AND Calculator
Perform bitwise AND operations on binary numbers with detailed step-by-step solutions
Calculate Bitwise AND
Maximum value: 255
Use only 0 and 1
AND Operation Results
AND Truth Table
| A | B | A & B |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
AND returns 1 only when both inputs are 1
AND Gate Symbol
Standard AND gate symbol in digital logic
AND Properties
Commutative
A & B = B & A
Associative
(A & B) & C = A & (B & C)
Identity
A & 1 = A
Zero
A & 0 = 0
Idempotent
A & A = A
Example Calculation
Problem
Calculate 1101 & 1011 (binary)
Solution
1101
& 1011
----
1001
Bit-by-bit: 1&1=1, 1&0=0, 0&1=0, 1&1=1
Understanding the AND Operation
What is the AND Operation?
The AND operation is a fundamental logical operation that returns true (1) only when all inputs are true (1). In bitwise operations, it compares corresponding bits of two numbers and returns 1 only when both bits are 1.
How it Works
For each bit position, the AND operation follows this rule:
- •0 & 0 = 0
- •0 & 1 = 0
- •1 & 0 = 0
- •1 & 1 = 1
Real-World Applications
Digital Electronics
AND gates are fundamental building blocks in digital circuits, used in processors, memory systems, and control logic.
Programming
Bitwise AND is used for bit masking, flag checking, and optimization in low-level programming and embedded systems.
Computer Graphics
Used in pixel manipulation, color blending, and implementing various graphical effects and filters.
Important Note
The AND operation is commutative and associative, making it predictable and useful for creating complex logical expressions and circuits.