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Binary Calculator

Perform arithmetic and bitwise operations on binary numbers: add, subtract, multiply, divide, AND, OR, XOR, NOT and bit shifts.

How it works Report a problem

Binary Studio Pro

Arithmetic, Bitwise logic, and Multi-base sync

About the Binary Calculator

Perform arithmetic and bitwise operations on binary numbers: add, subtract, multiply, divide, AND, OR, XOR, NOT and bit shifts.

How to use the Binary Calculator

  1. Enter Binary A.
  2. Choose an Operation.
  3. Enter Binary B (or the shift amount) and press Calculate.

Formula and method

Binary numbers use only 0 and 1, with each position worth a power of two. Bitwise operations act on each pair of bits independently: AND gives 1 only if both bits are 1, OR gives 1 if either is 1 and XOR gives 1 if the bits differ.

Worked example

1010 + 0110 = 10000 (10 + 6 = 16). 1010 AND 0110 = 0010.

Converting. Binary 1101 = 8 + 4 + 0 + 1 = 13 in decimal, and decimal 45 is 101101 in binary.

When to use the Binary Calculator

  • Converting between binary and decimal for computer science classes.
  • Doing binary arithmetic and bitwise operations.
  • Understanding how computers store numbers.

Common mistakes to avoid

  • Reading binary from the wrong end. The rightmost digit is the smallest.
  • Forgetting the fixed width when working with signed numbers.

Tips

  • Shifting left by one bit doubles a number; shifting right halves it.
  • Use the binary calculator with a decimal converter to check your work.

Frequently asked questions

How do I convert binary to decimal?
Add the powers of two for each position that has a 1. 1010 = 8 + 2 = 10.
How do I convert decimal to binary?
Divide by 2 repeatedly and write down the remainders, then read them from bottom to top.
Why do computers use binary?
Electronic circuits are simple and reliable with two states, on and off.