This is the Algodoo only version of my updated reusable 4-bit mechanichal binary adder.
The Phun only version is a response to this scene.
This machine uses the power of gravity to calculate small sums in binary. You give it two numbers and it finds their sum.
It's almost exactly the same machine as the 4-bit adder I made with logic gates way back before Algodoo when I was just RBS. The difference is this time you don't need to reload the scene to reset the machine.
The design is based off of mechanical adder I made in real life out of K'NEX. It can be seen on my blog calvinshobbies.blogspot.com.
INSTRUCTIONS:
At the top of the scene, below the big black box, there are four "input stations" labeled 8, 4, 2, and 1.
Each one has a ball nozzle and four possible slots for a ball to go in: True A, True B, False A, and False B.
You drag balls (with the drag tool) from the nozzles into these slots to define the numbers you want to add.
It's all in binary so
True = green sided slot = 1
and
False = red sided slot = 0
We'll call the two numbers you are adding A and B. You need to convert them to decimal and put them in the correct slots.
EXAMPLE: (hopefully this will clear up the confusion)
Lets say A = 7 and B = 11. Numbers must be between 0 and 15 inclusive.
In binary: (scroll down for a quick binary tutorial)
A = 0111
(0*8 + 1*4 + 1*2 + 1*1 = 7)
B = 1011
(1*8 + 0*4 + 1*2 + 1*1 = 11)
So to input A drag a ball from each nozzle to
False A in the 8 station
True A in the 4 station
True A in the 2 station
True A in the 1 station
And similarly for B
True B in the 8 station
False B in the 4 station
True B in the 2 station
True B in the 1 station
Overall it will look like this (B = ball, N = no ball)
8 N B B N : 4 B N N B : 2 B B N N : 1 B B N N
There should be exactly 2 balls at each "station", not just for 7 and 11, but for any operation.
Now finally, press ENTER to start adding. The balls you chose are dropped and slowly they work their way through the machine.
We know that 7 + 11 = 18, so the result at the bottom (where it says A + B = 00000) should be the binary equivalent of 18 when the machine is done.
In binary 18 is
10010
(1*16 + 0*8 + 0*4 + 0*2 + 0*1)
Try this example and you should get that result.
Then you can try some other numbers, nothing needs to be reset.
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Incidentally, this machine could be easily expanded to add much higher numbers or to do subtraction. It's made up of 3.5 one-bit adder modules that are linked together. Another four adders and you could add up to 1022!
If you are having problems with binary translation or something I'd be glad to help.
If you notice a bug and you are sure you are operating the machine correctly please mention it. It's probably two balls colliding at a path intersection in some special case that would be hard to fix, but still, I'd like to know.
Happy Adding
BINARY TUTORIAL:
Binary is a number system like the decimal number system that we use every day. The difference is that binary (base 2) only has two digits: 0 and 1. In the decimal system (base 10) there are ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
In decimal the digits are put into different places:
ones' place, tens' place, hundreds, thousands, etc.
The places are similar in binary but the factor in between places is two:
ones' place, twos' place, fours, eights, sixteens, etc.
In either system the digit in each place is the number of times that place number appears in the whole number.
For example:
936 (base 10) is equal to:
9 hundreds,
3 tens, and
6 ones
= 9*100 + 3*10 + 6*1 = 936 (base 10)
1101 (base 2) is equal to:
1 eight,
1 four,
0 twos, and
1 ones
= 1*8 + 1*4 + 0*2 + 1*1 (base 10) = 13 (base 10)
= 1*1000 + 1*100 + 0*10 + 1*1 (base 2) = 1101 (base 2)
Basically binary numbers can only contain ones and zeros and the place values are multiplied by two (instead of ten) as you move to the left.
Hopefully that made some sense because you need to know binary to properly use this machine.
