Input Controls
Live Display
| A | B | Output (Y = A ⊕ B) |
|---|---|---|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |
Current Observation
Set inputs A and B using the toggle switches and observe how the EX-OR gate processes the signals. Output becomes HIGH only when the two inputs are different.
Signal Flow Observation
Toggle the switches to observe signal propagation through the circuit. When inputs are different (0 and 1, or 1 and 0), the EX-OR gate activates and sends a HIGH signal to the LED.
Definition
An EX-OR (Exclusive-OR) gate is a digital logic gate that produces a HIGH (1) output only when the two inputs are different. The output is LOW (0) when both inputs are identical (both 0 or both 1).
Working Principle
The EX-OR gate performs exclusive disjunction (modulo-2 addition). It evaluates whether the binary inputs differ from each other:
- When A = 0 and B = 0 → inputs are identical → Output is LOW (0).
- When A = 0 and B = 1 → inputs are different → Output is HIGH (1).
- When A = 1 and B = 0 → inputs are different → Output is HIGH (1).
- When A = 1 and B = 1 → inputs are identical → Output is LOW (0).
Truth Table Summary
The 2-input EX-OR gate has 4 possible input combinations. Two combinations with unequal inputs produce a HIGH output. Two combinations with equal inputs produce a LOW output.
Boolean Expression
Y = A ⊕ B (Equivalent expansion: Y = A·B' + A'·B)
Industrial Applications
- Two-way Staircase Lighting: EX-OR gates model two-way light switching circuits where operating either switch toggles the light ON or OFF regardless of the other switch position.
- Binary Adders: Essential component of Half Adders and Full Adders for calculating the Sum bit (Sum = A ⊕ B).
- Parity Generators and Checkers: Used in telecommunication and data storage to generate and verify odd or even parity bits for error detection.
- Phase Comparators: Used in Phase-Locked Loops (PLLs) to compare the phase angle between two digital signals.
- Pseudorandom Number Generators: Key element in Linear Feedback Shift Registers (LFSR) for cryptography and test pattern generation.
Boolean Expression
Y = A ⊕ B
The encircled plus symbol (⊕) represents the Exclusive-OR operation. It can also be expressed using standard AND, OR, and NOT operations as: Y = A·B' + A'·B.
Boolean Algebra Properties of EX-OR
- Identity Law: A ⊕ 0 = A
- Null Law: A ⊕ 1 = A'
- Self-Inverse / Idempotent Property: A ⊕ A = 0
- Complement Law: A ⊕ A' = 1
- Commutative Law: A ⊕ B = B ⊕ A
- Associative Law: (A ⊕ B) ⊕ C = A ⊕ (B ⊕ C)
- Toggling Property: A ⊕ B ⊕ B = A
Current Calculation
A = 0, B = 0 → Y = 0 ⊕ 0 = 0
Two-way Staircase Lighting
This demonstrates a Two-way Staircase Lighting system powered by EX-OR gate logic. The lamp changes state (toggles ON or OFF) whenever either switch (S1 or S2) is operated.
When both switches are in the same position (both OFF or both ON), the inputs are equal and the light remains OFF. Operating either switch makes the inputs different (A ≠ B), causing the EX-OR gate output to become HIGH and turning the staircase lamp ON.