HEX to Binary

HEX to Binary: Converting Hexadecimal Numbers to Binary

When it comes to understanding computer systems, learning how numbers are represented is an essential part. In the world of digital electronics, the two most commonly used number systems are hexadecimal (hex) and binary. Hexadecimal numbers are often used to represent and express binary values in a more compact form. In this article, we will explore how to convert hexadecimal numbers to binary and understand the relationship between these two number systems.

What is Hexadecimal?

Hexadecimal is a number system that uses 16 unique digits to represent values. These digits are 0-9 for the first ten values and A-F for the remaining six values. The letters A to F are used to represent numbers 10 to 15.

The counting in hexadecimal starts from 0 and goes up to F. So, the first ten numbers in hexadecimal are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. After 9, the numbers continue with A, B, C, D, E, F. For example, 10 in hexadecimal is represented as A, and 15 is represented as F.

Each digit in a hexadecimal number carries a power of 16. The rightmost digit represents the 16^0 power, the second rightmost digit represents the 16^1 power, the third rightmost digit represents the 16^2 power, and so on.

What is Binary?

Binary is a number system that uses only two digits – 0 and 1. It is the fundamental system used in computers, where everything is represented using combinations of these two digits.

In binary, each digit represents a power of 2. The rightmost digit represents the 2^0 power, the second rightmost digit represents the 2^1 power, the third rightmost digit represents the 2^2 power, and so on.

Converting Hexadecimal to Binary

Converting a hexadecimal number to binary involves breaking down each digit in the hex number and converting it to its equivalent binary representation.

Here’s a step-by-step guide to converting a two-digit hexadecimal number to binary:

Step 1:

Assign the binary values to each hexadecimal digit as follows:

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

Step 2:

Divide the hexadecimal number into two digits, if it is not already in that format.

Step 3:

Refer to the table created in step 1 and write down the binary values for each digit. For example, if the hexadecimal number is AF, the binary equivalent would be 1010 1111.

Step 4:

Combine the binary values obtained in step 3 to get the final binary representation of the hexadecimal number. In our example, the final binary representation of AF would be 10101111.

Examples of Converting Hexadecimal to Binary

Let’s take a few examples and convert them from hexadecimal to binary:

Example 1:

Convert the hexadecimal number 1C to binary.

Hexadecimal	Binary
1	0001
C	1100

Combining the binary values, we get 0001 1100 as the final binary representation of the hexadecimal number 1C.

Example 2:

Convert the hexadecimal number 3F to binary.

Hexadecimal	Binary
3	0011
F	1111

Combining the binary values, we get 0011 1111 as the final binary representation of the hexadecimal number 3F.

Example 3:

Convert the hexadecimal number A5 to binary.

Hexadecimal	Binary
A	1010
5	0101

Combining the binary values, we get 1010 0101 as the final binary representation of the hexadecimal number A5.

Conclusion

Converting hexadecimal numbers to binary is an important skill for understanding the inner workings of computer systems. By following a simple step-by-step process, you can easily convert any hexadecimal number to its binary equivalent. Understanding the relationship between hexadecimal and binary allows you to work with both number systems interchangeably, helping you analyze and understand the binary representation of values more efficiently.

So the next time you come across a hexadecimal number, don't panic! Just follow these steps and convert it to binary with ease.