Introduction

In math subject, we see different types of numbers that are expressed in different ways. In short, we can also say that mathematics is a way to represent numbers. There are different types of numbers in math, all those types of numbers are given below:

  1. Binary number system (base 2)
  2. Octal number system (base 8)
  3. Decimal number system (base 10)
  4. Hexadecimal number system (base 16)

You can not deny the fact that in computer architecture, numbers have great importance, they play a major role in it. However, apart from the computers, there are various other electronic devices also that are based on number systems of math. Due to all these things, you should learn about how numbers are converted from one type to another. If you don’t know about the conversion of numbers from one type to another then you are at the right place. Here, you will get to learn about such conversion of numbers. We will make it easy for you to do binary to decimal conversion.

What do you understand by a binary number system?

You must have seen it or read about it either in your math book or computer book. This type of number system is only based on 2 numbers and those two numbers are 0 and 1. The whole computer language is based on these two numbers. After knowing about the binary number system, you also need to know about the decimal number system.

What do you understand by a decimal number system?

Whereas in a binary number system only two digits are used just like that a decimal number system is based on ten digits I.e. 0 to 9. You can also call it the base 10 numeral system. The numbers that are written or represented on the left side to the decimal represent the different values such as tenth, hundredth, thousandth, etc.

Conversion of binary numbers to decimal numbers

When it comes to converting binary numbers to decimal numbers, the multiplication method is brought into use. In this process of conversion, if a number that is having a base n to a base 10 then every digit that is given in the number is to be multiplied from MSB to LSB along with the reduction in the power of the base. MSB and LSB stand for a most significant bit and least significant bit respectively. We can also understand this process with an example, (1101)², you need to convert this value from binary to decimal in the following manner:

1X2³ + 1 X 2² + 0 X 2¹ + 1 X 2°, when you will calculate it, you will 8 + 4 + 0 + 1 as the answer. And on adding these numbers you will get 13. It means the value of binary number (1101)² is 13.

Just like this, for decimal to binary conversion, you need to follow a different process.

Conversion of decimal to binary numbers

  • In the first step, you need to divide the given number by 2. You may even get a remainder in the answer.
  • Having the remainder in the answer will depend on the number that is being divided. If you are dividing an even number then the remainder will be 0 and if you will be dividing an odd number by 2 then you will get 1 in the remainder.
  • After following the points given above, all you need to do is to place the remainders in the required way and that way is placing the LSB at the top position and MSB at the bottom position. By doing this, you will get the binary number.

By doing practice of these conversions, you will start finding them easy. However, there are many online sites also that can help in learning about these conversions. You can visit Cuemath and learn about these conversions in detail with easy examples. You can also watch online videos.

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Raushan Kumar
A Cook, Software analyst & Blogger.

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