i know it's complicated
But, it's not. A single switch is pressed or not. That's a 0 or 1 in one bit of a binary number. The three bits then look like:
000 = 0
001 = 1
010 = 2
011 = 3
100 = 4
101 = 5
110 = 6
111 = 7
If the columns represent switch states for switches 3, 2, and 1, you can see that pressing switch 3 contributes 4 to the value. Not pressing it contributes 0 to the value. Similarly, pressing switch 2 contributes 2 to the value. Not pressing it contributes 0 to the value. And, pressing switch 1 contributes 1 to the value. Not pressing it contributes 0 to the value. So, your multipliers should be 1, 2, and 4, not 1, 2, and 3.