Data structures & algorithms (Beginner to Intermediate)

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Introduction

Binary is the simple number system that uses only two digits of 0 and 1 (i.e. value of base 2). Whereas Hexadecimal(Hex) number is one of the number systems which has a value is 16 and it contains only 16 symbols − 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and A, B, C, D, E, F.

The number system also has a Binary to Hex Converter. The four number systems used in math are binary, octal, decimal, and Hexa-decimal. Each form may be changed to the alternative number system using the conversion table. Now we move ahead into Binary to Hex Converter.

To better understand, let's look at the methods for changing binary numbers to Hexa-decimal ones. This is one of the easiest topics that we are going to cover. This is one of the easiest topics we will explore. Now we move forward into Binary to Hex Converter.

What is Binary System?

The binary system is a number system. It uses only two digits, 0 and 1, to represent all the numbers. It is most commonly used in computer programming, digital electronics, and telecommunications. In the binary system, each digit position represents a power of 2. It starts from 2^{0} (1) and increases by a factor of 2 for each position to the left. For example, the binary number 1011 represents: 1 x 2^{3 }+ 0 x 2^{2} + 1 x 2^{1} + 1 x 2^{0 } = 8 + 0 + 2 + 1 = 11 The binary system is essential in computing. It allows digital devices to store and process information in a way that can be easily represented by electronic switches. Each switch can be in one of two states (on or off), which corresponds to the binary digits 1 and 0, respectively. By using binary digits to represent information, computers can perform complex operations quickly and efficiently.

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What is Hexadecimal System (Hex System)

The hexadecimal system is also known as the hex system. It is a base-16 number system that uses 16 digits to represent numbers. It is also commonly used in computer programming and digital electronics. It is mainly used for representing memory addresses and color codes.

The digits 0-9 represent the values 0-9, and the letters A-F represent the values 10-15 in the hexadecimal system. Each digit position represents a power of 16. It starts from 16^{0} (1) and increases by a factor of 16 for each position to the left. For example, the hexadecimal number 3A7B represents:

3 x 16^{3} + 10 x 16^{2} + 7 x 16^{1} + 11 x 16^{0}

= 3 x 4096 + 10 x 256 + 7 x 16 + 11 x 1

= 15,483

It allows programmers and engineers to represent binary numbers (which can be challenging to read and write) in a more compact and readable format. Each hexadecimal digit represents four binary digits (bits), so it is easy to convert between hexadecimal and binary representations.

Conversion from Binary to Hexadecimal Number System

Convert binary numbers into Hexa-decimal ( 0, 1, 2, 3, 4, 5, 6, 7, 8 and A to F) values are known as Binary to Hex Converter. Hexa-decimal has a base number of 16. At the same time, binary digits have a base number of 2. With the help of the base numbers, the binary is converted to Hexa-decimal. There are ways to complete the conversion. The first is changing the binary representation into a decimal number and then a Hexa-decimal number.

The second method involves using a table. That converts binary to Hexa-decimal. Before we discuss the conversion process, let's define binary and Hexa-decimal.

Here are the steps to convert binary to hex:

Convert the binary number to decimal.

Convert the decimal number to hexadecimal.

Let us understand this approach with the help of an example.

Consider a binary number (1101101)_{2}

So, its decimal conversion is

1 x 2^{6 }+ 1 x 2^{5 }+ 0 x 2^{4 }+ 1 x 2^{3 }+ 1 x 2^{2 }+ 0 x 2^{1 }+ 1 x 2^{0 }

=64 + 32 + 0 + 8 + 4 + 0 + 1

= (109)_{10}

Now, convert this to hexadecimal

9 x 16^{1 }+ 10 x 16^{0}

= (9A)_{16}

Using Grouping

In the grouping approach, there are only 16 digits (from 0 to 7 and A to F) in the hexadecimal number system, so we can represent any digit of the hexadecimal number system using only 4 bits. Here are the steps to convert a binary number to a hexadecimal number without using the grouping approach:

1. Write down the binary number.

2. Starting from the right-most digit, group the binary digits into sets of 4. If the left-most group has fewer than four digits, add zeros to the left to make it a four-digit group.

3. Write down the hexadecimal equivalent of each group of 4 binary digits. Use the following table to convert each group:

Binary

Hexadecimal

0000

0

0001

1

0010

2

0011

3

0100

4

0101

5

0110

6

0111

7

1000

8

1001

9

1010

A

1011

B

1100

C

1101

D

1110

E

1111

F

4. Combine the hexadecimal digits to get the final answer.

Let us understand this process with the help of an example. Here is an example to illustrate the process:

Suppose we need to convert the binary number 110110111011 to hexadecimal.

Write down the binary number: 110110111011

Group the binary digits into sets of 4: 1101 1011 1011

Write down the hexadecimal equivalent of each group of 4 binary digits:

1101 = D

1011 = B

1011 = B

Combine the hexadecimal digits to get the final answer: DBB

Binary Number Systems

To understand how to create a Binary to Hex Converter. We have to understand the binary number system. One of the most east number systems is the binary system, which uses the digits 0 and 1, and the base number is 2. Computers that are mainly useful for engineers, networking experts, and computer professionals typically use binary numbers. A byte has 8 bits, represented by the numerals 0 and 1. The binary number system excludes other numbers like 2, 3, 4, and so on. Don't you feel like it is easy?

The binary number system's examples of numbers include

Hexa-decimal Number Systems

To understand how to create a Binary to Hex Converter. We must understand the Hexa-decimal number system. The base number for the Hexa-decimal number system is 16. While the other sixteen digits or alphabets are A, B, C, D, E, and F, and 0, 1, 2, 3, 4, 5, 6, 7, 8. Here, the decimal numbers 10-15 are represented by the Hexa-decimal letters A via F. The base is defined by each digit in the Hexa-decimal number system ( 0,1, 2, 3, 4, 5, 6, 7,8 and A to F). For example: In the Hexa-decimal number system, some instances of numbers include.

Hexa-decimal to Binary Conversion Using a Table

Using the table is one of the simplest and quickest ways to get from binary to Hexa-decimal. Since Hexa-decimal numbers are also positional number systems ( 0,1, 2, 3, 4, 5, 6, 7, 8 and A to F). Binary numbers only include the digits 0 and 1. Every four bits are equal to one Hexa-decimal number. Which also consists of the letters A to F. After the below table we will focus of the Binary to Hex Converter. Don't you feel like it is easy?

The following is the conversion table:

Hexadecimal Number

Binary Number

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

Approach for Binary to Hex Converter

Start by entering a binary number.

Split the binary number into 4-bit groups. Add each bit in turn after multiplying it by the power of 2 for each set of four bits.

To get the output, combine the results of all groups.

Algorithm for Binary to Hex Converter

Enter a binary number into the variable value of binary as the input.

Split the input integer by 10 to get the remainder and quotient.

Increase the variable value of Hexa-decimal ( 0, 1, 2, 3, 4, 5, 6, 7, 8 and A to F) by multiplying the received remainder by variable i.

Increase the variable i by two. And replace the value of binary with the resulting quotient.

Continue doing steps 2-4 until the value of the binary variable is zero. And you will get the result.

/*
* Here is the C program's source code for Binary to Hex Converter.
*/
#include <stdio.h>
int main()
{
long int value_of_binary, value_of_Hexa-decimal = 0, i = 1, remainder;
printf("Enter the binary number: ");
scanf("%ld", &value_of_binary);
while (value_of_binary != 0)
{
remainder = value_of_binary % 10;
value_of_Hexa-decimal = value_of_Hexa-decimal + remainder * i;
i = i * 2;
value_of_binary = value_of_binary / 10;
}
printf("Hexa-decimal value: %lX", value_of_Hexa-decimal);
return 0;
}
/*
I hope you have understood the concept and it is now easier for you.
*/

Reason: As in the program Binary to Hex Converter, the while loop divides the input integer by 10 to get the remainder and quotient, traversing every digit.

Space complexity

O(1): We just need a variable in the program Binary to Hex Converter.

Reason: We are not creating any array or linked list in the programme Binary to Hex Converter. Everything is getting stored in a variable. So space complexity is O(1).

To convert binary to hexadecimal, group binary digits into sets of four (starting from the right), then match each group with its hexadecimal equivalent (0000=0, 1111=F).

What is the hexadecimal for 1010?

The hexadecimal representation of the binary number 1010 is "A." In hexadecimal, "A" corresponds to the decimal value 10, which is equivalent to the binary 1010.

How to convert 8 digit binary into hexadecimal?

To convert an 8-digit binary number to hexadecimal, divide it into two groups of 4 bits each. Then, find the hexadecimal equivalent for each group and combine them.

What is the binary number 1100 0011 in hexadecimal?

The binary number 1100 0011 is equivalent to the hexadecimal number C3. In hexadecimal, C represents the decimal value 12, and 3 represents the decimal value 3.

Conclusion

This blog covered Binary to Hex Converter, basically converting binary numbers to Hexa-decimal numbers. I hope you have understood the concept and it is now easier for you. Want to explore the same related topic? Check this Decimal to Binary in C.

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