Bitwise Calculator

Category: Algebra and General
- April 18, 2025
| |

Perform bitwise operations including AND, OR, XOR, NOT, shift operations and conversions between different number systems. This calculator helps you understand binary operations and bit manipulations.

Input Values

Bitwise Operation

Display Options

About Bitwise Operations

Bitwise operations work directly on the binary representation of numbers, manipulating individual bits. These operations are fundamental in computer science and are widely used in low-level programming, data compression, cryptography, and hardware control.

Basic Bitwise Operations
  • AND (&): Sets each bit to 1 if both corresponding bits are 1, otherwise 0.
  • OR (|): Sets each bit to 1 if at least one corresponding bit is 1, otherwise 0.
  • XOR (^): Sets each bit to 1 if exactly one corresponding bit is 1, otherwise 0.
  • NOT (~): Inverts all bits (0 becomes 1, 1 becomes 0).
  • Left Shift (<<): Shifts all bits to the left by a specified number of positions.
  • Right Shift (>>): Shifts all bits to the right, preserving the sign bit.
  • Unsigned Right Shift (>>>): Shifts all bits to the right, filling with zeros.
Common Applications
  • Flags and Masks: Using individual bits to store multiple boolean values efficiently.
  • Hardware Control: Setting or reading specific bits in hardware registers.
  • Optimizations: Using bit operations for faster calculations (e.g., multiplying by 2 using left shift).
  • Graphics Processing: Manipulating pixel color values and compositions.
  • Data Compression: Many compression algorithms rely on bitwise operations.
  • Cryptography: Implementing encryption and hash functions.
Bitwise Operation Formulas
AND: A & B
OR: A | B
XOR: A ^ B
NOT: ~A
Left Shift: A << n
Right Shift: A >> n
Unsigned Right Shift: A >>> n

What Is the Bitwise Calculator?

The Bitwise Calculator is a simple and interactive tool that helps you perform bit-level operations between numbers. It supports a variety of operations like AND, OR, XOR, NOT, and different shift operations. You can input numbers in decimal, binary, hexadecimal, or octal formats, choose the bit length (8, 16, or 32-bit), and view results in multiple number systems.

Why Use Bitwise Operations?

Bitwise operations are essential in computing and electronics. They allow efficient manipulation of data at the binary level and are used in:

  • Hardware programming (setting flags and registers)
  • Data compression and optimization
  • Encryption and cryptography
  • Graphics (pixel and color value manipulation)
  • Mathematical shortcuts (like multiplying or dividing by powers of 2)

How to Use the Bitwise Calculator

Follow these simple steps to get started:

  • Step 1: Enter two numbers in the input fields (Input A and Input B).
  • Step 2: Select the base (e.g., Decimal, Binary, Hexadecimal, Octal) for each input.
  • Step 3: Choose the bitwise operation you want to perform (e.g., AND, OR, XOR).
  • Step 4: Pick the bit length (8, 16, or 32-bit) depending on how detailed you want the result.
  • Step 5: For shift operations, enter the number of positions to shift.
  • Step 6: Select your preferred output base (binary, decimal, hexadecimal, or octal).
  • Step 7: Click Calculate to view the results instantly.

Features That Make It Easy

  • Input numbers in your preferred number system
  • Switch between various output bases effortlessly
  • See the result in all bases with one click
  • Detailed bit-by-bit operation table for visual clarity
  • Clear explanation of each operation and how the result was derived

Who Will Benefit from This?

Whether you’re a student learning binary arithmetic or a developer working with low-level code, this calculator is built to support your needs. It's also helpful as a quick reference when working with binary number systems or testing logic for circuit design.

It complements tools like a Binary Calculator for base-2 calculations, a Scientific Calculator for complex equations, or even a Matrix Calculator for linear algebra operations. If you're diving into number conversions, it's a handy partner to a Hex Calculator or Decimal Calculator.

Common Questions

What is a bitwise operation?

A bitwise operation works directly with the binary representation of numbers. Each number is seen as a series of 0s and 1s, and operations are applied to each bit individually.

What does the NOT (~) operation do?

The NOT operation flips every bit: 0 becomes 1, and 1 becomes 0. It's a unary operator and only needs one input.

When should I use shift operations?

Shift operations are useful for quick multiplications or divisions by powers of two. For instance, shifting left by 1 is the same as multiplying by 2.

Why is bit length important?

The bit length determines how many bits are used to represent the number. It controls truncation and how the calculator masks the output.

Can I view results in different formats?

Yes. You can view the result in binary, decimal, hexadecimal, and octal simultaneously. Just check the "Show result in all bases" option.

How This Tool Can Help

The Bitwise Calculator is a fast, user-friendly companion for anyone working with binary data or learning about how computers process numbers. It eliminates the need to convert numbers manually or remember operation rules. Plus, it’s a visual way to understand how each bit is affected by different logical operations.

It's also a great match for other math tools like:

Whether you're debugging a binary arithmetic issue, teaching bitwise logic, or just need a quick tool to verify results, this calculator simplifies your workflow and sharpens your understanding of bit-level math.