Learning Objectives
  • Define NAND as the inverted output of AND.
  • Define NOR as the inverted output of OR.
  • Complete truth tables for NAND and NOR.
  • Recognise NAND and NOR from their symbols and output patterns.
Key Terms
NAND gate
A two-input gate that produces the opposite output to AND.
NOR gate
A two-input gate that produces the opposite output to OR.
Inverted output
A normal gate result changed from 0 to 1 or from 1 to 0.
NAND expression
NOT (A AND B).
NOR expression
NOT (A OR B).
Output bubble
The small circle showing that the main gate result is inverted.
Summary diagram
Summary Of The Main Ideas In This Lesson
NAND As NOT AND

NAND combines an AND operation with inversion. First determine A AND B, then reverse that result. NAND therefore outputs 0 only when both inputs are 1. It outputs 1 for 00, 01 and 10.

The symbol is the ordinary AND shape with a small bubble at the output. The expression can be written X = NOT (A AND B).

The bubble applies to the complete AND result. It does not mean NOT A AND B.

Truth Table For NAND
A B A AND B X = NAND
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
NOR As NOT OR

NOR combines an OR operation with inversion. First determine A OR B, then reverse that result. NOR outputs 1 only when both inputs are 0. It outputs 0 for 01, 10 and 11.

The symbol is the ordinary OR shape with a small output bubble. The expression can be written X = NOT (A OR B).

Because OR is 0 only for 00, its inversion NOR is 1 only for 00.

Truth Table For NOR
A B A OR B X = NOR
0 0 0 1
0 1 1 0
1 0 1 0
1 1 1 0
Recognising Output Patterns

A gate that is 0 only for 11 is NAND. A gate that is 1 only for 00 is NOR. These distinctive patterns help when identifying a gate from a truth table.

Compare these patterns with AND and OR. AND is 1 only for 11, while NAND is the exact opposite. OR is 0 only for 00, while NOR is the exact opposite.

Every output row is inverted, not only one row.

Using Intermediate Columns

When completing a complex truth table, create a column for the underlying AND or OR result and another for the inverted output if space permits. This makes the logic transparent.

For P = A NAND B, calculate A AND B then invert. For Q = P NOR C, calculate P OR C then invert. Work one gate at a time.

Do not try to remember an entire multi-gate output pattern without tracing the intermediate stages.

Statements Describing NAND And NOR

NAND can be described as the output is false only when both inputs are true, or the output is true unless both inputs are true. NOR can be described as the output is true only when neither input is true.

The word neither often indicates NOR when it refers to two input conditions. The wording not both can indicate NAND, but read carefully because ordinary language may be ambiguous.

The safest method is to translate the statement into a bracketed expression and then select the corresponding gate.

Circuit Structure And Non-Simplification

A NAND symbol directly represents NOT (A AND B), and a NOR symbol directly represents NOT (A OR B). If a supplied expression is shown as an AND gate followed by a separate NOT gate, draw both stages as given rather than replacing them with one NAND symbol, because the syllabus says not to simplify the stated circuit.

Likewise, if the expression explicitly names NAND, use the NAND symbol rather than expanding it unless the question asks for the equivalent stages.

Worked Examples
NAND Output

Question: Find X for A = 1 and B = 1 when X = A NAND B.

  1. A AND B = 1.
  2. Invert 1.

Answer: X = 0.

NOR Output

Question: Find X for A = 0 and B = 0 when X = A NOR B.

  1. A OR B = 0.
  2. Invert 0.

Answer: X = 1.

Examination Guidance
  • Look for the output bubble before naming the gate.
  • Use brackets in NOT (A AND B) and NOT (A OR B).
  • Compare every NAND output with AND and every NOR output with OR.
  • Use intermediate columns in multi-gate truth tables.
  • Do not simplify a separately drawn AND-then-NOT structure unless the question names NAND.
Common Mistakes
  • Calling NAND an AND gate because the main shape is similar.
  • Forgetting to invert the 00, 01 and 10 rows.
  • Writing NOR = (NOT A) OR B.
  • Applying the bubble to only one input.
  • Replacing the given two-stage structure with one gate when simplification is not allowed.
Knowledge Check

1. When does NAND output 0?

Answer: Only when both inputs are 1.

2. When does NOR output 1?

Answer: Only when both inputs are 0.

3. What is NAND in expression form?

Answer: NOT (A AND B).

4. What is NOR in expression form?

Answer: NOT (A OR B).

5. What visual feature distinguishes NAND from AND?

Answer: The output bubble.
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