Bitwise Calculator

Category: Algebra and General
- August 10, 2025
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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.
  • Optimisations: Using bit operations for faster calculations (e.g., multiplying by 2 using left shift).
  • Graphics Processing: Manipulating pixel colour values and compositions.
  • Data Compression: Many compression algorithms rely on bitwise operations.
  • Cryptography: Implementing encryption and hash functions.

Introducing the Bitwise Calculator

The Bitwise Calculator is a handy tool that helps you perform various bitwise operations. Whether you're working with binary numbers or need to manipulate bits, this calculator makes it easy. It allows you to explore operations like AND, OR, XOR, NOT, and shifting. Understanding these operations is crucial in computer Science and programming.

How to Use Input Values

To get started, simply enter your numbers in the designated input fields. You can work with numbers in different bases: decimal, binary, hexadecimal, or octal. After choosing your values, you can perform your desired operations. This flexibility helps you learn and see how different numbers interact through bitwise calculations.

Understanding Bitwise Operations

  • AND (&): Both bits must be 1 for the result to be 1.
  • OR (|): If at least one bit is 1, the result is 1.
  • XOR (^): Only one bit can be 1 for the result to be 1.
  • NOT (~): Reverses the bits, turning 1s into 0s and vice versa.
  • Left Shift (<<): Moves bits to the left, effectively multiplying by 2.
  • Right Shift (>>): Moves bits to the right, which can divide by 2.

Choosing the Right Operation

When you're set with your input values, you can select the operation you'd like to perform from a drop-down menu. Each option serves a unique purpose, and understanding these operations helps you grasp how binary manipulation works. For example, you might want to shift bits left to double a number or use AND to filter out certain bits.

Advanced Display Options

The calculator provides advanced options for displaying results. You can choose your preferred output base and even opt to see results in all bases at once. This feature is helpful if you want to understand how numbers look in binary, decimal, hexadecimal, or octal forms. Additionally, you can view a bit-by-bit operation table to see how the calculations unfold.

Operands and Their Representations

Each input number can be represented in different formats. The calculator shows both the binary form and the decimal equivalent for each input. This way, you get a clear understanding of how your numbers are being manipulated on a bit-by-bit level. It’s a great tool for learning binary number systems and their applications in real-world scenarios.

Learning About Bitwise Operations

  • Flags and Masks: Storing multiple boolean values in a single number.
  • Hardware Control: Reading and setting bits in hardware.
  • Data Compression: Using bitwise operations for efficient data storage.
  • Graphics Processing: Manipulating colours and images directly at the bit level.

Why Use the Bitwise Calculator?

Using the Bitwise Calculator helps deepen your understanding of basic computer science principles. Whether you're a student learning about binary operations or a hobbyist exploring programming, this tool simplifies complex operations. It guides you through bit manipulations and helps you visualise the results, making learning interactive and engaging.