Binary Calculator
Perform binary arithmetic and logical operations. Add, subtract, multiply, divide, AND, OR, and XOR binary numbers with automatic conversion to decimal, hexadecimal, and octal.
Decimal to Binary:
Divide by 2, record remainders from bottom to top
Binary to Decimal:
Sum of (digit × 2^position)
Binary Addition:
0+0=0, 0+1=1, 1+1=10 (carry 1)
Divide by 2, record remainders from bottom to top
Binary to Decimal:
Sum of (digit × 2^position)
Binary Addition:
0+0=0, 0+1=1, 1+1=10 (carry 1)
Example: Convert 13 to binary
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Binary: 1101 (read remainders up)
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Binary: 1101 (read remainders up)
🔗 Related Calculators
📐 Formula
Decimal to Binary:
Divide by 2, record remainders from bottom to top
Binary to Decimal:
Sum of (digit × 2^position)
Binary Addition:
0+0=0, 0+1=1, 1+1=10 (carry 1)
Divide by 2, record remainders from bottom to top
Binary to Decimal:
Sum of (digit × 2^position)
Binary Addition:
0+0=0, 0+1=1, 1+1=10 (carry 1)
📝 Example Calculation
Example: Convert 13 to binary
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Binary: 1101 (read remainders up)
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Binary: 1101 (read remainders up)