What is Binary number system and how to convert it to decimal system?

The counting system that we usually follow is that of decimal system. A decimal system has base 10. The number system that is particularly followed in a computer or digital devices is that of binary system which has base 2 and consists only of two digits 0 and 1. We human beings do the entire calculations and express our numeric acumen with base 10, i.e. in the decimal system. But these electronic and digital devices are build around the concept of binary so he obvious question is that how can we interact with a system which does not follow the basic number system that we follow. The answer to this is quite simple. We follow a conversion method where the data entered by us in the form of decimal system gets converted to binary system so that the machine could interpret, comprehend and calculate and finally covert it back to decimal so that we can understand the results.

A binary digit is represented as 10001110. it is to be noticed that the bit which is at the far right is 0, and is known as Least significant bit and the bit which is located on the far left is called as the most significant bit. The binary system has a well defined chronology for the sequence and number of bits arranged. For instance a collection of four bits is termed as nibble and a collection of two nibbles or 8 bits is called as a byte. A word is comprised of 16 bits and similarly a paragraph is composed of 64 bits. One important distinction to be mentioned is appropriate here that binary digits 0 and 1 are also present is decimal system. Thus a number written in binary can also be deciphered in decimal and vice-versa. Therefore it is always made a point that a number system should be donated by its base. For instance a binary number should be indicated as base 2 and a decimal number should be denoted as base 10. 1102  will be a binary digit and 11010 will be a decimal number.

The binary number can be converted to the decimal system by following a simple formula:

Say a binary number is 100

We write a code as:

128, 64, 32, 16, 8, 4, 2, 1


After writing the binary number in the code we ascertain all the positive values for 1

In this illustration the total would be 4. Thus the decimal number of binary number 100 will be 4.

Let us consider another example:

If a binary number is 10011100

Then its decimal number would be:


128 + 16+ 8+ 4 = 156

Thus converting binary number system to decimal is very comfortable and involves a rational approach towards the conversion. Once understood it becomes very comprehensive and logical to convert binary data to decimal.