The binary to hexadecimal converter shows you how to convert binary to hexadecimal and hexadecimal to binary numbers. It also explains the commonalities and differences between those numeral systems.

Binary and hexadecimal numbers

We all grow up with the same numeral system: the decimal one. We learn how to understand the numbers presented in it and how to execute arithmetic operations on them. But the decimal system is not the only one existing:

  • The decimal system has the base 10, meaning that every digit can be in the range 0-9.

  • The binary system is based on the number 2. Every digit can only have two logical states: 0 and 1. Numbers represented in the binary system can be converted to the decimal system, but the basic arithmetic operations can also be executed in the binary system. Additionally, binary numbers allow for bitwise operations, like bit shifts and the bitwise operations AND, OR, and XOR.

  • The hexadecimal system is base 16. This fact means that every digit can represent a value from 0-15. But since 15 consists of 2 digits, it was agreed that hexadecimal numbers are made up of the numbers 0-9 and the letters A, B, C, D, E, and F. The table below shows the relations between binary and hexadecimal values. This article will explain how to convert binary to hexadecimal and how to convert hexadecimal to binary numbers.

Hex
Binary
Hex
Binary
0
0000
8
1000
1
0001
9
1001
2
0010
A
1010
3
0011
B
1011
4
0100
C
1100
5
0101
D
1101
6
0110
E
1110
7
0111
F
1111

Why do we need hexadecimal numbers?

Since every hexadecimal digit can represent 16 states, they allow for a very compact and concentrated representation of information. Furthermore, one hexadecimal digit holds the same amount of information as four bits. This fact allows for easy conversion from the binary system and a very dense portrayal of binary data.

How to convert binary to hexadecimal?

To convert a binary into a hexadecimal number, follow these steps:

  1. Starting from the right (the least significant bit), separate your binary number into groups of 4 digits each.
  2. Convert each group of 4 binary digits into the equivalent hexadecimal symbol, from 0 to F.
  3. Merge your hexadecimal digits in the same order as the binary digit groups to get your hexadecimal number.

Let's try this on the binary number 100101100011101:

  1. Separate in groups:
  • 0100 1011 0001 1101
  1. Convert each group to the hexadecimal digit (full free to use the table above for this):
  • 0100 = 4
  • 1011 = B
  • 0001 = 1
  • 1101 = D
  1. Merge the hex digits:
  • 4B1D

Here you go! So simple, it should be 4B1D'en.

How to convert hexadecimal to binary?

To convert a hexadecimal into a binary number, do the following:

  1. Convert each hexadecimal digit (0 to F) into the equivalent group of 4 binary digits (0000 to 1111).
  2. Merge the binary digits groups in the same order as the hexadecimal digits to get your binary number.

For an example, let us convert the hexadecimal number 2BAD into binary:

  1. Convert each hex digit (the table above is your friend):
  • 2 = 0010
  • B = 1011
  • A = 1010
  • D = 1101
  1. Merge all binary digit groups:
  • 0010 1011 1010 1101

And that's all. 2BAD you didn't know how easy this was up to now, right?

How to use the binary to hexadecimal converter?

You know what a binary and hexadecimal number is and how to convert one to the other. Let's get to what this article all boils down to: the binary to hexadecimal calculator and its use.

And it could not be simpler. Type the binary number you want to convert to hexadecimal in the field binary. And that's all!

If we try this with our example binary number 100101100011101 from above, we receive the expected hexadecimal result: 4B1D.

By default, the converter is limited to 16 bit. If you need to change that, enter the advanced mode, and you will be able to define a bit range up to 20.

FAQ

What is the hexadecimal number F1 equal to in binary?

To find the binary conversion for the hexadecimal number F1, do the following:

  1. Convert both hexadecimal digits to their binary representation: hex F = binary 1111, hex 1 = binary 0001.
  2. Merge the binary digits groups in the same order as the equivalent hexadecimal digits to get your binary number: 1111 0001.

How do I convert the binary number 1011010 into a hexadecimal number?

To convert the binary number 1011010 to a hexadecimal number, follow these steps:

  1. Starting from the right (the least significant bit), separate your binary number into groups of 4 digits each: 0101 1010.
  2. Convert each group of 4 binary digits into the hexadecimal digit: binary 0101 = hex 5, binary 1010 = hex A.
  3. Merge your hexadecimal digits in the same order as the binary digit groups to get your hexadecimal number: 5A.
Philip Maus
You can write a binary number with no more than 16 digits. You don't have to input leading zeros.
Binary
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