My ping pong ball computer

How does it work

Computers use binary numbers when they calculate. In the binary number system we have only got the two symbols "0" and "1". A symbol in the binary number system can be represented mechanically by a tilting "arm" with two stable positions. The figures to the right show a tilting arm in each of the two positions.
"0"
"1"
How large number can we represent by for example a 4 digit binary number?
  • In the decimal number system we have got 10 symbols (0-9). A four digit number can have (10*10*10*10)=1000 different values (0-9999).
  • In the binary number system we have got two symbols (0 and 1). A four digit number can have (2*2*2*2)=16 different values (0-1111).
To the right you can see examples of counting in the decimal and binary number systems.
  • In the decimal number system we get a carry and have to take into use a new digit when a digit passes 9. 
  • In the binary number system we get carry and have to take into use a new digit when we pass 1. 
As we in the decimal number system have got "ones", "tens", "hundreds" and "thousands", the binary number system has got "ones", "twos", "fours", "eights" and so on. 
0000
0001
0002
0003
0004
0005
0006
0007
0008
0009
0010
0011
0012
....
9998
9999
0000 =   0
0001 =   1
0010 =   2
0011 =   3
0100 =   4
0101 =   5
0110 =   6
0111 =   7
1000 =   8
1001 =   9
1010 = 10
1011 = 11
1100 = 12
1101 = 13
1110 = 14
1111 = 15
My calculator calculates with four digit numbers. Thus it can calculate with numbers between 0 and 15. To let the ping pong ball pass from digit to digit the digits are placed above one another instead of in a row. Theleast significant digit (right digit) is on the top. 1
0
1
0  =  5
0
0
1
1  =  12

 

A ping pong ball counter

Here I have shown a ping pong ball counter that can count up to three.
The red lines show the possible trails the ball can follow between the digits in the counter.
1

The counter shows:
'00'  =  0

2
One ball has passed through.
The counter shows:
'01'  =  1
3
Yet another ball.
The counter shows:
'10'  =  2
4
The last ball.
The counter shows::
'11'  =  3
What happens if you add a ball when the counter shows 3?  And still one more?

What happens if we add bore counter modules on top of each other?

The answers to these questions illustrate a property of the way computers usually calculate. 
Usually we see the numbers in a straight row from minus infinity to pluss infinity.
Computers instead use a circular number line. Below you can see an example:

Calculation on a circular number line from 0 to 7 is called calculation modulo 8.
Some examples:
1+1 => 2
2+4 => 6
7+1 => 0
7+2 => 1
2-1 => 1
2-4 => 6


 
 

A ping pong ball adder

Here I have shown a ping pong ball adder that can add three digit numbers (0-7).
The adder computes A + B = SUM. The two numbers to be added are first set one in each coloumn by tilting the arms to the correct side. A is set to the left as a binary number with the digits A2, A1, A0. B is set to the right with the digits B2, B1, B0. 

Add one ball on the top, and the sum modulo 8 can be read in the right coloumn.

More numbers can be added to the sum by entering them in the left coloumn and adding balls on the top.

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Last modified 22-Jan-00