Counting and Abacus

Reference: Course on Subject Clearing


This video explains counting and the Rule of Abacus.

Mathematics starts with Arithmetic, and Arithmetic starts with counting. We learn to count on our fingers as follows.

We have two hands with a total of ten fingers. We can count with these fingers to find out how many things there are.

But to count beyond ten, it requires many hands. Alternatively, we can use an Abacus.


The Abacus

An abacus is a counting board on which one can count to very large numbers. It has many wires. On each wire there are ten beads.

The count appears on the abacus when beads are moved to the right. The count on a wire is the number of beads on the right.


The Rule of Abacus

“When all beads are counted to the right on a wire, they are replaced by counting one bead to the right on the next wire.”

Obviously, when there is no bead on the right, the count is zero.


Counting beyond Ten

We count beyond 10 by moving beads on the first wire again.

Today, we may not use the abacus, but we still use the Rule of Abacus in our numbering system.

After 19, the next number is 20.
After 29, the next number is 30.

After 89, the next number is 90.
After 99, the next number is 100.


Computers and Binary Numbers

In our computers we use the numbers made up of 0’s and 1’s. These binary numbers may be created on an abacus that has only 2 beads on each wire. The Rule of Abacus applies to this “binary abacus” also.

The number of beads on a wire represent the “base” of the numbering system.

If you imagine an abacus with two beads on each wire, it will use the digits 0 and 1 only, because when two is counted the rule of abacus will apply and the number “two” will appear as “10”. The number “three” will appear as “11”.  At “four” the rule of abacus will be applied twice. The number “four” will appear as “100”. You may construct all binary numbers this way.


Check your Understanding

1. What is Counting?

The traditional way of counting consists of calling the first item as ONE, the next item as TWO, and so on. Counting can go on forever.


2. What is the Rule of Abacus?

The RULE OF ABACUS is, “When all beads are counted to the right on a wire, they are replaced by counting one bead to the right on the next wire.”


3. How is the Rule of Abacus helpful?

You need only as many digits to write the numbers as there are beads on a wire of abacus. One of those digits is always 0 (Zero). This is very useful when there are only two polarities to represent numbers as in the case of electronic computers.


Final Thoughts

The very fact of counting makes mathematics fundamentally discrete. It cannot duplicate continuous reality, such as, the reality of PI (𝜋).

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