101 LearnersLast updated on July 16th, 2025
Binary to Hexadecimal Conversion
In the world of computing, data is represented using various numeral systems, such as binary, decimal, and hexadecimal. Binary is a base-2 numeral system that uses only two symbols, typically 0 and 1, to represent data. Hexadecimal is a base-16 numeral system that uses sixteen distinct symbols, 0-9 and A-F. Sometimes, we need to convert between these systems to make data more readable or to simplify calculations. In this topic, we will learn how to convert binary to hexadecimal.
What is Binary?
Binary is a numeral system that represents numeric values using two symbols, typically 0 and 1.
It is the foundation of all binary code, which is used in computer and digital systems.
Each digit in a binary number is referred to as a bit. Binary is a base-2 system, meaning each digit represents a power of 2.
What is Hexadecimal?
Hexadecimal is a numeral system that represents values using sixteen symbols: 0-9 for values zero to nine, and A-F for values ten to fifteen.
It is a base-16 system commonly used in computing and digital electronics because it can represent large binary numbers more compactly.
Binary to Hexadecimal Formula
To convert binary to hexadecimal, follow these steps:
1. Divide the binary number into groups of four bits (starting from the right).
2. Convert each 4-bit binary group to its corresponding hexadecimal digit. For example, the binary group 1010 corresponds to the hexadecimal digit A.
How to Convert Binary to Hexadecimal?
Converting binary to hexadecimal involves grouping binary digits into sets of four and then translating each group to a single hexadecimal digit. Here’s how you can do it: Steps to convert binary to hexadecimal:
1. Write down the binary number and group the digits in sets of four, starting from the right.
2. Convert each group to its hexadecimal equivalent.
3. Combine these hexadecimal digits to get the final result.
Binary to Hexadecimal Conversion Chart
When converting binary to hexadecimal, it helps to have a chart for quick reference.
Below is a chart showing the conversions for 4-bit binary numbers to hexadecimal digits. ``` 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 ```
Common Mistakes and How to Avoid Them in Binary to Hexadecimal Conversion
When converting binary to hexadecimal, people often make mistakes.
Here are some common errors and tips to avoid them.
Mistake 1
Not grouping in sets of four
Skipping the step of grouping binary digits into sets of four can lead to incorrect conversions.
Always ensure each group is complete by adding leading zeros if necessary.
Mistake 2
Incorrect conversion of groups
Errors occur when converting binary groups to hexadecimal digits.
Double-check each group against a conversion chart to prevent mistakes.
Mistake 3
Misplacing digits
Reversing the order of hexadecimal digits can lead to incorrect results.
Ensure that you maintain the correct sequence as you convert and combine the groups.
Mistake 4
Confusing binary and hexadecimal symbols
Confusion arises when people mix up binary (0,1) and hexadecimal symbols (0-9, A-F).
Familiarize yourself with both systems to avoid errors.
Mistake 5
Overlooking leading zeros
Neglecting to add leading zeros in the binary groups can lead to incomplete conversions. Ensure each group has four bits by adding zeros where needed.
Binary to Hexadecimal Conversion Examples
Problem 1
Convert 11011110 to Hexadecimal
11011110 = DE
Explanation
Step-by-step conversion: 1. Group the binary number: 1101 1110 2. Convert each group: 1101 = D, 1110 = E 3. Result: DE
Problem 2
Convert 101010 to Hexadecimal
Solution: 101010 = 2A
Explanation
Step-by-step conversion: 1. Group the binary number (add leading zeros): 0010 1010 2.
Convert each group: 0010 = 2, 1010 = A 3. Result: 2A
Problem 3
Convert 11110001 to Hexadecimal
11110001 = F1
Explanation
Step-by-step conversion: 1. Group the binary number: 1111 0001 2. Convert each group: 1111 = F, 0001 = 1 3. Result: F1
Problem 4
Convert 100110 to Hexadecimal
The hexadecimal equivalent is 26.
Explanation
Step-by-step conversion: 1. Group the binary number (add leading zeros): 0010 0110 2. Convert each group: 0010 = 2, 0110 = 6 3. Result: 26
Problem 5
Converting 11111111 to Hexadecimal
11111111 = FF
Explanation
Step-by-step conversion: 1. Group the binary number: 1111 1111 2. Convert each group: 1111 = F, 1111 = F 3. Result: FF
FAQs on Binary to Hexadecimal
1.How many hexadecimal digits is 1 binary digit?
2.What is 1011 in hexadecimal?
3.Is hexadecimal used more than binary in computing?
4.How do I convert 1000 binary to hexadecimal?
Important Glossaries for Binary to Hexadecimal
- Conversion: The process of changing one numeral system into another, such as binary to hexadecimal.
- Bit: The smallest unit of data in a computer, represented by a binary digit (0 or 1).
- Digit: Any of the numerical symbols used in a numeral system, such as 0-9 in decimal, 0-1 in binary, or 0-9, A-F in hexadecimal.
- Numeral System: A writing system for expressing numbers; examples include binary, decimal, and hexadecimal.
- Leading Zero: A zero added to the left of a number to ensure uniformity in digit grouping, especially in binary conversions.
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
