Hex Calculator: Hexadecimal Converter & Calculator
A hexadecimal calculator performs arithmetic operations and conversions with hexadecimal numbers—the base-16 numeral system using digits 0-9 and letters A-F (representing values 10-15)—enabling calculations, conversions between hex, decimal, binary, and octal formats, bitwise operations, and number system translations essential for computer programming, digital electronics, memory addressing, color codes, cryptography, and low-level system programming. This comprehensive tool converts decimal to hexadecimal, hexadecimal to decimal, binary to hexadecimal with step-by-step solutions, hexadecimal to binary conversion, performs hex arithmetic (addition, subtraction, multiplication, division), handles all base conversions (hex-dec-oct-bin calculator), and provides detailed explanations for programmers, computer science students, hardware engineers, web developers working with color codes, and anyone requiring hexadecimal calculations and multi-base number system conversions.
🔢 Hexadecimal Calculator & Converter
Perform hex operations and conversions
Hexadecimal Arithmetic Operations
Enter hex numbers (0-9, A-F)
Hexadecimal to Decimal Converter
Convert hex to decimal with steps
Decimal to Hexadecimal Converter
Convert decimal to hex with steps
Hexadecimal to Binary Converter
Convert hex to binary with steps
Binary to Hexadecimal Converter
Convert binary to hex with steps
All Bases Converter (Hex, Dec, Oct, Bin)
Convert between all number bases
Understanding Hexadecimal Numbers
Hexadecimal (hex) is a base-16 number system that uses sixteen distinct symbols: digits 0-9 represent values 0-9, and letters A-F represent values 10-15. Hex is widely used in computing because each hex digit represents exactly four binary digits (bits), making it a compact way to represent binary data.
Hexadecimal Number System
Hexadecimal Place Values:
\[ \text{Hex: } 1A3_{16} = (1 \times 16^2) + (10 \times 16^1) + (3 \times 16^0) \]
\[ = 256 + 160 + 3 = 419_{10} \]
Each position represents a power of 16:
...16³ 16² 16¹ 16⁰ = ...4096 256 16 1
Hex digits: 0 1 2 3 4 5 6 7 8 9 A B C D E F
Values: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Conversion Formulas
Hex to Decimal Formula
Hexadecimal to Decimal:
\[ \text{Decimal} = \sum_{i=0}^{n-1} d_i \times 16^i \]
Where \( d_i \) is the digit value at position \( i \)
Example: 2F₁₆ = (2×16¹) + (15×16⁰) = 32 + 15 = 47₁₀
Decimal to Hex Formula
Decimal to Hexadecimal:
Divide decimal by 16 repeatedly, track remainders
Read remainders bottom to top for hex result
Example: 47₁₀ ÷ 16 = 2 remainder 15(F)
2 ÷ 16 = 0 remainder 2
Result: 2F₁₆
Detailed Conversion Examples
Example 1: Hex to Decimal
Problem: Convert hex A5 to decimal
Step 1: Identify hex digit values
A = 10, 5 = 5
Step 2: Apply positional notation
Position 1: A × 16¹ = 10 × 16 = 160
Position 0: 5 × 16⁰ = 5 × 1 = 5
Step 3: Sum the values
160 + 5 = 165
Answer: A5₁₆ = 165₁₀
Example 2: Decimal to Hex
Problem: Convert decimal 255 to hex
Step 1: Divide by 16, track remainders
255 ÷ 16 = 15 remainder 15 (F)
15 ÷ 16 = 0 remainder 15 (F)
Step 2: Read remainders bottom to top
FF
Answer: 255₁₀ = FF₁₆
Verification: (15×16) + 15 = 240 + 15 = 255 ✓
Example 3: Binary to Hex
Problem: Convert binary 10110101 to hex
Step 1: Group binary into 4-bit chunks (from right)
1011 | 0101
Step 2: Convert each 4-bit group to hex
1011₂ = 8+2+1 = 11₁₀ = B₁₆
0101₂ = 4+1 = 5₁₀ = 5₁₆
Answer: 10110101₂ = B5₁₆
Hex-Decimal-Binary-Octal Conversion Table
| Decimal | Hexadecimal | Binary | Octal |
|---|---|---|---|
| 0 | 0 | 0000 | 0 |
| 1 | 1 | 0001 | 1 |
| 2 | 2 | 0010 | 2 |
| 3 | 3 | 0011 | 3 |
| 4 | 4 | 0100 | 4 |
| 5 | 5 | 0101 | 5 |
| 6 | 6 | 0110 | 6 |
| 7 | 7 | 0111 | 7 |
| 8 | 8 | 1000 | 10 |
| 9 | 9 | 1001 | 11 |
| 10 | A | 1010 | 12 |
| 11 | B | 1011 | 13 |
| 12 | C | 1100 | 14 |
| 13 | D | 1101 | 15 |
| 14 | E | 1110 | 16 |
| 15 | F | 1111 | 17 |
| 16 | 10 | 10000 | 20 |
| 255 | FF | 11111111 | 377 |
Hexadecimal in Computing
Color Codes
RGB Color Format: #RRGGBB
Each pair represents Red, Green, Blue intensity (00-FF)
Examples:
#FF0000 = Red (255,0,0)
#00FF00 = Green (0,255,0)
#0000FF = Blue (0,0,255)
#FFFFFF = White (255,255,255)
#000000 = Black (0,0,0)
Real-World Applications
Programming & Development
- Memory addresses: RAM and storage locations in hex
- Color codes: Web design (CSS hex colors)
- Character encoding: ASCII, Unicode representations
- Debugging: Memory dumps, hex editors
- Cryptography: Hash values, encryption keys
Digital Electronics
- MAC addresses: Network hardware identifiers
- IPv6 addresses: Next-generation IP addressing
- Register values: Microcontroller programming
- Firmware: BIOS, embedded system code
- File formats: Binary file signatures
Common Hexadecimal Values
| Decimal | Hexadecimal | Common Use |
|---|---|---|
| 0 | 0x00 | Null, Empty |
| 10 | 0x0A | Line feed (LF) |
| 13 | 0x0D | Carriage return (CR) |
| 32 | 0x20 | Space character |
| 127 | 0x7F | Delete (DEL) |
| 255 | 0xFF | Max unsigned byte |
| 256 | 0x100 | Start of page 1 |
| 4096 | 0x1000 | Memory page (4KB) |
Tips for Hex Calculations
Quick Conversion Techniques:
- Memorize A-F values: A=10, B=11, C=12, D=13, E=14, F=15
- Binary grouping: Every 4 binary bits = 1 hex digit
- Powers of 16: 1, 16, 256, 4096, 65536
- Max values: F=15, FF=255, FFF=4095, FFFF=65535
- Color codes: #RGB shorthand = #RRGGBB expanded
Common Mistakes to Avoid
⚠️ Hexadecimal Errors
- Confusing letters: O (letter) vs 0 (zero), I (letter) vs 1 (one)
- Case sensitivity: A-F can be uppercase or lowercase (same value)
- Invalid digits: G-Z are not valid hex digits
- Wrong base: Don't mix decimal and hex without conversion
- Leading zeros: 0F = F (same value, but formatting matters in code)
- Missing 0x prefix: Convention to indicate hex in programming
- Binary grouping: Must group by 4 bits for hex conversion
Frequently Asked Questions
How do you convert hexadecimal to decimal?
Multiply each hex digit by its position value (power of 16), sum all products. Example: A5₁₆. A=10, position 1: 10×16=160. 5=5, position 0: 5×1=5. Total: 160+5=165₁₀. Remember A-F values: A=10, B=11, C=12, D=13, E=14, F=15. Position 0 is rightmost. Each position left increases power: 16⁰=1, 16¹=16, 16²=256, 16³=4096.
What is hexadecimal used for in computing?
Hex is compact representation of binary data. Uses: memory addresses (easier to read than binary), color codes in web design (#FF5733), MAC addresses (network hardware IDs), character encoding (Unicode: U+0041), debugging (memory dumps), file formats (headers, signatures), assembly language, IPv6 addresses. One hex digit = 4 binary bits, so byte (8 bits) = 2 hex digits (00-FF). More human-readable than long binary strings.
How do you convert binary to hexadecimal?
Group binary into 4-bit chunks from right, convert each group to hex. Example: 11010110₂. Group: 1101|0110. Convert each: 1101₂=13₁₀=D₁₆, 0110₂=6₁₀=6₁₆. Result: D6₁₆. If bits aren't multiple of 4, pad left with zeros. This works because 2⁴=16, so 4 binary bits equal 1 hex digit exactly. Fast method used in programming, digital electronics. Reverse works same way: each hex digit becomes 4 binary bits.
Why is hexadecimal called base-16?
Uses 16 distinct symbols (0-9, A-F), so base-16. Each position represents power of 16. Compare: decimal (base-10) uses 10 digits (0-9), binary (base-2) uses 2 digits (0-1). Base determines how many unique digits and position multiplier. Hex chosen for computing because 16 is power of 2 (2⁴=16), aligns perfectly with binary. Two hex digits = one byte (8 bits). Makes representing large binary numbers compact and readable.
What does 0x mean in hexadecimal?
0x is prefix indicating hex number in programming languages (C, C++, Java, Python, JavaScript). Example: 0xFF means hexadecimal FF (decimal 255). Without prefix, FF might be interpreted as variable name. Alternative notations: #FF (web colors), FFh (assembly), $FF (some older systems). Convention varies by context. Always use 0x in code to avoid ambiguity. Some systems use \x for hex bytes (\xFF). Prefix clarifies base, prevents confusion with decimal.
How many decimal numbers can 2 hex digits represent?
2 hex digits can represent 16²=256 values (0-255 decimal). Range: 00₁₆ to FF₁₆. This equals one byte (8 bits). Common uses: RGB color components (00-FF per color), ASCII characters (00-7F for standard), unsigned byte values in programming. 3 hex digits = 16³=4096 values (0-4095). 4 hex digits = 16⁴=65536 values (0-65535). Pattern: n hex digits represent 16ⁿ values.
Key Takeaways
Hexadecimal is an essential number system in computing, providing a compact and readable way to represent binary data. Understanding hex conversions, arithmetic, and applications is fundamental for programming, web development, digital electronics, networking, and computer science.
Essential principles to remember:
- Hex uses base-16: digits 0-9 and letters A-F (values 10-15)
- Each hex digit = 4 binary bits exactly
- Two hex digits = one byte (00-FF = 0-255)
- Position values: 1, 16, 256, 4096, 65536...
- 0x prefix indicates hex in programming
- Widely used for memory addresses, color codes, MAC addresses
- Group binary by 4 bits for hex conversion
- Case insensitive: A-F same as a-f
- Max single byte: FF₁₆ = 255₁₀ = 11111111₂
- Compact alternative to long binary strings
Getting Started: Use the interactive calculator at the top of this page to perform hexadecimal calculations and conversions. Choose your operation (hex arithmetic, conversions between hex-decimal-binary-octal), enter your values, and receive instant results with detailed step-by-step explanations. Perfect for programming, web development, digital electronics, or learning number system conversions.