How do you convert hexadecimal to binary?
The concept of convert hexadecimal to binary plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding hexadecimal to binary conversion helps students in fields like digital electronics, computer programming, and competitive exams. Let’s explore what hexadecimal to binary conversion means and how to do it easily!
What Is Convert Hexadecimal to Binary?
Hexadecimal to binary conversion means changing a number from base 16 (hexadecimal) to base 2 (binary). In the hexadecimal system, we use the symbols 0–9 and A–F, while in the binary system, we use just 0 and 1. This conversion is key in computer science, electronics, and digital number system topics. You’ll find this concept applied in digital circuits, coding, and data representation.
Key Formula for Convert Hexadecimal to Binary
Here’s the standard formula: To convert each hex digit to binary, replace it with its 4-bit equivalent using a table.
Example:
If hex digit = A, binary = 1010
If hex digit = F, binary = 1111.
Final binary = All 4-bit groups joined together.
Why Convert Hexadecimal to Binary?
In digital electronics and programming, computers use binary for calculations and storage. Hexadecimal makes it easier for humans to read long binary numbers in a compact form. So, converting between hexadecimal and binary is a vital skill when working with digital data, addressing, color codes, and more. Students preparing for exams like JEE or Olympiad will notice such conversions are asked in various questions.
Hexadecimal and Binary Basics
| System | Base | Valid Symbols | Example |
|---|---|---|---|
| Binary | 2 | 0, 1 | 1011 |
| Hexadecimal | 16 | 0–9, A–F | 2A7 |
How Do You Convert Hexadecimal to Binary?
To convert hexadecimal to binary, replace each hex digit with its 4-bit binary equivalent. For example, hex "A6" becomes 1010 0110 in binary. Just use a hex-binary table and work digit by digit.
Step-by-Step Illustration
- Write the hexadecimal number, separating each digit clearly.
- Use a reference table to find the 4-bit binary equivalent for each hex digit.
- Replace each hex digit with its binary value.
- Combine all binary groups for the final answer.
Hexadecimal to Binary Table (0–F)
| Hex Digit | Binary Equivalent |
|---|---|
| 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 |
Worked Examples: Convert Hexadecimal to Binary
Example 1: Convert A6 to Binary
1. Separate hex digits: A and 6
2. Convert A to binary: A = 1010
3. Convert 6 to binary: 6 = 0110
4. Final binary answer: 10100110
Example 2: Convert 5A to Binary
1. Separate hex digits: 5 and A
2. Convert 5: 0101
3. Convert A: 1010
4. Final binary answer: 01011010
Example 3: Convert E9A to Binary
1. E = 1110
2. 9 = 1001
3. A = 1010
4. Concatenate: 111010011010
Online Tools & Calculators
Want to check your work fast? You can use online calculators—like Vedantu’s Binary Calculator—to instantly convert hexadecimal to binary and verify your answers.
Frequent Errors and Misunderstandings
- Mixing up decimal, binary, and hexadecimal numbers.
- Missing out leading zeros in 4-bit groups.
- Trying to convert using decimal steps (not needed, convert each digit directly).
Try These Yourself
- Convert FDA16 to binary
- Convert 98B16 to binary
- Convert 5C16 to binary
- Convert 10016 to binary
Relation to Other Concepts
The skill to convert hexadecimal to binary connects closely with other number system conversions like decimal to binary, binary to decimal, and hexadecimal number system. Mastering this helps students handle computer science problems with ease.
Classroom Tip
A quick way to remember hexadecimal to binary is to associate each hex digit with its matching 4-bit value and practice with a conversion table. Vedantu’s teachers often use color-coded tables and daily doubles to make this memory trickier fun and effective!
Wrapping It All Up
We explored convert hexadecimal to binary—from definition, step-by-step method, tables, examples, frequent mistakes, and related topics. Keep practicing with help from Vedantu or join a live class to clear any doubts and get exam-ready confidence in number systems!
Related reads and practice topics:
- Number System Conversion (types and tricks)
- Binary Number System (foundation skill)
- Hexadecimal Number System (in-depth base 16)
- Decimal to Binary (see comparative methods)
FAQs on How to Convert Hexadecimal to Binary (with Table & Examples)
1. How do you convert hexadecimal to binary?
To convert hexadecimal to binary, replace each hex digit with its 4-bit binary equivalent. For example, A in hex equals 1010 in binary. This method makes it easy to read and use the binary number system.
2. What is 1010111 in binary code?
The number 1010111 is already in binary code. Each digit represents powers of 2, which is the base of the binary number system. No conversion is needed unless changing to another number system.
3. How to convert binary to hexadecimal with example?
To convert binary to hexadecimal, group the binary digits in sets of four (right to left) and write their hex equivalent. For example, 1101 0110 becomes D6 in hexadecimal format.
4. What is 1010111 binary to hexadecimal?
Binary 1010111 is grouped as 0101 0111. Each group converts to its hex digit: 0101 = 5 and 0111 = 7, so 1010111 equals 57 in hexadecimal representation.
5. Why are 4 bits used to represent a hexadecimal digit?
Each hexadecimal digit can show values from 0 to 15, which fits exactly into 4 bits (since $2^4 = 16$). This makes converting between hexadecimal and binary very efficient.
6. What is the importance of hexadecimal in computers?
The hexadecimal system is important because it shortens long binary sequences, making it easier for humans to read and write computer code without errors. Hex simplifies binary for programming.
7. Can every binary number be converted to hexadecimal?
Yes, every binary number can be converted to hexadecimal. You just group the binary digits into sets of four. Add leading zeros if needed to complete the last group before conversion.
8. What’s a real-life example of converting hexadecimal to binary?
A real-life example: converting hex code 2F for colors in web design. 2 in hex equals 0010 and F equals 1111, so 2F is 00101111 in binary form.
