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The NAND and NOR gates are the inverted versions of AND and OR respectively. They are formed by combining AND or OR with NOT. These gates are covered in OCR J277 Section 2.5 and are particularly important because NAND and NOR gates are considered universal gates — any logic circuit can be built using only NAND gates or only NOR gates.
NAND stands for NOT AND. It performs an AND operation and then inverts the result. The NAND gate outputs 0 only when both inputs are 1 — the exact opposite of AND.
| A | B | A AND B | A NAND B |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
Notice that the NAND output is the exact inverse of the AND output. Every 0 becomes 1 and every 1 becomes 0.
OCR Exam Tip: To find the output of a NAND gate, first work out what AND would give, then invert it. This two-step approach avoids mistakes.
The NAND symbol is the AND symbol with a bubble (small circle) at the output:
A ----+ +o---- Q
| AND |
B ----+ +
The bubble represents the NOT (inversion) applied to the AND output.
NOR stands for NOT OR. It performs an OR operation and then inverts the result. The NOR gate outputs 1 only when both inputs are 0 — the exact opposite of OR.
| A | B | A OR B | A NOR B |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 |
The NOR output is the exact inverse of the OR output.
The NOR symbol is the OR symbol with a bubble at the output:
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