Break the base

Consider the following number: abcdefg Each letter stands for a different place. "g" is the ones place, "f' is the tens, "e" is the hundreds, and so on. This is true regardless of base. So when we look at 100 in base 10, we see that we have zero ones, zero tens, and one hundred. That of course gives us 100.

The trick is looking at the different places as exponents of the base. So the ones place is actually 10^0, the tens is 10^1, the hundreds is 10^2, etc. The same will be true when we write a number in base 2. The ones place will be 2^0, the tens 2^1, the hundreds 2^2, etc.
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