Binary Calculator
Perform binary arithmetic operations and convert between binary and decimal
Binary Calculator
Use the following calculators to perform the addition, subtraction, multiplication, or division of two binary values, as well as convert binary values to decimal values, and vice versa.
Quick Navigation
🧮 Binary Calculation—Add, Subtract, Multiply, or Divide
📊 Result
Note: Binary calculations use only digits 0 and 1. Each position represents a power of 2 (2⁰, 2¹, 2², etc.).
➡️ Convert Binary Value to Decimal Value
Result
= 128 + 0 + 32 + 0 + 8 + 0 + 2 + 0 = 170
⬅️ Convert Decimal Value to Binary Value
Result
85 ÷ 2 = 42 remainder 1
42 ÷ 2 = 21 remainder 0
21 ÷ 2 = 10 remainder 1
10 ÷ 2 = 5 remainder 0
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Reading remainders from bottom to top: 10101010
📚 Understanding Binary Numbers
Binary System Basics
The binary system uses only two digits: 0 and 1. Each position represents a power of 2, making it perfect for digital systems that work with on/off states.
Position Values
From right to left, each position represents 2⁰, 2¹, 2², 2³, etc. For example, 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 11 in decimal.
Computer Applications
Binary is fundamental to all digital technology. Computers use binary to represent data, instructions, and perform all calculations internally.
Binary Operations
Addition Rules
- 0 + 0 = 0
- 0 + 1 = 1
- 1 + 0 = 1
- 1 + 1 = 10 (carry the 1)
Multiplication Rules
- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1
Conversion Examples
1010 = (1×8) + (0×4) + (1×2) + (0×1) = 10
10 ÷ 2 = 5 remainder 0
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Result: 1010