Binary Calculator
Perform binary arithmetic (addition, subtraction, multiplication, division) and convert binary numbers to decimal and hexadecimal instantly.
How Binary Math Works
The binary system (Base 2) uses only two digits: 0 and 1. It is the fundamental language of computers.
Binary Addition
Binary addition works just like decimal addition but carries over when the sum reaches 2 (which is '10' in binary).
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (write 0, carry 1)
Binary Subtraction
Similar to decimal subtraction, but you borrow from the next column which is worth 2 times the value.
- 1 - 1 = 0
- 1 - 0 = 1
- 10 - 1 = 1 (borrow 2, subtract 1)
Conversions
- Decimal (Base 10): The standard system using digits 0-9. Example: 10 in decimal is 1010 in binary.
- Hexadecimal (Base 16): Uses digits 0-9 and letters A-F. It is often used in programming to represent large binary numbers more compactly. Example: 1111 (Binary) = 15 (Decimal) = F (Hex).
? Frequently Asked Questions
Computers use transistors which act as switches. They can only be in two states: On (1) or Off (0). Binary is the most efficient way to represent data using these physical limitations.
Each digit in a binary number represents a power of 2. For example, 101 = (1 × 2^2) + (0 × 2^1) + (1 × 2^0) = 4 + 0 + 1 = 5.
1111 in binary equals 15 in decimal. It is calculated as 8 + 4 + 2 + 1.