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To Convert Binary To Hexadecimal

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To Convert Binary To Hexadecimal

How to Convert Binary to Hexadecimal A Simple GuideIn the world of computing, different number systems are used to represent data. Two of the most commonly used systems are the binary system and the hexadecimal system. The binary system uses only two digits, 0 and 1, while the hexadecimal system uses sixteen digits, including numbers 0 to 9 and letters A to F (representing the values 10 to 15).

Converting between these two systems is essential, especially when working with low-level programming, memory addresses, or digital electronics. This guide will explain how to convert binary to hexadecimal, step-by-step, in an easy-to-understand way.

What Is Binary?

Before diving into the conversion process, it’s helpful to understand the binary system. Binary is a base-2 number system, meaning it only uses two digits 0 and 1. Every binary digit (also called a bit) represents an increasing power of 2, starting from the rightmost bit. This makes it the natural system for representing data in computers, as computers operate using electrical signals that are either on or off (1 or 0).

What Is Hexadecimal?

Hexadecimal, or base-16, is a number system that uses sixteen symbols to represent values. These symbols are

  • 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

  • A (for 10), B (for 11), C (for 12), D (for 13), E (for 14), and F (for 15)

Hexadecimal is often used in computing because it is more compact and easier for humans to read compared to binary. Each hexadecimal digit represents four binary digits (or bits), making the conversion process straightforward.

Steps to Convert Binary to Hexadecimal

Now that you have a basic understanding of binary and hexadecimal, let’s explore how to convert a binary number into a hexadecimal number.

1. Group the Binary Digits into Sets of Four

To start the conversion, divide the binary number into groups of four digits, starting from the right. If the number of digits is not a multiple of four, add leading zeros to the leftmost group.

For example, if we have the binary number

101110110

We group it as

0010 1110 110

Then, we add one more zero to the leftmost group to make it a full set of four digits

0010 1110 0110

2. Convert Each Group of Four Binary Digits to Hexadecimal

Each group of four binary digits corresponds to one hexadecimal digit. To convert each group, you can use the following conversion table

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

Let’s convert the groups from our example

  • 0010 is 2 in hexadecimal.

  • 1110 is E in hexadecimal.

  • 0110 is 6 in hexadecimal.

So, the hexadecimal equivalent of 101110110 is

2E6

3. Write the Final Hexadecimal Number

After converting all groups of binary digits to their hexadecimal equivalents, you can now write the final hexadecimal number. For our example, the binary number 101110110 becomes

2E6

Example 2 Converting a Larger Binary Number to Hexadecimal

Let’s go through another example with a larger binary number

1101011110110101

Step 1 Group the binary digits into sets of four

1101 0111 1011 0101

Step 2 Convert each group to hexadecimal

  • 1101 is D in hexadecimal.

  • 0111 is 7 in hexadecimal.

  • 1011 is B in hexadecimal.

  • 0101 is 5 in hexadecimal.

So, the hexadecimal equivalent of 1101011110110101 is

D7B5

Why Use Hexadecimal Instead of Binary?

While binary is essential for computer systems, hexadecimal is preferred for several reasons

  1. Compact Representation A single hexadecimal digit represents four binary digits, making it much shorter and easier to read than binary.

  2. Human Readability Hexadecimal is easier to work with and debug, especially when working with memory addresses or data dumps. It is far more readable than long strings of 1s and 0s.

  3. Common in Programming Hexadecimal is widely used in programming and computing for tasks like memory addressing, defining colors in graphics, and working with low-level operations like assembly language.

Tips for Easy Conversion

  • Memorize the Binary to Hexadecimal Conversion Table This will make manual conversion much faster.

  • Use Online Tools Many websites provide tools to convert binary numbers to hexadecimal. While manual conversion is good for learning, online tools are convenient for quick calculations.

  • Practice The more you practice converting binary to hexadecimal, the easier and faster you will become.

Conclusion Mastering Binary to Hexadecimal Conversion

Converting binary to hexadecimal is a valuable skill in computer science and programming. By following a few simple steps, you can easily convert any binary number into its hexadecimal equivalent. Whether you are working on low-level programming, debugging, or analyzing data, knowing how to perform this conversion will make your work more efficient and manageable.

With practice, you will be able to quickly and accurately convert binary numbers to hexadecimal, making it an indispensable tool in your tech toolkit.