39. 3-Input Logic Optimization
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To optimize the circuit, the truth table outputs are mapped 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 |
Grouping the adjacent 1s yields two minimal prime implicants:
- A pair in the first row representing the term where A is 0 and C is 1: (~A · C)
- A pair in the second row representing the term where A is 1 and B is 1: (A · B)
Combining these product terms through an OR gate yields the minimized SOP expression.
Boolean Equation:
Output = (~A · C) + (A · B)