Base Two to Base Ten

Recall that X-n means 1/Xn.   So,  2-2 = 1/4  and   2-3 = 1/8.

To convert an expression in base two notation to base ten notation, just do the arithmetic:

1
 
0
 
0
 
 . 
 
1
 
0
 
1


1×22 +
 
0×21 +
 
0×20 +
 
 .
 
1×2-1 +
 
0×2-2 +
 
1×2-3



1×4 +
 
0×2 +
 
0×1+
 
 .
 
1×0.5 +
 
0×0.25 +
 
1×0.125



4 +
 
0  +
 
0 +
 
 .
 
0.5 +
 
0 +
 
0.125


 
 
 
 
4
 
 .
 
625
 
 
 
 

As you work, keep track of what parts of the expression are in base two and what parts are in base ten. In the above, the first row is entierly in base two, the bottom row is entierly in base ten, and the middle rows are mixed.