The binary system (base-2) is used internally by almost all modern computers and digital systems, while the hexadecimal system (base-16) is a more human-friendly way to represent large binary values. Converting binary to hexadecimal is essential in many fields, such as computer programming, networking, and system design, where binary values need to be translated into a more readable format.
What is Binary?
A binary number system is a base-2 numeral system that uses only two digits: 0 and 1. Binary is used by computers because it matches the digital logic states of on (1) and off (0).
- Example: 101101 (binary)
Each binary digit represents a power of 2, starting from the right. For instance:
1011012 = 1×25+0×24+1×23+1×22+0×21+1×20 = 4510What is Hexadecimal?
A hexadecimal (hex) number system is a base-16 system that uses sixteen symbols: the digits 0-9 and the letters A-F (where A = 10, B = 11, C = 12, D = 13, E = 14, F = 15).
- Example: 2F (hexadecimal)
Each hexadecimal digit represents a power of 16. Hexadecimal numbers are often used to represent large binary numbers more compactly.
Binary to Hexadecimal Conversion
Converting binary numbers to hexadecimal is straightforward because 16 is a power of 2 ((16 = 2^4)). This means every 4 binary digits (bits) can be grouped into a single hexadecimal digit.
- Binary group: 0000, 0001, 0010, 0011, … 1111
- Hexadecimal equivalent: 0, 1, 2, 3, … F
Steps to Convert Binary to Hexadecimal
- Group the binary digits into sets of four, starting from the right. If there are fewer than four digits in the last group, pad with zeros on the left.
- Convert each group of four binary digits into its hexadecimal equivalent using the binary-to-hexadecimal conversion table.
- Write the hexadecimal digits in the same order as the grouped binary digits.
Example Conversions
Let’s look at a few examples of converting binary numbers to hexadecimal.
Example 1: Convert 11011011 (binary) to hexadecimal.
- Group the binary digits into sets of four: 1101 and 1011.
- Convert each group:
- 1101 (binary) = D (hex)
- 1011 (binary) = B (hex)
- Combine the hexadecimal digits: DB
So, 11011011 (binary) is equal to DB (hexadecimal).
Example 2: Convert 10101 (binary) to hexadecimal.
- Group the binary digits, padding with zeros: 0001 and 0101.
- Convert each group:
- 0001 (binary) = 1 (hex)
- 0101 (binary) = 5 (hex)
- Combine the hexadecimal digits: 15
So, 10101 (binary) is equal to 15 (hexadecimal).
Example 3: Convert 1110110101 (binary) to hexadecimal.
- Group the binary digits, padding with zeros: 0001, 1101, and 1010.
- Convert each group:
- 0001 (binary) = 1 (hex)
- 1101 (binary) = D (hex)
- 1010 (binary) = A (hex)
- Combine the hexadecimal digits: 1DA
So, 1110110101 (binary) is equal to 1DA (hexadecimal).
Binary to Hexadecimal Conversion Table
Here is a quick reference table showing the conversion of binary groups to their hexadecimal equivalents:
| 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 |
Online Binary to Hexadecimal Converter
Online tools make it easy to convert binary numbers to hexadecimal. These tools are especially useful when dealing with long binary numbers. They are commonly used in computer science, networking, and embedded system applications.
Steps to Use an Online Converter
- Enter the binary number in the input field.
- Click the “Convert” button.
- The tool will display the equivalent hexadecimal value.