OR Calculator
Perform logical OR operations on binary numbers with step-by-step calculations
Calculate Logical OR Operation
Example Calculation
Binary OR Example
Number 1: 10110 (binary) = 22 (decimal)
Number 2: 11101 (binary) = 29 (decimal)
Operation: 10110 OR 11101
Step-by-Step Solution
10110
OR 11101
-------
11111
Result: 11111 (binary) = 31 (decimal)
OR Truth Table
| A | B | A OR B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |
The OR operation returns 1 if either input is 1, and 0 only when both inputs are 0.
OR Gate Symbol
Standard OR gate symbol in digital logic
OR Operation Properties
•
Commutative: A OR B = B OR A
•
Associative: (A OR B) OR C = A OR (B OR C)
•
Identity: A OR 0 = A
•
Idempotent: A OR A = A
•
Annihilator: A OR 1 = 1
Understanding the Logical OR Operation
What is the Logical OR?
The logical OR is a fundamental boolean operation that performs an inclusive disjunction between two or more operands. The result is true (1) when at least one of the operands is true (1), and false (0) only when all operands are false (0).
Applications
- •Digital circuit design and logic gates
- •Computer programming and conditional statements
- •Boolean algebra and mathematical logic
- •Database queries and search operations
How to Calculate Bitwise OR
- 1. Align the binary numbers from right to left
- 2. Compare each bit position
- 3. Apply OR logic: 0 OR 0 = 0, all other combinations = 1
- 4. Write the result bit in the corresponding position
- 5. Continue for all bit positions
Symbols and Notation
- Logic: A ∨ B
- Programming: A || B (logical), A | B (bitwise)
- Electronics: A + B
- Boolean algebra: A + B