I don't understand the math of binary code.

binary, or base 2, works just like base 10, the 'normal' counting system. each position in a number starting from the right and going left is an integer exponent of the base, starting with 0, so 2^0, or 10^0. anything to the 0 power is 1, and a 1 in that position means there is 1 base^0 in the number. 0 would mean 0. when the number in a given position goes beyond the base-1, so 1 in binary, or 9 in base 10, you add a position to the left. so in base 10, the highest we go in the 1s (or 10^0) position, is 9 (10-1), and in base 2, it would be 1 (2-1). the position we add to the left of base^0 is base^1. in base 10 that's the tens position, because 10^1=10. in binary, it's the 2s (2^1=2). any number is expressed like this and is made up of however many are in its left-most position, plus however many in the next to the right, etc. so 123 in base 10 is 1 10^2 (100) plus 2 10^1 (20) plus 3 10^0 (3)==100+20+3==123. in base 2 it would be 1 2^6 (64) plus 1 2^5 (32) plus 1 2^4 (16) plus 1 2^3 (8) plus 0 2^2 (0) plus 1 2^1 (2) plus 1 2^0 (1) == 1111011.