How To Understand Binary System of Number Counting

Well, we are all acquainted with decimal system of number counting. It has ten digits from 0 to 9. We are keeping here counting restricted to what we call as natural numbers, such as 1 mango, 2 mangoes, and so on. Now, what about binary system of number counting where you have only two digits, 0 and 1. We will discuss the concept behind zero as a dummy variable in this article, and would see that whether it is decimal or binary or any other system of number counting, the fundamental rule is the same.

As zero by itself represents nothing while counting, we can call that there are nine core digits in the decimal system. Once nine core digits (1,2,3,4,5,6,7,8,and 9) that represent increasing weightage by 1 unit are exhausted, zero (0) comes into action. It is also logical that 0 (zero) should be preceded by 1 after nine. Thus the number formed is 10.

Zero is thus used as a dummy to move forward with counting. Now, navigating on the escape vehicle that has been devised using 10, it is easier to count nine more mangoes just the same way when we started originally. So, nine following numbers (11,12,13,14,15,16,17,18,and 19) and again we are looking for a number that should follow 9 in 19. So, put zero as savior. This time it will be accompanied by 2 which is a successor of 1. This form of filling would continue up to 99 when we will again run out of constraints of 9 core digits, one dummy digit in the form of zero, and two places. (for easy understanding of what we mean by places in this context here, we can call that all numbers starting with 100 and ending with 999 in decimal system represents three places. While 99 represents two places, 1001 represents four places). Now, this time, 2 zeros come to rescue preceded by 1, and the number formed is 100. And the cycle goes on.

Now, what about binary system of number counting? Here, you have only two digits, 0 and 1. As usual, zero represents nothing (zero mango means there is no mango). So, there is only one core digit which is 1 that in our case represents one mango. Once one core digit (1) is exhausted, how will we count two mangoes? Well again, zero (0) comes into action. So, after 1 is exhausted, you put 0 to count further unit where 0 is preceded by 1. So two mangoes in binary system will read 10. Again to represent three mangoes in binary system, you leverage on zero (in 10 that we saw just now represented two mangoes in binary system) that can be substituted with a weapon in hand 1. So, you have 11 representing three mangoes in binary system, since 10 that represented 2 mangoes left with a scope to change 10 to 11.

You rightly understood that you can only have 10 and 11 as two numbers in binary system using 2 places. You cannot have 00 representing any core number in binary system just as in decimal system. It would simply mean zero (0) or nothing.

Now, what about four mangoes? Well, you are out of resource to represent a number using two places and two digits. Now, you take recourse to three places. This time put 2 zeros preceding 1. So, four mangoes in binary system will read 100. Again for five mangoes, why not start with 101. You are correct. Now, you also rightly guess that starting 100 as binary number, you can have only 101, 110 and 111 as three more representations using three places.

You have already noted that 100 and 101 are logically represented in binary system for four and five mangoes. Now, obviously only six and seven mangoes can be represented by 110 and 111 in binary system. You guess by your hunches that 110 in binary system should represent six mangoes and 111 in binary system should represent seven mangoes. You are absolutely correct. Why? You may now by yourself explain this to your friends.

The concept that rules decimal or binary or octal or any other system of counting that uses zero as dummy variable is the same. Zero which by itself represents nothing comes into action as a joker to fill the vacuum when the number of core digits (such as 9 in decimal system, 1 in binary system, 7 in octal system) are exhausted.

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