8. 3-Input Logic Optimization
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To optimize the circuit, we map the output values onto a 3-variable Karnaugh map:
| BC=00 | BC=01 | BC=11 | BC=10 | |
|---|---|---|---|---|
| A=0 | 0 | 1 | 1 | 0 |
| A=1 | 0 | 0 | 1 | 1 |
By grouping the adjacent 1s in the K-map, we derive two prime implicants:
- A group of two 1s in the first row (where A is 0, covering C=1): (NOT A) AND C
- A group of two 1s in the second row (where A is 1, covering B=1): A AND B
Output Equation:
Output = ((NOT A) AND C) OR (A AND B)
Calculation breakdown:
- (NOT A) AND C: This term accounts for the inputs where A is 0 and C is 1.
- A AND B: This term accounts for the inputs where A is 1 and B is 1.
- OR Operation: The OR gate combines these two terms to produce the final output.
Circuit Implementation:
- Inversion: Connect input A to a NOT gate to obtain NOT A.
- Product Terms: Connect NOT A and C to the first AND gate. Connect A and B to the second AND gate.
- Summation: Connect the outputs of the two AND gates to the inputs of an OR gate.
Connect: Map the output of the OR gate to the Output probe.