Binary Arithmetic Operations
| Operation | Description | Example |
|---|---|---|
| ADD | Binary addition with carry | 1010 + 0110 = 10000 |
| SUB | Binary subtraction with borrow | 1010 − 0110 = 0100 |
| AND | 1 only when both bits are 1 | 1010 AND 0110 = 0010 |
| OR | 1 when at least one bit is 1 | 1010 OR 0110 = 1110 |
| XOR | 1 when bits are different | 1010 XOR 0110 = 1100 |
| NOT | Flips all bits (bitwise complement) | NOT 1010 = …11110101 |
Bitwise Truth Table
| A | B | AND | OR | XOR |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 0 |
Real-World Uses of Bitwise Operations
- AND: Masking — extracting specific bits. Setting flags in operating systems. Checking if a number is even: (n AND 1) = 0 if even.
- OR: Setting specific bits. Combining flags.
- XOR: Toggling bits. Encryption (simple XOR cipher). Swap two numbers without a temp variable: a=a XOR b; b=a XOR b; a=a XOR b
- NOT: Creating bitmask complements. Two's complement for negative numbers.
Frequently Asked Questions
We support binary Addition, Subtraction, bitwise AND, OR, XOR, and logical NOT operations.
No, the calculator handles varying length binary inputs and performs operations correctly without requiring leading zeros.
Yes, the tool displays the calculation result in binary, decimal, and hexadecimal formats simultaneously.
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