NOT, OR, AND from NOR — universal gates
exam standardthe dual cost table
Answer
3 NOR gates realising A · B
Why this example is worth doing
The NOR-family costs, transposed from the NAND family: OR is cheap at two gates and AND is dear at three. Setting the two tables side by side is what makes the duality concrete rather than asserted, and it yields the design rule the page exists to deliver — minimise to SOP and implement in NAND, or minimise to POS and implement in NOR, and never mix the decision.
Try your own input in the Universal gates. Rebuild any of the other gates using only NAND, or only NOR, with the gate count.
How the answer is reached
Gate list
| Node | Gate | Inputs |
|---|---|---|
| g1 | nor | A, A |
| g2 | nor | B, B |
| g3 | nor | g1, g2 |
NOR-only realisation
A ↓ A ↓ (B ↓ B)A · B— 3 NOR gates, verified by reading the network back out.
Truth table
| # | A | B | A ↓ A ↓ (B ↓ B) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 2 | 1 | 0 | 0 |
| 3 | 1 | 1 | 1 |