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Financial and mathematical calculation tools to help with your computations
Number Base Converter
Understanding Number Systems
Decimal (Base 10)
The decimal system is the most common number system, using digits 0-9. Each position represents a power of 10.
12310 = 1×102 + 2×101 + 3×100 = 100 + 20 + 3 = 123
Binary (Base 2)
The binary system uses only 0 and 1. Each position represents a power of 2.
11012 = 1×23 + 1×22 + 0×21 + 1×20 = 8 + 4 + 0 + 1 = 1310
Hexadecimal (Base 16)
The hexadecimal system uses digits 0-9 and letters A-F (representing values 10-15). Each position represents a power of 16.
1A16 = 1×161 + 10×160 = 16 + 10 = 2610
Octal (Base 8)
The octal system uses digits 0-7. Each position represents a power of 8.
528 = 5×81 + 2×80 = 40 + 2 = 4210
Conversion Methods
Decimal to Binary Conversion
- Divide the decimal number by 2
- Record the remainder (0 or 1)
- Divide the quotient by 2
- Repeat until the quotient becomes 0
- Read the remainders from bottom to top
Binary to Decimal Conversion
- Multiply each binary digit by its position value (power of 2)
- Add all the results
Common Applications
- Binary is used in computer memory and digital systems
- Hexadecimal is commonly used in programming for memory addresses and color codes
- Octal was historically used in some computing systems