The Abacus and Numbers

The system of how counting numbers are written today can be demonstrated visually on a device called Abacus. Check it out on this electronic version of abacus where you may drag the beads using your mouse cursor.

Electronic Abacus

You count by moving 1 bead at a time on the first wire on the top. As beads are moved to the right, a “digit” appears at the bottom right, which corresponds to the number of beads moved.

The digit 0 corresponds to no bead moved.
The digit 1 corresponds to one bead moved.
The digit 2 corresponds to two beads moved.
The digit 3 corresponds to three beads moved….
 
And so on.
 

When all the ten beads are moved to the right on the wire you may find that they are automatically regrouped as one bead to the right on the next wire. Thus, TEN is expressed as a combination of one bead on the second wire and no bead on the first.

In terms of digits, TEN is expressed as “10”.

Please note that the place of a digit in a number corresponds to the order of the wire from the top.

As you continue to count, the beads are regrouped not only on the first wire but also on subsequent wires per the following rule:

WHEN ALL BEADS ON A WIRE ARE TO THE RIGHT, THEY ARE REGROUPED AS ONE BEAD TO THE RIGHT ON THE NEXT WIRE.

For further details, please see, Numbers and Place Values.

  

NUMBER BASE

We are used to dealing with numbers in the decimal system, where we use a base of 10, counting up from 0 to 9 and then resetting our number to 0 and carrying 1 into another column. This is probably a result of having ten fingers.

Suppose we had only eight fingers, then we would most probably work in base 8, counting from 0 up to 7 and then resetting to 0 and carrying 1. So the number 10 in this system would mean 8 in the decimal system. Base 8 is called the Octal system.

OCTAL NUMBERS MAY BE REPRESENTED BY A SPECIAL VERSION OF ABACUS WITH EIGHT BEADS ON EACH WIRE INSTEAD OF TEN.

If an intelligent race had only two fingers, then it would most probably work in base 2, counting from 0 up to 1 and then resetting to 0 and carrying 1. So the number 10 in this system would mean 2 in the decimal system. Base 2 is called the Binary system.

BINARY NUMBERS MAY BE REPRESENTED BY A SPECIAL VERSION OF ABACUS WITH ONLY TWO BEADS ON EACH WIRE INSTEAD OF TEN.

Using this “binary abacus” it can be seen that the decimal numbers 1, 2, 3, 4, 5, 6, 7, 8, etc., will appear as 0, 1, 10, 11, 100, 101, 110, 111, 1000, etc., respectively.

The binary numbers may be represented very accurately with a series of switches, each of which can be set to either OFF or ON corresponding to 0 and 1. This is the secret underlying the powerful computers.

The elegance of abacus is that young children can use this device to learn different number systems quite easily.

 
 
 
Note: An Octal and Binary version of Electronic abacus may be added.

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