Bitwise Calculator

About Bitwise Calculator

Welcome to the Bitwise Calculator, a powerful online tool for performing bitwise operations on integers with interactive visual bit diagrams. Whether you are a software developer working with low-level code, a computer science student learning binary arithmetic, or an engineer optimizing algorithms, this calculator helps you understand and visualize bitwise AND, OR, XOR operations with step-by-step bit-level analysis.

What Are Bitwise Operations?

Bitwise operations work directly on the binary representation of numbers, processing each bit (0 or 1) individually. These operations are fundamental to computer science and are used extensively in systems programming, cryptography, graphics, networking, and performance optimization.

Bitwise AND (&)

The AND operation compares each bit of two numbers and returns 1 only when BOTH bits are 1.

Common uses:

• Masking specific bits (e.g., extracting lower 4 bits with n & 0xF)
• Checking if a bit is set (e.g., n & (1 << k))
• Clearing bits (e.g., clearing bit k with n & ~(1 << k))
• Checking if a number is even (n & 1 == 0)

Bitwise OR (|)

The OR operation compares each bit and returns 1 when AT LEAST ONE bit is 1.

Common uses:

• Setting specific bits (e.g., set bit k with n | (1 << k))
• Combining flags or permissions
• Merging bit patterns

Bitwise XOR (^)

The XOR (exclusive OR) operation returns 1 when the bits are DIFFERENT.

Common uses:

• Toggling bits (e.g., toggle bit k with n ^ (1 << k))
• Swapping values without temporary variable (a ^= b; b ^= a; a ^= b;)
• Simple encryption and checksums
• Finding unique element in array where all others appear twice
• Error detection and correction

Why Use This Calculator?

Visual Bit Diagrams

Unlike simple calculators that only show the result, our tool displays interactive bit-by-bit diagrams showing exactly how each position is calculated. This visual approach makes understanding bitwise operations intuitive and educational.

Multiple Number Formats

Enter numbers in the format most convenient for your use case:

• Decimal: Standard base-10 numbers (e.g., 42, 255)
• Binary: Base-2 using 0 and 1 (e.g., 101010, 11111111)
• Hexadecimal: Base-16 using 0-9 and A-F (e.g., 2A, FF)

Configurable Bit Width

Choose the bit width that matches your application:

• Auto: Automatically uses the minimum bits needed
• 8-bit: For byte-level operations (0-255 unsigned)
• 16-bit: For short integers (0-65535 unsigned)
• 32-bit: Standard integer size in many languages
• 64-bit: For large integers and modern systems

How to Use This Calculator

1. Select input format: Choose Binary, Decimal, or Hexadecimal from the dropdown.
2. Enter your numbers: Type two integers in the input fields.
3. Choose bit width: Select a specific width or leave on Auto.
4. Select operation: Click AND, OR, XOR, or Calculate All.
5. Analyze results: View results in all three formats plus the visual bit diagram.

Practical Examples

Example 1: Checking Permissions

Permission flags: READ=4, WRITE=2, EXECUTE=1

• User permission = 6 (READ + WRITE = 110 in binary)
• Check READ: 6 & 4 = 4 (true, has READ)
• Check EXECUTE: 6 & 1 = 0 (false, no EXECUTE)

Example 2: Toggling a Feature Flag

Toggle bit 2 in value 5:

• 5 XOR 4 = 0101 XOR 0100 = 0001 = 1 (bit 2 was on, now off)
• 1 XOR 4 = 0001 XOR 0100 = 0101 = 5 (bit 2 was off, now on)

Example 3: Masking Lower Nibble

Extract lower 4 bits from 0xAB:

• 0xAB & 0x0F = 10101011 & 00001111 = 00001011 = 0x0B = 11

Frequently Asked Questions

What is a bitwise AND operation?

Bitwise AND compares each bit of two numbers and returns 1 only when BOTH bits are 1. For example, 5 AND 3: 0101 AND 0011 = 0001 (decimal 1). It is commonly used for masking specific bits, checking if a bit is set, and clearing bits.

What is a bitwise OR operation?

Bitwise OR compares each bit of two numbers and returns 1 when AT LEAST ONE bit is 1. For example, 5 OR 3: 0101 OR 0011 = 0111 (decimal 7). It is commonly used for setting specific bits and combining flags.

What is a bitwise XOR operation?

Bitwise XOR (exclusive OR) compares each bit and returns 1 when the bits are DIFFERENT. For example, 5 XOR 3: 0101 XOR 0011 = 0110 (decimal 6). XOR is used in cryptography, toggling bits, swapping values without a temporary variable, and error detection.

What are bit shift operations?

Bit shift operations move all bits in a number left or right by a specified number of positions. Left shift (<<) multiplies by powers of 2, while right shift (>>) divides by powers of 2. For example, 5 << 2 shifts 0101 left by 2 to get 10100 (decimal 20).

What is the NOT operation in bitwise arithmetic?

Bitwise NOT inverts every bit: 0 becomes 1 and 1 becomes 0. The result depends on the bit width. For an 8-bit number, NOT 5 (00000101) = 250 (11111010). This is also called ones complement.

Related Operations

For bit shift operations (left shift, right shift) and bitwise NOT, visit our Bit Shift Calculator.

Additional Resources

To learn more about bitwise operations:

• Bitwise operation - Wikipedia
• Bitwise operators - MDN Web Docs

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