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   x = c * (2**p)   # the value you want to express
   c                # the coefficient
...
   
   x = k * (10**-n) # since n is finite and k is an integer, 
                    # x is exactly representable in decimal

x       c*(2**-n)   binary      decimal         d   log10(x)
1/2     1*(2**-1)   0b0.1       0.5             1   -0.301029996
...
5/128   5*(2**-7)   0b0.0000101 0.0390625       2   -1.408239965
9/128   9*(2**-7)   0b0.0001001 0.0703125       2   -1.152967460
13/128  13*(2**-7)  0b0.0001101 0.1015625       1   -0.993266617

1.0000 0000 0000 000f ffff ffff ffff ffff ffff ffff ffff ffff ffff
  ^1              16^                                          52^    
+  
      
  ^ points to the nth digit after decimal point