Binary Calculator

How to calculate in binary

Binary arithmetic is similar to decimal arithmetic but uses a base of **2** instead of **10**.

• Addition: * 0 + 0 = 0 * 0 + 1 = 1 * 1 + 0 = 1 * 1 + 1 = 10 (write 0, carry 1) * 1 + 1 + 1 (carried) = 11 (write 1, carry 1)
• Subtraction: If subtracting 1 from 0, borrow 1 from the next column to the left. The borrowed 1 becomes 2 in the current column (2 - 1 = 1).
• Multiplication: Multiply column by column, shifting left each line, then add the results. Since binary digits are only 0 or 1, each line is either all zeros or a copy of the top number.
• Division: Standard long division can be performed, or numbers can be converted to decimal, divided, and the quotient converted back to binary.

FAQ

What is base 2?

Base 2, or binary representation, is a numeric system that represents numbers using only two digits: **0** and **1**. It is the native language of digital circuits and computer hardware.

How do you convert binary to decimal?

Multiply each digit by 2 raised to the power of its column index (starting at 0 for the rightmost digit). For example: **1101₂ = (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 8 + 4 + 0 + 1 = 13₁₀**.

How do you convert fractional binary to decimal?

For digits to the right of the binary point, use negative powers of 2. For example: **10.1₂ = (1 × 2¹) + (0 × 2⁰) + (1 × 2⁻¹) = 2 + 0 + 0.5 = 2.5₁₀**.