Binary to Hexadecimal Converter
Convert binary numbers to hexadecimal numbers easily and accurately.
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Table of Contents
Understanding Number Systems
Number systems are foundational to computing and provide different ways to represent numerical values. Understanding them is essential for effective programming, computer science, and digital electronics.
What Are Number Systems?
A number system is a mathematical notation for representing numbers using digits or symbols in a consistent manner. Each system has a "base" that determines how many unique digits are used before place values shift.
Decimal (Base-10)
Our everyday number system using digits 0-9. Each position represents a power of 10.
Example: 358₁₀
= 3×10² + 5×10¹ + 8×10⁰
= 300 + 50 + 8
Binary (Base-2)
Computer's native language using only digits 0-1. Each position represents a power of 2.
Example: 1011₂
= 1×2³ + 0×2² + 1×2¹ + 1×2⁰
= 8 + 0 + 2 + 1 = 11₁₀
Hexadecimal (Base-16)
Uses digits 0-9 and letters A-F (representing 10-15). Each position represents a power of 16.
Example: 1A3₁₆
= 1×16² + 10×16¹ + 3×16⁰
= 256 + 160 + 3 = 419₁₀
Why Computer Systems Use Different Number Bases
Computers use binary because electronic components naturally exist in two states: on (1) and off (0). However, binary numbers can become very long and difficult for humans to work with efficiently.
The Relationship Between Binary and Hexadecimal
Hexadecimal serves as a compact representation of binary data, making it much easier for humans to read and work with:
- Each hexadecimal digit represents exactly 4 binary digits (a nibble)
- 4 binary digits can represent values from 0 to 15, matching the range of a single hex digit
- This creates a perfect 4:1 compression ratio for representing binary information
Practical Applications
Programming
Memory addresses, color values (RGB), and bit manipulation in code often use hexadecimal notation.
Networking
MAC addresses and IPv6 addresses are written in hexadecimal format.
Computer Architecture
Low-level memory dumps, machine code, and debugging tools frequently use hexadecimal.
Digital Electronics
Hardware registers and configuration values are typically represented in binary or hexadecimal.
Binary-Hexadecimal Conversion Table
| Decimal | Binary | Hexadecimal |
|---|---|---|
| 0 | 0000 | 0 |
| 1 | 0001 | 1 |
| 2 | 0010 | 2 |
| 3 | 0011 | 3 |
| 4 | 0100 | 4 |
| 5 | 0101 | 5 |
| 6 | 0110 | 6 |
| 7 | 0111 | 7 |
| 8 | 1000 | 8 |
| 9 | 1001 | 9 |
| 10 | 1010 | A |
| 11 | 1011 | B |
| 12 | 1100 | C |
| 13 | 1101 | D |
| 14 | 1110 | E |
| 15 | 1111 | F |
How to Convert Binary to Hexadecimal
To convert binary to hexadecimal, we group the binary digits into sets of 4 (starting from the right) and convert each group to its hexadecimal equivalent.
Steps to Convert:
-
1Group the binary digits into sets of 4, starting from the right
-
2Convert each group of 4 binary digits to its hexadecimal equivalent
-
3Combine all hexadecimal digits in order
11010 = 0001 1010
0001 = 1
1010 = A
Result: 1A
Binary to Hexadecimal Conversion Table:
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 Examples
Example 1 Basic Numbers
0 = 0
1 = 1
10 = 2
Example 2 Common Values
100 = 4
1000 = 8
10000 = 10
Example 3 Mixed Numbers
1010 = A
1100 = C
1111 = F
Example 4 Larger Numbers
10000 = 10
100000 = 20
1000000 = 40