Bitwise Calculator 🔢
Free online bitwise calculator for AND, OR, XOR, NOT operations with step-by-step solutions. Convert between binary, decimal, hexadecimal, and octal number systems instantly.
Bitwise Operations Truth Tables
AND Operation (&)
| A | B | A & B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Returns 1 only if both bits are 1
OR Operation (|)
| A | B | A | B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
Returns 1 if at least one bit is 1
XOR Operation (^)
| A | B | A ^ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Returns 1 if bits are different
NOT Operation (~)
| A | ~A |
|---|---|
| 0 | 1 |
| 1 | 0 |
Inverts all bits (flip 0 to 1, 1 to 0)
Calculator Performance Metrics
How to Use Bitwise Calculator
Step 1: Enter First Number
Type your first number and select its format (Binary, Decimal, Hexadecimal, or Octal). For binary, use only 0 and 1. For hexadecimal, use 0-9 and A-F. The calculator validates input automatically to ensure correct format for the selected number system.
Step 2: Select Operation
Choose from AND, OR, XOR, NOT, NAND, NOR, Left Shift, or Right Shift operations. Each operation performs specific bitwise logic. NOT operation requires only one number, while others need two operands. Shift operations move bits left or right by specified positions.
Step 3: Enter Second Number
For two-operand operations, enter second number with its format. Numbers can have different formats—calculator converts them automatically for calculation. NOT operation hides this field since it only requires one number. Shift operations use second number as shift amount.
Step 4: Calculate & Review
Click Calculate to see results in all formats: Binary, Decimal, Hexadecimal, and Octal. Review step-by-step solution showing bit-level operations. Understand how each bit position was calculated. Use Reset to start new calculation with cleared fields.
Understanding Bitwise Operations
What are Bitwise Operations?
Bitwise operations manipulate individual bits within binary numbers. These operations work at the bit level, performing logical operations (AND, OR, XOR, NOT) or shifting bits left or right. Essential in low-level programming, embedded systems, cryptography, and performance optimization.
Common Uses: Setting, clearing, or toggling specific bits in flags or registers. Efficient multiplication/division by powers of 2 using shifts. Cryptographic algorithms and hash functions. Network protocol implementations. Graphics programming and color manipulation. Data compression algorithms.
Bitwise Operators Explained
AND (&): Returns 1 only when both bits are 1. Used for masking bits or checking if specific bits are set. Example: \(1010 \& 1100 = 1000\)
OR (|): Returns 1 if at least one bit is 1. Used for setting bits or combining flags. Example: \(1010 | 1100 = 1110\)
XOR (^): Returns 1 when bits are different. Used for toggling bits or simple encryption. Example: \(1010 \wedge 1100 = 0110\)
NOT (~): Inverts all bits (0 becomes 1, 1 becomes 0). Used for bit flipping or creating masks. Example: \(\sim 1010 = 0101\) (in 4-bit representation)
Common Use Cases
💻 Programming & Development
Debug bitwise operations in code, understand bit manipulation algorithms, optimize performance-critical sections. Essential for systems programming, embedded development, and low-level optimizations. Verify bitwise logic before implementation in production code.
🔐 Cryptography
XOR operations fundamental to many encryption algorithms. Understand cipher operations, create simple encryption schemes, or analyze cryptographic protocols. Test encryption logic before deploying security-critical applications requiring bit-level data manipulation.
🌐 Network Engineering
Calculate subnet masks, understand IP address operations, work with network protocols using bitwise logic. Essential for CIDR notation, subnetting calculations, and understanding how network devices process addresses at bit level for routing decisions.
🎓 Education & Learning
Students learning computer science, digital logic, or computer architecture use bitwise calculators to understand binary operations. Visualize how computers perform logical operations. Practice for exams or verify homework problems with step-by-step solutions.
🎨 Graphics Programming
Manipulate color values, work with pixel data, or create visual effects using bitwise operations. RGB color mixing, alpha blending, and pixel manipulation often require bit-level operations for optimal performance in games and graphics applications.
⚙️ Embedded Systems
Control hardware registers, set device flags, or communicate with peripherals using bitwise operations. Essential for microcontroller programming where direct hardware manipulation required. Test register configurations before programming embedded devices.