What Is the Binary Arithmetic System?

In our daily life we use the decimal arithmetic system for our calculations. On the other hand computers do not use the decimal system but the binary one. If someone wants to easily understand the binary system it is good to start realizing some meanings for the decimal system and then apply them to clarify the binary system. This article is going to shortly, clearly and effortlessly explain what the binary system is.

In the decimal system we can construct every decimal number using 10 unique digits which are the following: 0,1,2,3,4,5,6,7,8,9. This is the reason we say that the base of the decimal system is 10. So for instance, the decimal number 1034 consists of the digits 1, 0, 3 and 4. By getting digits from 0 to 9 we can construct every string of a decimal number. The digits might be repeated or not. For example the number 1041 is a valid decimal number even though the digit 1 repeats twice.

Each decimal number has 2 major characteristics. The first one is the digits of which it consists of and the second one is the place of the digits. What do we mean with the term place? Let’s take as an example the number 123. You see that the digit 3 defines units, the digit 2 defines decades (10 times the units) and the digit 1 defines hundreds (100 times the units). So we can say that the most significant (the most weighted factor) digit is the left one and the least significant digit is the right one. In our case the most significant is the digit 1 and the least significant is the digit 3.

Now, we can easily explain and understand the binary system. In relation to the decimal system the binary system consists of numbers made by unique digits 0 and 1. Since these digits are only 2 this is the reason we call it binary system. The base of the binary system is 2. By getting digits from 0 to 1 we can construct every string of a binary number. For example the number 101010101 is a valid binary number. The number 1012010 is not valid because it uses the digit 2 which is not valid binary digit. The most significant digit is the left one and the least significant digit is the right one exactly the same as the decimal system. I would like to notice that computers and in general electronic devices use this system because they can get one of two unique states every moment, to have voltage (or current) or not.

So far we have clarified some meanings of the decimal system and applied them to the binary system aiming to easily understand it. I hope you enjoyed this article.