Binary Calculator

Perform arithmetic operations with binary numbers and convert between binary, decimal, hexadecimal, and octal number systems. Perfect for computer science students and programmers.

Binary Calculator

First Binary Number

Operation

Second Binary Number

Quick Examples

Number System Converter

Input Number

Input Base

Calculation Result

10110

Binary Result

Decimal:22

Hexadecimal:16

Octal:26

Step by Step

Binary A: 1010 = Decimal 10

Binary B: 1100 = Decimal 12

Operation: add

Result: 10110 = Decimal 22

Number Conversions

Binary:1010

Decimal:10

Hexadecimal:A

Octal:12

How to Use This Calculator

This binary calculator allows you to perform arithmetic and bitwise operations with binary numbers, as well as convert between different number systems.

Enter your first binary number (using only 0s and 1s)
Select the operation you want to perform
Enter the second binary number (if required)
View the result in binary, decimal, hexadecimal, and octal formats
Use the converter section to convert numbers between different bases

Binary Operations

Arithmetic Operations

Addition: Add two binary numbers following binary arithmetic rules
Subtraction: Subtract one binary number from another
Multiplication: Multiply two binary numbers
Division: Divide one binary number by another

Bitwise Operations

AND (&): Returns 1 only when both bits are 1
OR (|): Returns 1 when at least one bit is 1
XOR (^): Returns 1 when bits are different
NOT (~): Inverts all bits (0 becomes 1, 1 becomes 0)
Left Shift (<<): Shifts bits to the left by specified positions
Right Shift (>>): Shifts bits to the right by specified positions

Example Calculations

Binary Addition

1010 + 1100 = 10110

In decimal: 10 + 12 = 22

Bitwise AND

1010 & 1100 = 1000

Each bit position: 1&1=1, 0&1=0, 1&0=0, 0&0=0

Left Shift

1010 << 2 = 101000

Shifts all bits 2 positions to the left (equivalent to multiplying by 4)

Frequently Asked Questions

What is binary number system?

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

How do I convert decimal to binary?

Divide the decimal number by 2 repeatedly and collect the remainders in reverse order. For example, 10 ÷ 2 = 5 remainder 0, 5 ÷ 2 = 2 remainder 1, 2 ÷ 2 = 1 remainder 0, 1 ÷ 2 = 0 remainder 1. Reading remainders from bottom to top: 1010.

What's the difference between logical and arithmetic shifts?

Logical shifts fill with zeros, while arithmetic right shifts preserve the sign bit. This calculator performs logical shifts for simplicity.

Binary Calculator