Free Bitwise Calculator

What Is a Bitwise Calculator?

A Bitwise Calculator is a specialized tool that performs logical operations – AND, OR, and XOR – at the bit level. This free online Bitwise Calculator accepts numbers in binary, octal, or decimal formats and returns the result in all three numeral systems, making it a versatile bit operation calculator for students, programmers, and digital engineers.

Bits and Numeral Systems

At the heart of any bitwise operation lies the bit (binary digit), the smallest unit of information in digital systems. A bit can hold only one of two values: $0$ or $1$ (also interpreted as false/true, off/on). Because a single bit conveys very little data, bits are grouped into larger units such as bytes (8 bits, capable of representing $2^{8}=256$ distinct states).

The human‑friendly decimal system (base‑10) uses digits 0–9, where each digit’s weight is a power of 10. For instance, the decimal number $123$ means $1 \times 10^{2} + 2 \times 10^{1} + 3 \times 10^{0}$. Binary numbers (base‑2) use only 0 and 1, with each position representing a power of 2. The binary number $101_{2}$ equals $1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0} = 5_{10}$. Other common bases include octal (base‑8) and hexadecimal (base‑16); while this calculator accepts octal inputs directly, hexadecimal conversions remain available through standard conversion tools.

When negative numbers are involved, the calculator employs the signed two’s complement representation, a universal method in computing that allows integers to be stored as binary strings.

Bitwise Operators: AND, OR, XOR

A bitwise operation compares two binary numbers bit by bit, from the most significant position to the least. The three operators supported by this tool follow these rules:

• Bitwise AND: The output bit is $1$ only if both corresponding input bits are $1$.
• Bitwise OR: The output bit is $1$ if at least one of the input bits is $1$.
• Bitwise XOR (eXclusive OR): The output bit is $1$ when exactly one of the input bits is $1$.

The truth table below summarizes all four possible combinations for a single‑bit pair:

Input A	Input B	AND	OR	XOR
0	0	0	0	0
0	1	0	1	1
1	0	0	1	1
1	1	1	1	0

These elementary operations underpin countless real‑world applications: data compression (setting/clearing bits), encryption algorithms, finite‑state machines, and network address calculation by masking an IP address with a subnet mask.

Step‑by‑Step Use of the Bitwise Calculator

Let’s perform a bitwise AND on the decimal numbers $87$ and $101$ as a concrete example.

1. Set the number of bits – The binary representation width must be chosen first. With 8 bits, the valid input range is $-128$ to $127$ (signed) or $0$ to $255$ (unsigned). For our small values, 8 bits are sufficient.
2. Select the input system – Choose binary, octal, or decimal. We’ll pick decimal.
3. Enter the numbers – Type $87$ into the first field and $101$ into the second. Their order is irrelevant.
4. Pick the operator – Select AND from the AND/OR/XOR options.
5. Read the results – The calculator instantly shows the outcome:
   • Binary: 0100 0101
   • Octal: 105
   • Decimal: 69

If the binary result could be interpreted as either a negative signed number (if the most significant bit is $1$) or a positive unsigned number, both decimal values are displayed. This dual‑display feature is particularly helpful when working with signed two’s complement data.

The same steps apply for OR and XOR operations – simply change the operator selection. After trying a few examples, you’ll quickly master bit manipulations using this free online Bitwise Calculator.