Hexadecimal to Binary Conversion

Computers cannot understand human language. All the internal processing in a computer takes place in O’s and 1’s the binary format. So, whatever the data input is given it is first converted in the form of binary bits by the internal IC and then given to the processing unit for interpretation of the instruction and processing. Although we use different formats of data, internally it is stored in the form of binary bits in the memory unit. Different formats used to represent data are the Binary format, Decimal format, Hexadecimal format, Grey code, etc… In this article let us look at the Hexadecimal to Binary Conversion of the data.

What is a Binary Numbering System?

The format we use to write numbers is the decimal format, also known as base 10 format. But machines cannot understand those numbers. So, the binary numbering system was introduced, which represents these decimal numbers as a string of 0’s and 1’s.

In the binary number system, only two symbols are used to represent the number. They are 0 and 1.  Machines understand these symbols are ‘ON’ and ‘OFF’ sequence. The binary numbering system is also known as the base-2 numbering system. Each symbol is known as ‘Bit’. The group of four bits is known as ‘Nibble’ and a group of 8 bits is known as ‘Byte’.

Uses of Binary Numbering System

The use of binary numbering simplifies computer architecture and programming. Binary numbering is used in digital signal coding. This numbering system can be simply defined as the numbering system that uses only two digits to represent numbers instead of digits from 0 to 9. Binary numbers are very useful for bitwise calculations and programming of digital circuits.

Hexadecimal To Binary Conversion Table

To make the computing and interpretation of larger numbers easier, Hexadecimal format is used for larger calculations. But computers still internally convert them into binary and does the processing. So, it is important to know the Hexadecimal To Binary Conversion.

Hexadecimal format is also known as the base-16 format. It uses 16 symbols to represent the numbers. It uses symbols 0-9 to represent the numbers zero-nine and for numbers from 10-15, it uses symbols A-F. A Hexadecimal number is represented with an ‘h’ before the number or with an ‘ox’ after it. Example of a hexadecimal number ‘h56’ or ‘ox56’.

The binary representation of the Hexadecimal digits is given in the table. For the conversion of larger numbers, this table has to be referred.


Hexadecimal To Binary Conversion Method

To convert a Hexadecimal number into binary some steps have to be followed. Each hexadecimal bit represents a nibble .i.e. it is a combination of four binary bits. For example, the number ‘1’ of hexadecimal is a four-bit number is binary and written as ‘0001’.

Step 1: Write the four-digit binary equivalent for every hexadecimal digit starting for the Least significant bit of the given hexadecimal number.

Step 2: Combine all the digits to form a binary number.

Hexadecimal To Binary Conversion Example

Let us consider a Hexadecimal number ‘BC21’. To convert the given number into binary first step is to write the four-digit binary equivalent of its every digit starting from the Least significant bit. Refer to the conversion table for this step.

From the conversion table, binary equivalent of

1 = ‘0001’

2 =’0010′

C = ‘1100’

B =’ 1011′.

The next step in conversion is to combine these digits. i.e.

‘B’ | ‘C’|’ 2′ | ‘1’

‘1011’| ‘1100’ | ‘0010’ |’0001′

Thus the Binary equivalent of the given hexadecimal number is ‘1011110000100001’

Hexadecimal To Binary Encoder

For Hexadecimal To Binary Conversion, an Encoder IC is also available. As each hexadecimal digit is associated with four binary, each input should give a 4-bit output. Here the number of inputs is 16 .i.e. n = 16 and number of output are log 16 = 4


The above truth table is used for designing the encoder. B0,B1,B2,B3 gives the output . When the Hexadecimal input 2 is given, then the encoder gives the binary output as “0010”. Binary numbers are written with base-2.

The binary system is highly adopted as the language off electronics. It is highly useful for understanding the state of the electronic signals. The binary system, Hexadecimal System are the positional numerical where the position of the digits also contributes to the value of the numerical.

There are many numerical systems introduced over time. Hindu-Arabic numbering is popularly used. In the digital world to make the languages compatible with machines many different representations of numbers are being introduced. Due to its simplicity and ability to interpret the electrical states of the machine Binary Number System is highly preferred. What is the binary representation of the hexadecimal number ‘c5’?