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Math

Binary Calculator

Add, subtract, multiply, and divide binary numbers. Shows binary, decimal, and hex results.

What is Binary Calculator?

A binary calculator performs arithmetic operations — addition, subtraction, multiplication, and division — directly on binary (base-2) numbers. It accepts numbers made up of only 0s and 1s and returns results in binary, decimal (base-10), and hexadecimal (base-16), making it essential for computer science, digital electronics, and programming tasks.

How to use

  1. 1 Enter Binary Number A (only 0s and 1s).
  2. 2 Enter Binary Number B (only 0s and 1s).
  3. 3 Select the operation: Add, Subtract, Multiply, or Divide.
  4. 4 The result is shown in binary, decimal, and hexadecimal. The conversion table below shows both inputs in all three bases.

Formula

Binary arithmetic follows the same rules as decimal but with only two digits. Binary addition: 0+0=0, 0+1=1, 1+1=10 (carry 1). To compute, convert both binary numbers to decimal integers using parseInt(n, 2), perform the operation, then convert back using .toString(2) for binary and .toString(16) for hex.

Example calculation

1101 (13) + 1011 (11) = 11000 (24, 0x18). 1111 (15) − 0110 (6) = 1001 (9, 0x9). 1010 (10) × 0011 (3) = 11110 (30, 0x1E).

Frequently asked questions

What is binary arithmetic?

Binary arithmetic is math performed in base 2, where the only digits are 0 and 1. Each digit position represents a power of 2, unlike decimal where each position represents a power of 10.

How do you add binary numbers?

Add column by column from right to left, just like decimal. 0+0=0, 1+0=1, 1+1=10 (write 0, carry 1), 1+1+1=11 (write 1, carry 1).

What happens with negative results in binary subtraction?

If the result is negative, this calculator shows a minus sign before the binary representation of the absolute value.

How is binary related to hexadecimal?

Every 4 binary digits map directly to one hex digit (0–F), because 2⁴ = 16. This makes hex a convenient shorthand for long binary strings in programming.

Can I divide binary numbers?

Yes. The calculator performs integer division and shows the quotient. If the divisor is zero, an error is shown.