Hexadecimal Calculator
Calculate with hexadecimal numbers and convert between hexadecimal and decimal.
Hexadecimal calculation – Addition, Subtraction, Multiplication or Division
Result
Hexadecimal value:
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Decimal value:
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Convert Hexadecimal to Decimal
Convert Decimal to Hexadecimal
The Hexadecimal System
The hexadecimal system (or hex) is a base-16 number system with 16 different symbols: the digits 0 to 9 and the letters A to F. Each hexadecimal digit corresponds to 4 bits (a nibble) in binary, making it particularly well-suited for computing.
Conversion Table
| Hexadecimal | Binary | Decimal |
|---|---|---|
| 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 |
| A | 1010 | 10 |
| B | 1011 | 11 |
| C | 1100 | 12 |
| D | 1101 | 13 |
| E | 1110 | 14 |
| F | 1111 | 15 |
Convert Decimal to Hexadecimal
To convert a decimal number to hexadecimal, divide the number repeatedly by 16 and note the remainders. The remainders read from bottom to top give the hexadecimal number. Example:
1500 in Hexadecimal:
1500 ÷ 16 = 93 Remainder 12 (C)
93 ÷ 16 = 5 Remainder 13 (D)
5 ÷ 16 = 0 Remainder 5
Result: 5DC
Convert Hexadecimal to Decimal
To convert a hexadecimal number to decimal, multiply each digit by the corresponding power of 16 (starting from the right) and add the results. Example:
2AA in Decimal:
2 × 16² + 10 × 16¹ + 10 × 16⁰
= 2 × 256 + 10 × 16 + 10 × 1
= 512 + 160 + 10
= 682
Applications in Computing
The hexadecimal system is frequently used in computing because it compactly represents binary values. One hexadecimal digit corresponds exactly to 4 bits, which makes reading and writing binary data easier. Used for example in:
- RGB color codes (e.g. #FF0000 for red)
- Memory addresses
- Program debugging
- Unique identifiers (UUID)
Quick Guide to Hexadecimal
Base 16 uses 0–9 and then A–F (A=10, B=11, …, F=15). The 0x notation is common in computing for memory addresses, colors and codes.
- Decimal → Hex: repeated division by 16, read remainders from bottom to top.
- Hex → Decimal: sum of digits × 16ⁿ according to position.
- Binary relation: 1 hex digit = 4 bits, so 2 hex digits = 1 byte.
1500₁₀ → 5DC₁₆ (Remainders 12=C, 13=D).
2AA₁₆ → 2×16² + 10×16¹ + 10×16⁰ = 682.
0xFF → 255 in Decimal, 11111111 in Binary.
Tip: For verification, convert back to decimal and compare. Errors often occur due to incorrect position of powers of 16.
Need a detailed explanation (division by 16, 0x notation, binary relation)? Ask the Math AI assistant.