(A + B̄)·(B + C̄)·(C + Ā) — logic gate diagram
edge case8 primitives: 3 ORs, 3 inverters, 2 ANDs; cyclic structure
Answer
7 gates, 3 inputs; output column 10000001
Why this example is worth doing
Three OR gates feeding an AND, wired in a cycle so that each variable appears once true and once complemented. It is deliberately the least symmetric-looking diagram in the set, and it exists to test the layout engine rather than the reader: wires cross, and the router has to place junction dots and choose crossing points deterministically so that the same input always yields the same picture. Stable layout is what makes a diagram safe to paste into a lab report.
Try your own input in the Logic gate diagram builder. Draw an expression as a gate schematic in IEEE or IEC symbols and copy it as an image.
How the answer is reached
Netlist
| Node | Gate | Inputs |
|---|---|---|
| g0 | not | i1 |
| g1 | or | i0, g0 |
| g2 | not | i2 |
| g3 | or | i1, g2 |
| g4 | not | i0 |
| g5 | or | i2, g4 |
| g6 | and | g1, g3, g5 |
Truth table
| # | A | B | C | F |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 2 | 0 | 1 | 0 | 0 |
| 3 | 0 | 1 | 1 | 0 |
| 4 | 1 | 0 | 0 | 0 |
| 5 | 1 | 0 | 1 | 0 |
| 6 | 1 | 1 | 0 | 0 |
| 7 | 1 | 1 | 1 | 1 |