +  1
                           60        +  1  
                                       61

  (remember to left pad exponent with zeros, it is a 7 bit number)


Finally, we need to record the sign of the whole value  .431 is positive.

  Sign bit 0 (positive)
  Biased Exponent 011 1101
  Significand 1011 1001 0101 1000

  Floating point 0 0111101 1011100101011000

Conversion back