Binary numbers are in base-2 (using only 0 and 1), while hexadecimal numbers are in base-16 (using digits 0-9 and letters A-F). The beauty of this conversion lies in the fact that four binary digits perfectly map to one hexadecimal digit, making the process straightforward.
Why Convert Binary to Hexadecimal?
Binary numbers can get very lengthy, especially in computer memory. Hexadecimal provides a shorter way to represent these numbers. For example, the binary 1010 1100 can be compactly written as AC in hexadecimal. Hexadecimal numbers are easier to read and use for humans, particularly when dealing with large binary values like those in programming or digital electronics.
Step-by-Step Conversion Process
1. Group Binary Digits into Sets of Four
Start from the rightmost digit of the binary number and break it into groups of four. If the number of digits isn’t a multiple of four, add zeros to the left to complete the last group.
Example: To convert 101101 to hexadecimal:
- Group into sets of four:
10 1101 - Add leading zeros to complete the leftmost group:
0010 1101
2. Convert Each Group to a Hexadecimal Digit
Each 4-bit binary group can be treated as a separate number. Convert each group to its hexadecimal equivalent. Use this quick reference table:
| 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 |
- For our example (
0010 1101):0010= 21101= D
3. Combine the Hexadecimal Digits
Combine the hexadecimal digits you obtained from each group to form the final hexadecimal number.
Example: The binary 101101 converts to hexadecimal as 2D.
Worked-Out Examples
Example 1: Convert 11011100 to Hexadecimal
Step 1: Group into sets of four: 1101 1100
Step 2: Convert each group to hexadecimal using the table:
1101= D1100= C
Step 3: Combine the hexadecimal digits: DC
Example 2: Convert 101010011 to Hexadecimal
Step 1: Group into sets of four: 101 0100 011
- Add leading zeros:
0001 0100 011
Step 2: Convert each group:
0001= 10100= 40011= 3
Step 3: Combine the digits: 143
Example 3: Convert 100111011011 to Hexadecimal
Step 1: Group into sets of four: 1001 1101 1011
Step 2: Convert each group:
1001= 91101= D1011= B
Step 3: Combine the digits: 9DB
Quick Tips for Conversion
- Always Group in Fours: To convert binary to hexadecimal, split the binary number into groups of four. If the leftmost group has fewer than four digits, add zeros to its left to make it a full group of four.
- Memorize the Basic Table: Having the binary-to-hexadecimal table handy or memorized makes the process faster. Each 4-bit binary group directly translates to a single hexadecimal digit.
- Cross-Check Your Work: After converting, the hexadecimal number should only contain digits (0-9) and letters (A-F). If it doesn’t, double-check your grouping and conversion steps.
Practice Table: Binary to Hexadecimal
Here’s a practice table with a few binary numbers to try converting on your own:
| Binary | Grouped | Hexadecimal |
|---|---|---|
| 101011 | 0001 0101 | 15 |
| 110101011010 | 1101 0101 1010 | D5A |
| 100101 | 0001 0010 1 | 92 |
| 111010101111 | 1110 1010 011 | EA7 |
Binary to hexadecimal conversion is an essential skill in computing, and with practice, you’ll find it becomes second nature.