Conversion between different number systems

Hello, everyone!
Today, we will learn how the different number systems get converted. In this article, with the help of examples, you will get an idea about conversion from one base to another, including:

• Binary to Decimal Number System
• Decimal to Binary Number System
• Octal to Decimal Number System
• Hexadecimal to Decimal Number System
• Octal to Binary Number System
• Binary to Octal Number System
• Binary to Hexadecimal Number System
• Hexadecimal to Binary Number System

First of all, let me explain the concept in a little more detail. The number system is a way of writing or giving representation to numbers using symbols under certain rules. There are four types of number systems:

• Binary - Base 2
• Decimal - Base 10
• Octal - Base 8
• Hexadecimal - base 16

Binary to Decimal Number system

We want, for example, 110₂ to convert to a decimal number, which is 6. How did we do it?
Write the power of two from right to left under each digit. As you go left, the exponent begins at 0 and increases by one for each next digit.
Let's look at the example:
The rightmost 0 is the "ones" place (2⁰).
The middle 1 is the "twos" place (2¹).
The leftmost 1 is the "fours" place (2²).
For each binary digit, multiply it by its corresponding power of 2:
Then, write down the power of 2 under each binary digit, multiply them, and add

Decimal to Binary Number System
In our daily life, we use decimal numbers; as an example, let's take 12. We want to convert it into base 2; it would be 1100. In converting a decimal number to its binary form, the decimal number is repeatedly divided by 2, and the remainder obtained at every step is noted. The binary equivalent is obtained by reading the remainders from bottom to top.

Octal and Hexadecimal to Binary Number System
This process is similar to converting between decimal and binary. Instead of dividing by 2 (as in binary), you divide by 8 for octal and by 16 for hexadecimal.

331 = 14B

461 = 715

Octal and Hexadecimal to Binary Number System
To convert the number from octal into binary, each digit of the given number should be written as a three-digit binary number (triple) for octal and as a four-digit binary number for hexadecimal, and then combined. You'll see how it will work in the example.

Binary to Octal and Hexadecimal Number System
Actually, it works pretty similarly, and the above example works, too. To convert the binary number to octal or hexadecimal, you have to divide the binary number into groups of 3 digits for octal and 4 digits for hexadecimal starting from the right. If there are not enough digits in the last group on the left, fill up with leading zeros.