Have you ever encountered a decimal number and wondered how you could convert it to its hexadecimal equivalent? Decimal (base 10) and hexadecimal (base 16) numbering systems are commonly used in computer programming and digital systems. In this guide, we will walk you through the process of converting a decimal number to hexadecimal in a step-by-step manner.

Step 1: Understanding the Decimal and Hexadecimal Systems

Before diving into the conversion process, it’s important to grasp the fundamentals of the decimal and hexadecimal numbering systems.

In decimal, we count from 0 to 9, and then carry over to the next digit when we reach 10. Hexadecimal, on the other hand, uses a combination of numbers and letters from 0 to 9 and A to F. The letter A represents 10, B represents 11, and so on, until F, which represents 15.

Step 2: Breaking Down the Decimal Number

Let’s take an example decimal number, 342, and convert it to hexadecimal. The first step is to break down the number into its powers of 16.

We start from the rightmost digit and assign powers of 16 to each digit from right to left. In our example:

  • The rightmost digit (2) is multiplied by 16 raised to the power of 0, which is 1.
  • The middle digit (4) is multiplied by 16 raised to the power of 1, which is 16.
  • The leftmost digit (3) is multiplied by 16 raised to the power of 2, which is 256.

Step 3: Calculating the Hexadecimal Equivalent

Now that we have the powers of 16 for each digit, we can calculate the hexadecimal equivalent.

Multiply each digit by its corresponding power of 16 and sum the results:

  • 2 * 1 = 2
  • 4 * 16 = 64
  • 3 * 256 = 768

Add these values up: 2 + 64 + 768 = 834.

Step 4: Converting to Hexadecimal

The final step is to convert the sum (834) to hexadecimal. Begin by dividing the sum by 16.

  • 834 ÷ 16 = 52 remainder 2

The remainder (2) becomes the least significant digit. Next, divide the quotient (52) by 16 again:

  • 52 ÷ 16 = 3 remainder 4

This time, the remainder (4) becomes the next digit. Lastly, divide the new quotient (3) by 16:

  • 3 ÷ 16 = 0 remainder 3

The remainder (3) is the most significant digit. When reading the remainders (from bottom to top), the hexadecimal equivalent of 834 is 342.

By following these step-by-step instructions, you can efficiently convert a decimal number to its hexadecimal representation. Decimal to hexadecimal conversion plays a crucial role in various areas of computer science, including programming, networking, and digital logic. Now that you have a solid understanding of the process, you can confidently tackle any decimal-to-hexadecimal conversion task that comes your way.

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