No. 10 in base 10 isn't 1. It's 10.

In base 10, numbers are made up of 1's, 10's, 100's, 1000's and so on, because they are 10¹, 10², 10³ and so on.

Base 13 is similar, but it's made up of 13°'s, 13¹'s, 13²'s and so on.

That means that 13 in base 13 is 1*13+3 = 16, half of which is 8.