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How does this work?

Converting between bases is really quite simple. You have to understand the powers of the base of the number. This rule applies for any base. Lets use binary for example. 10110 is a value in binary. Ok but how to we understand it. Well first lets look at the length of the number as in digits. We see it is five digits long. That simply means we multiply the first number by 2 (since it is base 2) to the 4th power, as 4 is the 5th digit. For every other digit in the number this applies although we subtract 1 from the exponent. So lets try this for 10110. (1 * 2^4) + (0 * 2^3) + (1 * 2^2) + (1 * 2^1) + 0 = 22. There we go, we have recived a conversion between base 2 binary and our standard number base, base 10 or decimal