How do you convert 10001 base 2 into base 10?

Base 2 works like this: the first digit (from the right) is worth 1, next over is worth 2, next over is worth 4, and so on multiplying by 2 each time (Other bases work the same but multiply by whatever base it is, such as multiplying by 10 for base 10). So:

1=1

0=2

0=4

0=8

1=16

If it's a 1, you add it in, if it's a zero, you don't add it in. So, ignoring the zeros:

1=1

1=16

Add those up and get 17.