Float 1 bit sign, 5 bit exponent, 8 bit significand.

Convert the float   11010100110111  to a real

First separate into sign, exponent, significand

    1  10101  00110111

Bias = 2^(5-1) - 1  = 15

Biased exponent :

   10101   1  0  1   0   1
           1  2
              2  4 
                 5  10
                    10  20
                        21

   21 - 15 = 6  actual exponent

Significand    00110111 
Add invisible 1. back    1.00110111 * 2^6
Shift decimal            1001101.11

Integer portion                   Decimal portion

   1  0  0   1   1   0   1        .  
   1  2                           1  * .5     .5
      2  4                        1  * .25    .75
         4   8
             9  18
                19  38
                    38  76
                        77
          
Stored real   -77.75  (remember sign bit set to 1)