Converting a to can seem like a complex task, but it’s actually quite simple once you know the basics. Hexadecimal is a base-16 that uses sixteen digits, including the numbers 0-9 and the letters A-F, to represent numbers. This system is used in a variety of applications, including programming, computer science, and digital electronics. In this article, we will guide you through the steps involved in ing a decimal number to hexadecimal.

Step 1: Understand the basics of hexadecimal

Before we get started, it’s important to have a solid understanding of how the hexadecimal number system works. The digits in a hexadecimal number represent amounts of powers of 16, just like the digits in a decimal number represent amounts of powers of 10. The first digit of a hexadecimal number represents amounts of 16^0 (which equals 1), the second digit represents amounts of 16^1 (which equals 16), the third digit represents amounts of 16^2 (which equals 256), and so on.

Step 2: Divide the decimal number by 16

To convert a decimal number to hexadecimal, we first need to divide the decimal number by 16. The remainder of this division will be the first digit in the hexadecimal number. For example, let’s say we want to convert the decimal number 234 to hexadecimal. We would start by dividing 234 by 16:

234 ÷ 16 = 14 with a remainder of 10

In this case, the quotient is 14 and the remainder is 10. The remainder of 10 corresponds to the letter A in hexadecimal, so the first digit of our hexadecimal number is A.

Step 3: Divide the quotient by 16

Next, we need to divide the quotient from step 2 by 16. The remainder of this division will be the second digit in our hexadecimal number. Continuing with our example, we would divide 14 by 16:

14 ÷ 16 = 0 with a remainder of 14

In this case, the quotient is 0 and the remainder is 14. The remainder of 14 corresponds to the letter E in hexadecimal, so the second digit of our hexadecimal number is E.

Step 4: Write the hexadecimal number

Now that we have found the first two digits of our hexadecimal number, we can write the number in hexadecimal form. The digits are written in reverse order, starting with the least significant digit on the right. Using our example, the hexadecimal number for 234 is AE.

Step 5: Check your work

Finally, it’s important to check your work to make sure you didn’t make any mistakes. You can easily convert the hexadecimal number back to decimal to verify that you did everything correctly. To do this, you simply multiply each digit in the hexadecimal number by its corresponding power of 16 and add up the results. Using our example of 234, we would calculate:

A × 16^1 + E × 16^0
= 10 × 16^1 + 14 × 16^0
= 160 + 14
= 174

Therefore, we can be confident that our conversion was correct.

In conclusion, converting a decimal number to hexadecimal is a simple process that involves dividing the decimal number by 16 and using the remainder as the first digit in the hexadecimal number. By following the steps outlined in this article, you can easily convert any decimal number to hexadecimal and verify your work using a simple calculation.

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