A basic diagram of how my Binary Counting machine works.

Now for a very interesting thing I discovered about the binary Adding machine.
Looking at the link may help you to understand what I mean by 'switches' and 'slopes'.

There are (dependant on the amount of K'nex you have) infinite switches on a vertical column, with slopes beneath, to direct the ball to the desired place.

attached are the layouts to add the numbers 1 - 8 to whatever number is currently on the machine.

Now for the interesting part:

Label each switch as the bits to make up the binary of number you're adding, so 1 would be:

1
0
0
0

and 5 would be

1
0
1
0

etc.

The Four rules:

a) the top '1' is the first switch changed (so for 3 it would be switch 1, but 4 would be switch 3 - any switches above this one are left unchanged).

b) A left-pointing slope beneath a right one (or vice versa) must have an extended slope.

c) A '0' switch means that the slopes above point right.

d) A '1' switch means that the slopes above point left.