Convert binary numbers to hexadecimal is a process that occurs within the number system. There are four types of number systems used in mathematics: binary, octal, decimal, and hexadecimal.
Each number system can be converted to another type using conversion tables or specific procedures. We will explore the methods for converting binary integers to hexadecimal numbers and provide examples for better understanding.
What is Binary to Hexadecimal Conversion?
The process of converting binary numbers into hexadecimal values is called binary to hexadecimal conversion. Hexadecimal uses a base of 16, while binary uses a base of 2. These base numbers are used to convert binary to hexadecimal.
There are multiple ways to perform the binary to hexadecimal conversion. One method is to convert the binary representation into a decimal number and then into a hexadecimal number. Another option is to use a table that directly converts binary to hexadecimal.
System of Binary Numbers
The binary number system, which uses the digits 0 and 1 and has a base of 2, is commonly used by computer engineers, networking experts, and computer specialists. The binary system is one of the simplest number systems. The digits 0 and 1 are called bits, and a byte is composed of 8 bits. Numbers other than 0 and 1, such as 2, 3, 4, 5, etc. are not included in the binary system.
System of Hexadecimal Numbers
The hexadecimal number system is a positional numeral system that uses a base of 16 and employs sixteen digits/alphabets: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
In the hexadecimal number system, each digit represents a power of the base (16). The digits A-F in hexadecimal correspond to the numbers 10-15 in the decimal number system, respectively.
How to convert Binary to Hexadecimal?
Number systems play an important role in mathematics. This article covers the binary, hexadecimal, and binary to hexadecimal number systems. Different branches of mathematics and computer science utilize number systems and their conversions.
It is noted that converting from binary to decimal is relatively straightforward. The binary number system uses base-2 notation and only the digits 0 and 1 to represent numbers. These digits are referred to as bits or binary digits in the binary number system.
Steps to Convert Binary to Hexadecimal
In order to convert binary to hexadecimal values, we must use the base numbers 2 for binary and 16 for hexadecimal. In the binary-to-hexadecimal conversion table, one hexadecimal integer is equivalent to four binary digits.
The first method used in the conversion process is converting the binary number to decimal, then to hexadecimal. The second method involves converting the hexadecimal number to decimal, then to binary format.
Method 1
Using a conversion table is one of the easiest and fastest ways to convert binary to hexadecimal. As hexadecimal numbers are also a positional number system, binary numbers only consist of the digits 0 and 1. Every four bits make up one hexadecimal number, including the letters A through F.
Method 2
It is possible to convert binary integers to hexadecimal numbers without using a conversion table. Binary numbers are first converted to decimal values before being converted to hexadecimal. The base number for decimal is 10.
One way to convert binary to decimal is by multiplying each digit of the binary number by the corresponding power of 2, whether it is 1 or 0. To convert from decimal to hexadecimal, the number is divided by 16 repeatedly until the quotient equals zero.
Convert Binary to Hexadecimal With Decimal Point
Similar to the previous method, we can use a technique to convert binary numbers with a decimal point to hexadecimal. The conversion table is used to convert binary integers into hexadecimal numerals.
When a binary number has a decimal point, it also includes a fractional portion, which is considered to come after the decimal point. The location of the digits is not affected by the decimal point during the conversion process.
Why is it important?
The hexadecimal numerals, which are part of the base-16 numbers, are the largest set. They range from 0 to 9 and include the letters A, B, C, D, E, and F.
Hexadecimal numbers are considered to be a more advanced form of binary numbers by experts. They are increasingly being used to replace zeroes and ones in many modern organizations.
Hexadecimal numerals are also used to enhance the security of websites. It is a common practice among developers to convert decimal numbers to hexadecimal before storing them in a database.
When displaying the numbers to the users, they convert the number from hexadecimal to decimal first. This translation is useful for embedded systems that typically require decimal numbers.
Humans can easily read and understand decimal numbers. However, decimal numbers can also pose a security risk. Therefore, the conversion from hexadecimal to decimal is important to ensure security.
In addition to that, hexadecimal numbers have the following advantages and disadvantages. The main advantage of hexadecimal numerals is that they are highly compact.
As it is a base-16 integer, it can be represented with the minimum number of characters. A decimal, which is a base-10 number, requires around 16 characters while a hexadecimal number only requires half as many. In contrast, binary numbers only use zeroes and ones, so representing a number in binary requires eight times as many digits as in hexadecimal.
Replace zero
This advantage has led to hexadecimal numbers being used in place of binary numbers in many large organizations. Additionally, hexadecimal numbers are easy for computer processors and other electronic systems to process, which improves their performance. As a result, companies that prioritize speed in their processors often prefer hexadecimal numerals over other number systems.
Another example of hexadecimal numbers being used is the Media Access Control (MAC) address, which uses hexadecimal integers to provide a unique identification for each electronic device on a network. Additionally, advanced computer and electronic systems often require hexadecimal digits.
Many experts in the field view hexadecimal numbers as the future of the numbering system. Therefore, gaining the necessary knowledge and skills to work with hexadecimal numbers is essential for pursuing a career in this area.
Conclusion
Computers use binary to hexadecimal conversion to calculate and display data. The binary system is used in computers because it has only two states, on and off. Computers are built with binary, and understanding binary can be helpful in solving logical problems. Therefore, understanding hexadecimal numerals is important for working with computers.
About Author
Comment here