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Getting to Know the Binary Numbers System

Whether you know it or not, you as a human being are accustomed to certain number systems from birth. It is important to live your daily lives knowing that you can count to a reasonable degree. The number system we use as human beings is the Decimal Numbers system. That is not our focus today. Today we will be taking a look at the Binary Numbers system.

You might also be interested in knowing how to do Binary arithmetic here. There you will learn how to do Binary addition and Subtractions as well as Binary multiplication and division.

Before we talk about Binary, it is good to know there are a bunch of number systems. These all work similarly to each other. It is just the way they are clustered. In addition to the two mentioned earlier, there are two other common number systems used today. These are Hexadecimal, and Octal Number systems.

Examining the Binary Numbers System

Let’s start with a number system that we are all familiar with. The Decimal Numbers system. As human beings, we have ten digits on our limbs. That ten fingers and ten toes. This makes it convenient for us to count in decimal. If you notice, Decimal derived from the word Deci meaning tenth, groups numbers in clusters of ten or Base-10. These clusters repeat all through to infinity.

The digits used in the Decimal Numbers system are `[0,1,2,3,4,5,6,7,8,9]` . The next numbers in the series are repetitions of these numbers `[10,11,12,13,14,15,16,17,18,19]` and so on. The initial list of numbers has an implicit leading zero or sets of zeros. The reason why we exclude them is the leading zeros can be infinite and it would just beat the purpose of simplicity when dealing with Number systems.

So What are Binary Numbers?

Binary just like Decimal has a prefix with a meaning. Bi meant in-twos therefore, we can see this number system consists of only 2 digits set in Base-2. The digits used in Binary are `[0,1]`. In this number system, all numbers are represented with only these two digits. So take a number like 275,000 (Decimal), The same number can be represented in Binary as 1000011001000111000. You can see as a human being that number is quite disturbing.

Why would anyone conceive of using Binary Numbers systems for anything? Well because this is the number that computers work with for computation and for addressing and storing things in memory. Remember everything a computer CPU does is to read stuff from memory, process it using some simple arithmetic, and store it back into memory.

This seems trivial but believe me, you can get a lot done with that. Anyway, history goes back to the way the states of electricity work. Either off or one. Off-state is represented by zero and on the state is represented by one.

The following is the layout of Binary numbers from 0 to 9 (Decimal)

``````0 0 0 0   Decimal Value 0
0 0 0 1   Decimal value 1
0 0 1 0   Decimal value 2
0 0 1 1   Decimal value 3
0 1 0 0   Decimal value 4
0 1 0 1   Decimal value 5
0 1 1 0   Decimal value 6
0 1 1 1   Decimal value 7
1 0 0 0   Decimal value 8
1 0 0 1   Decimal value 9``````

In our next article, we will be showing you how to work with the Binary Numbers system and be able to do some arithmetic on the system.

Ref:

http://home.ica.net/~roymanju/Binary.htm – Binary Numbers in Ancient India