NAND and NOR Gates: Truth Tables and Symbols

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.

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The NAND Gate

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.

NAND Boolean Expression

• NOT (A AND B)
• (A . B) with a bar over the entire expression
• A NAND B

NAND Truth Table

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.

NAND Gate Symbol

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.

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The NOR Gate

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.

NOR Boolean Expression

• NOT (A OR B)
• (A + B) with a bar over the entire expression
• A NOR B

NOR Truth Table

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.

NOR Gate Symbol

The NOR symbol is the OR symbol with a bubble at the output: