Base Calculator — Arithmetic in Any Number Base
Perform addition, subtraction, multiplication, and division in any number base from 2 (binary) to 36. Shows the result in the same base plus the decimal equivalent. See also our Binary to Decimal Converter and Hex to Decimal Converter.
How to Perform Arithmetic in Different Bases
- Enter the first number using valid digits for the chosen base.
- Select the arithmetic operation (+, -, ×, ÷).
- Enter the second number in the same base.
- Set the base (2 for binary, 8 for octal, 16 for hex, etc.).
- Click Calculate to see the result in that base and in decimal.
Formula
1. Convert both numbers from base-N to decimal
2. Perform the arithmetic in decimal
3. Convert the result back to base-N
Valid digits by base:
Base 2 (binary): 0, 1
Base 8 (octal): 0-7
Base 10 (decimal): 0-9
Base 16 (hex): 0-9, A-F
Base 36: 0-9, A-ZExample
Add 1010 + 1101 in base 2 (binary):
1010₂ = 10 in decimal
1101₂ = 13 in decimal
10 + 13 = 23 in decimal
23 in binary = 10111₂
Number Base Reference Table
| Decimal | Binary (2) | Octal (8) | Hex (16) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 8 | 1000 | 10 | 8 |
| 10 | 1010 | 12 | A |
| 15 | 1111 | 17 | F |
| 16 | 10000 | 20 | 10 |
| 32 | 100000 | 40 | 20 |
| 64 | 1000000 | 100 | 40 |
| 100 | 1100100 | 144 | 64 |
| 255 | 11111111 | 377 | FF |
Frequently Asked Questions
What digits are valid in each base?
A base-N system uses digits 0 through N-1. For bases above 10, letters A-Z represent values 10-35. Base 16 (hex) uses 0-9 and A-F.
Why is binary (base 2) important?
Computers use binary because digital circuits have two states (on/off). All computer data is ultimately stored and processed in binary.
What is hexadecimal used for?
Hexadecimal (base 16) is a compact way to represent binary data. Each hex digit represents exactly 4 binary bits. It is used for memory addresses, color codes, and MAC addresses.
Can I use base 36?
Yes. Base 36 uses digits 0-9 and letters A-Z (26 letters + 10 digits = 36 symbols). It is the highest base that uses standard alphanumeric characters.
How does division work in other bases?
Division returns the integer quotient (floor division). The result is converted back to the specified base. Remainders are not shown separately.