How to convert Binary to Decimal ?

In this blog article, we will explore the process of converting a binary number to a decimal number system. Understanding this conversion is essential in computer science and programming, as binary is the fundamental language of computers.

By the end of this article, you will have a clear understanding of the steps involved in converting binary to decimal, allowing you to work with different number systems confidently.

So let's get started!

What are Binary numbers ?

Binary numbers are numbers that are expressed in base-2, meaning that they only contain two digits: 0 and 1. Binary numbers are used to represent data in computers, including digital images, sound, and text.

What is a Decimal number system ?

A decimal number system is a base 10 number system, which means that it uses 10 distinct symbols (0,1,2,3,4,5,6,7,8 and 9) to represent different values.

There are two terms which are used to describe the ordering of bits in a binary number:

• LSB (Least Significant Bit)

  LSB stands for Least Significant Bit and is the bit located at the right most position in a byte or word. It is the lowest order bit and its value is usually 0 or 1.

  For example in the byte

  11010100, the LSB is 0

• MSB (Most Significant Bit

  MSB stands for Most Significant Bit and is the bit located at the left most position in a byte or word. It is the highest order bit and its value is usually 0 or 1.

  For example in the byte

  11010100, the MSB is 1

How to convert Binary to Decimal ?

To convert a binary number to decimal, follow these steps:

1. Start from the rightmost digit of the binary number.

2. Multiply each digit by 2 raised to the power of its position, starting from 0 for the rightmost digit.

3. Add up all the results of the multiplications.

4. The final sum will be the decimal equivalent of the binary number.

You can easily understand by the help of below example

Explanation of above problem

To convert a binary number (100101) to its decimal number, we have to follow these steps:

1. Begin by assigning each digit of the binary number a value based on its position. In binary, the rightmost digit is the 1's place, the second digit from the right is the 2's place, the third digit from the right is the 4's place, and so on.

2. For the number 100101, the values would be:

3. =2^5x1 + 2^4x0 + 2^3x0 + 2^2x1 + 2^1x0 + 2^0x1

   =32x1 + 16x0 + 8x0 + 2^2x1 + 4x1 + 2x0 + 1x1

   =32 + 0 + 0 + 4 + 0 + 1

   =37

4. The decimal equivalent of 100101 is 37.

By following those above steps, you can easily convert any binary to its decimal equivalent.

Conclusion

In conclusion, converting a binary number to its decimal equivalent is a relatively simple process. All you need to do is understand the concept of place values and powers of two, and then apply them to each digit in the binary number. With practice, you will be able to quickly and accurately convert any binary number into its decimal value.