Hexadecimal to Binary Conversion with Examples

This post is all about the conversion of a number from hexadecimal to binary. That is, in this article, you will learn the way that is used to convert a number from the hexadecimal number system to its binary equivalent. But before we begin, let's understand what these two numbers mean.

• Hexadecimal number: The hexadecimal number system has a base of 16, therefore it allows 16 digits that can be used to create or form a hexadecimal number. For example: 25D, 4A3, and FA, etc.
In other words, a number that consists of 16 digits, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, is considered to be a hexadecimal number. The characters A-F refer to 10–15. That is, A refers to 10, B refers to 11, and so on.
• Binary number: On the other hand, binary numbers have a base of 2, which indicates that a binary number is comprised of a total of two digits, which are the digits 0 and 1. For example, 11, 11011001, and 1101, etc.

It is necessary to adhere to the following rules in order to convert any hexadecimal number to its binary equivalent:

1. Convert each hex digit to its 4-bit binary equivalent.
2. Combine all the 4-bit binary equivalents.

To better understand and apply the rules outlined above, let's look at an example.

(AFB2)16 = ( ? )2

In this situation, we need to change the hexadecimal representation of the number AFB2 into its binary equivalent. Take a look at the table that has been provided for you below; it will demonstrate how to convert the hexadecimal number that was just discussed to its equivalent in binary.

Hex Digit 4-bit Binary Equivalent
A 1010
F 1111
B 1011
2 0010

From the above figure, we have four 4-bit binary equivalents: the first one is 1010, the second one is 1111, the third one is 1011, and the fourth one is 0010. On combining all the four 4-bit binary numbers, we get 1010111110110010. Therefore, (AFB2)16 = (1010111110110010)2.

The hexadecimal system is commonly referred to as "hex" in mathematics. Each hex digit represents four binary digits. Or, in other words, you can say that each hex value gives four binary digits. The table given below shows the equivalent binary value of all the 16 hex characters:

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

I am confident that you are now able to convert any value given in hexadecimal to its equivalent value in binary after reading the information that has been provided in the table that has been presented above. As an illustration, convert the value 2AD3, which is written in hexadecimal, to binary. Please proceed in the following manner:

• The binary equivalent of 2 is 0010.
• The binary equivalent of A is 1010.
• The binary equivalent of D is 1101.
• The binary equivalent of 3 is 0011.

After combining all the binary values, we will get 0010101011010011. Therefore, (2AD3)16 = (0010101011010011)2.

Programs Created on Hexadecimal to Binary Conversion

Computer Fundamentals Quiz

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