Binary to Hex Calculator

Definition of Binary and Hex

We often use Binary and Hex numbers while dealing with different branches of science. In fact, depending on their purpose and use, we might need to convert them from one system to another. Here, we would see how we can convert from a Binary number system to the Hex or Hexadecimal number system. However, before that, let us understand what the Binary and Hex number systems are.

The Binary number system is a format of representing numbers using only two digits, 0 and 1. In a number, each digit is referred to as a Bit or a Binary digit and the numbering system is also known as the base-2 numbering system.

The Hex or Hexadecimal number system is a format of representing numbers using a base of 16. Digits from 0-9 and alphabets from A-F are used to represent numbers in this number system.

How to Convert Binary to Hex?

The process of converting Binary to Hexadecimal numbering system is given below.

1. Count the number of digits in the Binary number. If it is not divisible by 4, then add as many zeros as required to the left of the number.
2. Make groups of 4 digits beginning from the right.
3. For the 4-bit groups, write their corresponding decimal numbers.
4. For every 4-bit group, assign the number or alphabet corresponding to the Hexadecimal number system.
5. Write the Hexadecimal numbers or alphabets from left to right.

The final number is your required Hexadecimal number. Let us show this with an example. Let us take the Binary number 1100100101.

Step 1:

• Binary number: 1100100101
• Number of digits: 10
• Since 10 is not divisible by 4, we add 2 more zeros to the left.
• So, the final Binary number: 001100100101

Step 2:

• We make groups of 4 digits in the Binary number we got.

Step 3:

• We write their corresponding decimal numbers below them.

Step 4:

• We write the corresponding Hex numbers in the row below.

Step 5:

The final Hex representation is: (325)16.

Binary to Hex Formula

Converting from Binary to Hexadecimal number systems does not require a formula. Rather, it is a process and follows a few steps. The steps are as given below.

1. Make groups of 4 bits from the right end of the Binary number and write them in a row. Add zeros to the left if required
2. Write the respective decimal number representation of these 4-bit groups in the next row and the corresponding Hexadecimal number below them.

Binary to Hex Conversion Table

Binary number system uses only two bits, whereas the Hexadecimal system uses 16 different bits. Hence, there will be a lot of difference in how a number is represented in the Binary and in the Hexadecimal system. Let us look at how each of the first 16 numbers in Binary is represented in Hexadecimal.

We use different combinations of these Hexadecimal bits to represent each Binary number. Check out the examples given below for a better understanding.

Binary to Hex Solved Examples

Example 1: Convert (10001011111)₂ to Hexadecimal

Following the steps mentioned above, we break down the Binary number into groups.

Next, we write their decimal representation below, followed by their Hexadecimal digit. 

So, Hexadecimal representation is (45F)₁₆.

Example 2: Convert (11111101)₁₆ to Hexadecimal

We divide the Binary number into 4-bit groups and write their decimal and Hex representation under them.

The required Hexadecimal number is (FD)₁₆.

As you can see from the above examples, it is very easy to convert from Binary to the Hex number system. You can take any Binary number and convert it to a Hex or Hexadecimal number system to get a better understanding of the concept.