Bitwise Operations Calculator
Perform bitwise AND, OR, XOR, NOT, NAND, NOR, and XNOR operations on binary numbers with detailed bit-by-bit analysis.
What are Bitwise Operations?
Bitwise operations are logical operations that work directly on individual bits of binary numbers. These operations manipulate data at the bit level, making them extremely efficient for low-level programming, cryptography, graphics processing, and embedded systems. The main bitwise operations are AND (&), OR (|), XOR (^), NOT (~), NAND (⊼), NOR (⊽), and XNOR (⊙).
For example, performing AND operation on 1010 and 1100 gives 1000. This works by comparing each bit position: if both bits are 1, the result is 1; otherwise, it's 0. Bitwise operations are fundamental in computer science because computers process data as binary numbers internally. These operations are significantly faster than arithmetic operations because they work directly with the CPU's native binary representation.
Our free bitwise operations calculator performs all seven major bitwise operations with detailed bit-by-bit breakdown. Perfect for programmers, students, and engineers working with binary logic. For other binary conversions, try our Binary Calculator or Binary to Decimal Converter.
Bitwise Operations Explained
Understanding each bitwise operation with truth tables and examples:
1. AND (&) Operation
Returns 1 only if both bits are 1. Used for masking bits and checking flags.
| A | B | A & B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
2. OR (|) Operation
Returns 1 if at least one bit is 1. Used for setting bits and combining flags.
| A | B | A | B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
3. XOR (^) Operation
Returns 1 if bits are different. Used for toggling bits and encryption.
| A | B | A ^ B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
4. NOT (~) Operation
Inverts all bits (0→1, 1→0). Used for bit flipping and complement operations.
| A | ~A |
|---|---|
| 0 | 1 |
| 1 | 0 |
Real-World Applications of Bitwise Operations
Bitwise operations are used extensively in computer science and programming:
🔐 Cryptography
XOR operations are fundamental in encryption algorithms like AES and stream ciphers.
🎮 Graphics Programming
AND/OR operations for pixel manipulation, color blending, and alpha compositing.
🚀 Performance Optimization
Bitwise operations are 2-10x faster than arithmetic for division/multiplication by powers of 2.
🏁 Flags & Permissions
File permissions (chmod), feature flags, and state management using bit masks.
🌐 Network Protocols
IP address masking, subnet calculations, and packet header manipulation.
💾 Data Compression
Bit-packing for efficient storage and compression algorithms like Huffman coding.
For file permission analysis, check our Octal to Binary Converter tool.
Bitwise Operations Cheat Sheet
Quick reference for all bitwise operations:
| Operation | Symbol | Description | Example |
|---|---|---|---|
| AND | & | Both bits must be 1 | 1010 & 1100 = 1000 |
| OR | | | At least one bit is 1 | 1010 | 1100 = 1110 |
| XOR | ^ | Bits are different | 1010 ^ 1100 = 0110 |
| NOT | ~ | Inverts all bits | ~1010 = 0101 |
| NAND | ⊼ | NOT of AND | 1010 ⊼ 1100 = 0111 |
| NOR | ⊽ | NOT of OR | 1010 ⊽ 1100 = 0001 |
| XNOR | ⊙ | NOT of XOR (equality) | 1010 ⊙ 1100 = 1001 |
Benefits of Using Our Calculator
ProURLMonitor's free bitwise operations calculator offers:
- ✓All 7 Operations: AND, OR, XOR, NOT, NAND, NOR, XNOR in one tool.
- ✓Bit-by-Bit Breakdown: See exactly how each bit position is calculated.
- ✓Multiple Formats: Get results in binary, decimal, and hexadecimal instantly.
- ✓Input Validation: Automatically filters invalid binary input.
- ✓Educational: Perfect for learning logic gates and digital circuits.
- ✓100% Free: No registration or downloads required.
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📚 Frequently Asked Questions (FAQs)
Q: What is the difference between AND and OR?
A: AND returns 1 only if both bits are 1. OR returns 1 if at least one bit is 1. Example: 1010 & 1100 = 1000, but 1010 | 1100 = 1110.
Q: When should I use XOR?
A: XOR is perfect for toggling bits, swapping values without temp variables, simple encryption, and checking if bits are different. Property: A ^ B ^ B = A.
Q: What is NAND and why is it special?
A: NAND is NOT of AND (opposite of AND). It's universal—you can build all other logic gates using only NAND gates. Used extensively in digital circuit design.
Q: How is NOT different from NAND?
A: NOT inverts a single input (~A), while NAND performs AND on two inputs then inverts the result (~(A & B)).
Q: Why use bitwise operations instead of regular operators?
A: Bitwise operations are 2-10x faster because they work directly with CPU's native binary. Use for: flags, permissions, masks, fast multiplication/division by powers of 2.
Q: What does XOR with itself return?
A: A ^ A always equals 0. This property is used for swapping variables: A = A ^ B; B = A ^ B; A = A ^ B.
Q: Can I use bitwise operations on hexadecimal?
A: Yes! Convert hex to binary first, perform the operation, then convert back. Example: 0xF & 0xC = 0x8 (1111 & 1100 = 1000).
Q: What are bitwise shifts?
A: Left shift (<<) multiplies by 2, right shift (>>) divides by 2. Example: 1010 << 1 = 10100 (10 → 20), 1010 >> 1 = 0101 (10 → 5).
🚀 Start Using Bitwise Operations Calculator Now!
Use our free bitwise operations calculator to perform AND, OR, XOR, NOT, NAND, NOR, and XNOR operations instantly. Perfect for programmers debugging bit-level code, students learning digital logic, embedded systems engineers working with registers, and anyone dealing with binary data manipulation. Get bit-by-bit breakdown with results in binary, decimal, and hex formats.
No registration required. Unlimited calculations. Completely free forever!
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