9. Parity Bit Generator

The XOR gate is inherently a parity generator. When two inputs are fed into an XOR gate, the output is high only if the number of high inputs is odd. By cascading these gates, we extend this property to three inputs.

Output Equation:

Output = (A XOR B) XOR C

Calculation breakdown:

• First XOR (A XOR B): This gate produces a 1 if A and B have different values (i.e., if exactly one of them is high).
• Second XOR ((A XOR B) XOR C): This gate takes the result of the first operation and XORs it with C. The final output is 1 if the total count of high signals (A, B, and C) is 1 or 3 (both odd numbers).
• Example (1, 1, 1): (1 XOR 1) = 0. Then, 0 XOR 1 = 1. The result is 1 (correct).
• Example (1, 1, 0): (1 XOR 1) = 0. Then, 0 XOR 0 = 0. The result is 0 (correct).

Circuit Implementation:

• First XOR: Connect inputs A and B to the first XOR gate.
• Second XOR: Connect the output of the first XOR gate and input C to the second XOR gate.
• Connect: Map the output of the second XOR gate to the Output probe.