Binary to Hexadecimal Conversion

‘Number ‘is a mathematical object used to count things, do calculations, record, and label things. A written symbol that represents a number is known as numerical, such as the numerical 5.  A numerical system shows us an organized way to write these numerical and manipulate them. These are many numerical systems introduced but the most commonly used numerical system is the Hindu-Arabic numerical system. A numerical system that uses 10 symbols to represent numbers is known as Decimal Numerical System. Similary there is a Binary system, which uses two symbols, Octa numerical system that uses 8 symbols and a Hexa-Decimal numerical system that uses 16 symbols for representation. In this article, Binary to Hexadecimal conversion is described.

What is a HexaDecimal System?

The greatest contribution to the numerical system is the Place-value notation developed by Aryabatta in the 5th century. This is also known as Positional Numerical System. Here the position of the digit and the base of the system are used to determine the value of the number.

Hexadecimal Numerical System is a Positional Numerical System that represents numbers using a base 16. It uses 16 distinct symbols to represent numbers. Symbols ‘0-9’ are used to represent values from zero to nine and symbols ‘A-F’ are used to represent values ten to fifteen.

On the other hand, Binary Numbering System uses only two symbols ‘0’ and ‘1’ to represent the decimal values. Here the base is 2. Machines can only understand the 0’s and 1’s so, Binary Number System is used to convert the decimal numbers into a bit sequence of 0’s and 1’s.

Uses of Hexadecimal Numbering System

Hexadecimal Numbering System is commonly used by programmers and computer system designers to represent larger numbers. The number of digits used to represent a larger number is decreased compared to the binary representation. This provides human-friendly representation and interpretation of large binary numbers. Here, the 4 binary bits are combined and written as 1 bit.

Each bit of the hexadecimal system represents a half-byte. Many CPU architectures use a dedicated instruction set that uses hexadecimal numbering which makes the processing easier for hardware.

Binary To Hexadecimal Conversion Method

The hexadecimal system uses 16 symbols for representation whereas the Binary System uses two symbols. For Binary to Hexadecimal Conversion, the binary number is divided into groups with 4-bits in each group, starting from the Least Significant Bit.

These groups are considered independently and decimal representation of each group is written. Then the hexadecimal equivalent of each decimal number is written directly.

Binary to Hexadecimal conversion Table

For representing values from zero to nine, hexadecimal uses the symbols ‘0-9’ and for representing values from ten to fifteen, it takes the symbols ‘A-F’. To distinguish a hexadecimal number from decimal numbers and other numerical systems, the number is written with either an ‘h’ after it or ‘ox’ before it. Example ’25h’ or ‘ox25’ represents a hexadecimal number.

In the table below the Hexadecimal representation of the Binary numbers is given.


Binary To Hexadecimal Conversion Example

In computer programming and while programming a processor it is easier to consider the numbers in hexadecimal format. By this, it is easier to work with huge numbers and calculations. Let us look at an example to understand the Binary to Hexadecimal conversion process.

Binary To Hexadecimal Conversion of the binary number ‘11000001’.

Step1: Divide the binary number into groups with each group containing 4-bits, starting from the right-hand side. Add extra zeros at the end if there are no sufficient 4-digit bits.

1100 | 0001

Step2: Write the decimal equivalent of the binary

 = 1100 | 0001

= 12 | 1

Step3: From the conversion table, write the hexadecimal equivalent of the decimal number.

= 1100 | 0001

= 12 | 1

= C 1

Thus the Hexadecimal conversion of the given binary ‘11000001’ is ‘C1’.

Binary To Hexadecimal Encoder

Code converters are used to convert the Binary number into Hexadecimal. A combination of decoder and encoder systems can be designed for conversion. Online encoders are largely preferred for binary to hexadecimal conversion as they make the task a lot easier comparatively.

Although the numerical are displayed in the form of hexadecimal or decimal digits, in a computer internally they are stored in the form of binary numbers. Besides literals, online encoders can also convert a text string into the hexadecimal format, also known as base-16 encoding.

Representation of literals in the hexadecimal format improves the readability and interpretation of the data. It is easier to read 0x8080 compared to 32896, the decimal format. Modern computers are equipped with a calculator to convert the numbers between different radices. Integer division and remainder operations are used in source code or conversion of binary to hexadecimal. what is the hexadecimal representation of ‘00101101’?

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