Just 1's

The Concept

A base-b number of the form $a_na_{n-1}a_{n-2}........a_3a_2a_1a_0.c_0c_1c_2c_3.............$ (where the point between $a_0$ and $c_0$ is the radix point) can be expressed in base-10 form by:

$a_n\times b^n+a_{n-1}\times b^{n-1}.............a_1\times b^1+a_0\times b^0+c_0\times b^{-1}+c_1\times b^{-2}...............$

Working in this manner,we get the value(in base-10) of the base 2 numeral as:

$\dfrac12+\dfrac14+\dfrac18..............=1$

Try Geometric Progressions for understanding the summation.