Binary Addition
Adding 10 and 13 in decimal gives 23, which equals 10111 in binary.
1010 + 1101
Result: 10111
Binary Calculator
Use this binary calculator to solve binary arithmetic and bitwise operations in one place. It accepts binary inputs, shows decimal interpretation, and returns the result with a step-by-step explanation.
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
Enter valid binary values made of only 0 and 1, choose the operation you need, and review the binary and decimal result instantly.
- Enter the first binary number using only 0s and 1s.
- Select the operation you want to perform (addition, subtraction, multiplication, division, or bitwise operations).
- Enter the second binary number (not required for NOT operation).
- Click 'Calculate' to see the result and step-by-step solution.
Tip: the NOT operation only uses the first input and flips every bit in that value.
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.
Example Binary Calculations
Binary Multiplication
Multiplying 5 by 3 gives 15, and 15 is written as 1111 in binary.
101 × 11
Result: 1111
Bitwise AND
Each position stays 1 only where both binary digits are 1.
1101 AND 1011
Result: 1001
Bitwise XOR
XOR returns 1 where the bits differ and 0 where they match.
1101 XOR 1011
Result: 0110
Binary Calculator FAQ
What does a binary calculator do?
A binary calculator performs arithmetic and bitwise operations on binary values and shows the result in binary, often alongside the decimal value for easier verification.
Why can I only enter 0 and 1?
Binary is a base-2 number system, so every valid binary number is built only from the digits 0 and 1.
What is the difference between binary arithmetic and bitwise operations?
Binary arithmetic treats the inputs as whole numbers for addition, subtraction, multiplication, and division. Bitwise operations compare or invert each bit position individually.
Why is the NOT operation different from the others?
NOT is a unary bitwise operation, so it works on a single binary input and flips each bit from 0 to 1 or from 1 to 0.