Bitwise Calculator
Perform bitwise AND, OR, XOR, NOT, left shift, and right shift operations on integers.
What Is the Bitwise Calculator?
The Bitwise Calculator performs bitwise AND, OR, XOR, NOT, left shift (<<), and right shift (>>) operations on integers, showing the binary representations of inputs and outputs alongside the decimal results. Essential for bit manipulation in programming, networking, and embedded systems.
Formula
How to Use
Enter two integer values (or one for NOT and shift operations). Select the bitwise operation: AND, OR, XOR, NOT, left shift, or right shift. The calculator shows the binary representations of both inputs, applies the operation bit-by-bit, and displays the result in both binary and decimal.
Example Calculation
12 AND 10: 1100 AND 1010 = 1000 = 8. 12 OR 10: 1100 OR 1010 = 1110 = 14. 12 XOR 10: 1100 XOR 1010 = 0110 = 6. NOT 12 (8-bit): NOT 00001100 = 11110011 = −13 (signed) or 243 (unsigned).
Understanding Bitwise
Bitwise operations work directly on the binary bits of integer values, making them the fastest operations a processor can perform. Unlike arithmetic operations (+, −, ×, ÷) which treat numbers as magnitudes, bitwise operations treat each bit independently according to Boolean logic tables. Every processor instruction set includes bitwise operations as primitive instructions.
In programming, bitwise operations are used for performance-critical code, embedded systems programming, network protocol implementation, graphics (pixel color component extraction), cryptography, data compression, and Boolean flag management. The bit manipulation idioms (checking bits, setting bits, clearing bits, toggling bits) are used constantly in systems programming.
Bit shifting is the most efficient way to multiply or divide by powers of 2. Many compilers automatically replace multiplication/division by power-of-2 constants with shifts. Left shifts fill vacated positions with zeros; right shifts fill with the sign bit for arithmetic right shifts (preserving sign for negative numbers) or with zeros for logical right shifts.
Frequently Asked Questions
What is a bitwise AND used for in programming?
Bitwise AND is used to check or extract specific bits (masking): value & 0xFF extracts the lowest byte. Also used to check if a number is odd: n & 1 == 1 means odd.
What is XOR used for?
XOR is used to toggle bits (flip specific bits without affecting others), swap two variables without a temp variable (a^=b; b^=a; a^=b), check if two values differ, and in cryptography (one-time pad, stream ciphers).
What does left shift do?
Left shift (a << n) multiplies a by 2ⁿ: 5 << 2 = 20 (5×4). It is faster than multiplication for powers of 2. Right shift (a >> n) divides by 2ⁿ (for unsigned integers).
What is bit masking?
Bit masking uses AND, OR, or XOR with a mask value to manipulate specific bits while leaving others unchanged. Common in hardware register programming, flag management, and network address calculations.
Is this calculator free?
Yes, completely free with no account required.