Binary Calculator

Use this binary calculator for adding, subtracting, multiplying and dividing binary numbers. You can also perform bitwise operations like AND, OR, XOR, and NOT.

Binary Calculator

Enter binary numbers (using only 0s and 1s), select an operation, and click Calculate to see the result with step-by-step solution.

Result

What is Binary?

Binary is a base-2 number system that uses only two digits: 0 and 1. It is the fundamental language of computers and digital systems.

Each digit in a binary number is called a 'bit' (binary digit), and each bit represents a power of 2, starting from the rightmost bit (2^0 = 1) and increasing as you move left.

Binary Arithmetic Operations

  • Addition: Binary addition follows the same principles as decimal addition, but with different carrying rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (carry the 1).
  • Subtraction: Binary subtraction follows similar rules to decimal subtraction, with borrowing when necessary: 0-0=0, 1-0=1, 1-1=0, 0-1=1 (after borrowing).
  • Multiplication: Binary multiplication is simpler than decimal: you only multiply by 0 or 1, where multiplying by 0 gives 0 and multiplying by 1 gives the original number.
  • Division: Binary division follows the same long division process as in decimal, but with binary rules for subtraction and multiplication.

Bitwise Operations

  • AND (&): Performs a logical AND operation on each pair of bits. The result is 1 only if both bits are 1, otherwise it's 0.
  • OR (|): Performs a logical OR operation on each pair of bits. The result is 1 if at least one of the bits is 1, otherwise it's 0.
  • XOR (^): Performs an exclusive OR operation on each pair of bits. The result is 1 if the bits are different, otherwise it's 0.
  • NOT (~): Inverts all bits in a binary number, changing 0s to 1s and 1s to 0s.

How to Use the Binary Calculator

  1. Enter the first binary number using only 0s and 1s.
  2. Select the operation you want to perform (addition, subtraction, multiplication, division, or bitwise operations).
  3. Enter the second binary number (not required for NOT operation).
  4. Click 'Calculate' to see the result and step-by-step solution.

Applications of Binary Numbers

  • Computer systems use binary for all internal operations and data storage.
  • Digital electronics and circuit design rely on binary logic for signal processing.
  • Network protocols use binary for data transmission and addressing.
  • Programming at the machine level involves direct manipulation of binary data.