Hexa and systems are often used when working with computers, programming, and networking. While numbers (base 16) are easier to read and understand than their binary counterparts (base 2), there are times when you may need to a hexadecimal number to binary or decimal. In this article, we’ll discuss how to do just that.

Converting Hexadecimal to Binary

The key to converting hexadecimal numbers to binary is to understand that each digit in a hexadecimal number corresponds to four bits in a binary number. For example, the hexadecimal number 2F is equivalent to a binary number in the following way:

2 = 0010

F = 1111

So, the binary equivalent of 2F is 00101111. To convert any hexadecimal number to binary, simply follow the steps below:

Step 1: Write down the hexadecimal number.

Step 2: Substitute each digit in the hexadecimal number with its four-bit binary equivalent.

Step 3: Combine all the binary digits to give the final binary equivalent of the hexadecimal number.

Let’s take another example and convert the hexadecimal number 9A to binary.

Step 1: Write down the hexadecimal number: 9A.

Step 2: Substituting each digit in the hexadecimal number with its binary equivalent:

9 = 1001

A = 1010

So, the binary equivalent of 9A is 10011010.

Converting Hexadecimal to Decimal

To convert a hexadecimal number to decimal, there are different methods you can use. Let’s discuss two of them.

Method 1: Using the Power of 16

One way to convert a hexadecimal number to decimal is to using the power of 16. Here’s how:

Step 1: Write down the hexadecimal number.

Step 2: Starting from the rightmost digit, multiply each digit by 16 raised to the power of n, where n is the position of the digit counting from the rightmost digit. The rightmost digit’s position starts at 0.

Step 3: Add up the results from step two to get the decimal equivalent of the hexadecimal number.

For example, let’s convert the hexadecimal number 2B to decimal using the power of 16 method.

Step 1: Write down the hexadecimal number: 2B.

Step 2: Starting from the rightmost digit, multiply each digit by 16 raised to the power of n:

B = 11 x 16^0 = 11

2 = 2 x 16^1 = 32

Step 3: Add up the results from step two:

11 + 32 = 43

So, the decimal equivalent of the hexadecimal number 2B is 43.

Method 2: Using the Divisibility Rule of 16

Another method to convert a hexadecimal number to decimal is to use the divisibility rule of 16. Here’s how:

Step 1: Write down the hexadecimal number.

Step 2: Write down the decimal number 16.

Step 3: Divide the hexadecimal number by 16 and write down the quotient and remainder.

Step 4: If the quotient is greater than 16, divide it by 16 and repeat the process until the quotient is less than 16.

Step 5: Write out all the remainders in reverse order.

Step 6: Convert the remainders to decimal and add them up to give the decimal equivalent of the hexadecimal number.

For example, let’s convert the hexadecimal number 3E to decimal using the divisibility rule of 16 method.

Step 1: Write down the hexadecimal number: 3E.

Step 2: Write down the decimal number 16.

Step 3: Divide the hexadecimal number by 16:

3E ÷ 16 = 2 remainder 14

Step 4: Since 2 is less than 16, we stop here.

Step 5: Write out all the remainders in reverse order:

14 2

Step 6: Convert the remainders to decimal and add them up:

14 x 16^0 + 2 x 16^1 = 14 + 32 = 46

So, the decimal equivalent of the hexadecimal number 3E is 46.

Conclusion

Converting a hexadecimal number to binary or decimal is not difficult once you know the right method. Whether you need to convert a hexadecimal number as part of your computer science studies, or for practical purposes, it’s important to understand the basic principles behind these conversions. By following the steps outlined in this article, you can convert any hexadecimal number to binary or decimal with confidence.

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