INTRODUCING "OR GATES"
Suppose you need to add one more bottle, but you wish to place it in the same box you use for the red bottle. Suppose the bottle is clear and the sensor will look for the brown liquid in the bottle.

You would add a gate where if A or B = 1, C = 1.

The gate you add is called an "OR Gate."

If you look at the uppermost level of the gates, you will see that the binary "word" driving the drop of the red box is "1000." At the next level down, the word becomes "1010." If we look at all of the possibilities available with four lines, we see the following:

0000 = 0
0001 = 1
0010 = 2
0011 = 3
0100 = 4
0101 = 5
0110 = 6
0111 = 7
1000 = 8
1001 = 9
1010 = A
1011 = B
1100 = C
1101 = D
1110 = E
1111 = F

This adds up to 16 characters. Since our counting system cannot handle base-16, we create a new one that uses six alphabetical characters. If we begin with a binary counting system, it is not possible to end up with a base-10 system.

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To make it possible to have either one color or the other drop the same box, you add an OR Gate.