Binary to Hex Converter

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Hexadecimal, or base-16, is a numeral system that represents numbers using 16 distinct symbols: 0-9 to represent values zero to nine, and A-F to represent values ten to fifteen. This numeral system is widely used in computer science and electronics due to its more compact representation compared to binary, which uses only two symbols: 0 and 1.

Converting binary numbers to hexadecimal is a useful skill for those working with digital systems and programming. In this article, we will explore the process of converting binary numbers to hexadecimal, including the step-by-step method, grouping, and using programming languages for automation.

1. Step-by-Step Conversion Method

To manually convert a binary number to hexadecimal, you can follow these steps:

  1. Divide the binary number into groups of four bits, starting from the least significant bit (rightmost).
  2. If the most significant group has less than four bits, add leading zeros to make it a group of four.
  3. Convert each group of four bits to its equivalent hexadecimal value.
  4. Concatenate the hexadecimal values to obtain the final result.

Example: Convert the binary number 11010110 to hexadecimal.

Step 1: 43 ÷ 2 = 21, remainder = 1
Step 2: 21 ÷ 2 = 10, remainder = 1
Step 3: 10 ÷ 2 = 5, remainder = 0
Step 4: 5 ÷ 2 = 2, remainder = 1
Step 5: 2 ÷ 2 = 1, remainder = 0
Step 6: 1 ÷ 2 = 0, remainder = 1

Reading the remainders in reverse order, we get the binary equivalent: 101011.

2. Double Dabble Algorithm

The double dabble algorithm is an efficient technique for converting decimal numbers to binary, especially for larger numbers. It uses a process called "shift and add-3" that eliminates the need for division. The steps for the double dabble algorithm are as follows:

  1. Set up a binary register and a counter.
  2. Shift the binary register left and add the decimal number.
  3. If the result is greater than or equal to 5, add 3.
  4. Increment the counter and repeat steps b and c until the counter reaches the desired number of bits.
  5. The binary equivalent is the final value in the binary register.

3. Using Programming Languages for Conversion

In addition to manual conversion methods, you can use programming languages to automate the process of converting decimal -in functions or libraries to perform this conversion easily. Here's an example using Python:

binary_number = '11010110'
hexadecimal_number = hex(int(binary_number, 2))[2:]

This short code snippet converts the binary number 11010110 to hexadecimal and prints the result, which is D6.


Mastering binary to hexadecimal conversion is essential for anyone working with digital systems and programming, as it allows for more efficient representation of data and simplifies complex binary strings. By understanding the step-by-step method, utilizing grouping techniques, and leveraging programming languages for automation, you can become proficient in converting binary numbers to hexadecimal and enhance your skills in the digital world.