Numbering System: Part-1

Numbering System: Part-1

How did the counting process start?

At the very beginning, the ancient people count something with the help of small pieces of stones or with the help of likely solid substances. But it is no more comfortable way when they learnt to scratch on the surface of the stones and on the wall of the cave or on the ground. They scratched a single line for each single thing they ware counting. But it was not again comfortable for large number of things. So they changed the way. They took more symbols and start counting and this time it was more easier than before. But what was the logic behind their counting system?

Lets go for a overview of mostly used decimal numbering system. Here the base is ten. It is called the radix of the decimal numbering system. Here we can say the there are ten basic symbols. The ten basic symbols are '0','1','2','3','4','5','6','7','8','9'. Probably you have noticed that obviously there is an order. So we can say that decimal number is based on ten basic ordered symbol. Probably it is not so clear to you. Now come to the point, count zero to forty-nine and write it. Here is the form:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Now place an extra 0 before the single numbers. Here my intention is to upgrade every number to two digit. Now this is the form:
00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49


Now look at the first digit of the first ten numbers. Yap, you are right, it is 0 (zero) then look at the second digit and you will see that it is the basic ordered symbols. Now look at the first digit of the next ten numbers. You are right, it is 1, the second basic ordered symbol. And now look at the second digits, it is again the ten basic ordered symbol you have noticed for the case of 0 as the first digit. Do this again and again for the next ten numbers. If we assume that two or more basic symbols form the secondary single symbol. For example, 1 and 2 makes 12, here 1 and 2 are basic symbols and 12 is secondary symbol. Then it is always true that the ordered basic symbols will be repeating after every ten numbers and the previous secondary symbol increased by one after every period. This is the logic behind the decimal numbering system.