Learning Objectives
  • Define the function of a two-input AND gate.
  • Complete and interpret the AND truth table.
  • Recognise AND conditions in problem statements.
  • Use cascaded two-input AND gates for three conditions.
Key Terms
AND gate
A two-input gate that outputs 1 only when both inputs are 1.
Both
A word indicating that two conditions must be true together.
Conjunction
A combined condition requiring all stated parts to be true.
Cascade
Connecting gates in stages so the output of one becomes an input to another.
Intermediate output
The result from a gate before the final output.
Summary diagram
Summary Of The Main Ideas In This Lesson
Function Of AND

A two-input AND gate outputs 1 only for the input combination 1,1. Every other combination produces 0. The rule can be remembered as all required conditions must be true.

AND is represented by a symbol with a flat left side and a rounded right side. It has two input lines and one output line. There is no output bubble.

An expression can be written as X = A AND B.

Truth Table For AND
A B X = A AND B
0 0 0
0 1 0
1 0 0
1 1 1
Language That Indicates AND

Words and phrases such as both, and, all conditions, at the same time, provided that each, or only when A and B often indicate an AND relationship.

For example, a motor runs only when the power switch is on and the safety cover is closed. If P = 1 for power on and C = 1 for cover closed, then X = P AND C.

The word and in ordinary English does not automatically guarantee a single AND gate; read the complete structure. A statement may contain AND inside one clause and OR between clauses.

Three Inputs Using Two-Input Gates

The syllabus limits AND to two inputs. To require A, B and C all to be 1, first calculate P = A AND B. Then calculate X = P AND C.

The output is 1 only for A = 1, B = 1 and C = 1. The order of pairing does not change this truth table, but the circuit should reflect the expression or statement provided.

In a truth table, include an intermediate column for P if it helps show the two stages.

AND In A Larger Expression

For X = (A OR B) AND C, evaluate A OR B first because it is inside the brackets. Then AND that intermediate result with C.

The final output can be 1 only if C = 1 and at least one of A or B is 1. Do not apply one three-input AND gate because A and B are combined by OR, not AND.

The circuit shape should make the order obvious: an OR gate feeds one input of an AND gate, while C feeds the other.

Interpreting The Output

If an AND output is 0, this tells you that at least one input was 0, but it does not identify which one. The possible input combinations are 00, 01 and 10.

If an AND output is 1, both inputs must have been 1. This can be useful when completing missing values in a truth table.

Practical Decision Example

A school door unlocks only when a valid card is detected and the door is within permitted hours. Let V = 1 for a valid card and H = 1 for permitted hours. Then U = V AND H.

The AND gate enforces two simultaneous requirements. The truth table shows that a valid card alone is insufficient and permitted time alone is insufficient.

Worked Examples
Simple AND

Question: Find X when A = 1 and B = 0 for X = A AND B.

  1. AND requires both inputs to be 1.
  2. B is 0.

Answer: X = 0.

Three Conditions

Question: A warning is produced only when temperature high T, pressure high P and machine running R are all 1. Describe a valid circuit.

  1. Use AND gate 1 for T and P.
  2. Connect its output to AND gate 2.
  3. Connect R to the other input of AND gate 2.

Answer: Two two-input AND gates in sequence; the second output is the warning.

Examination Guidance
  • Use the phrase both inputs are 1 when defining AND.
  • For three required conditions, use two AND gates.
  • Show intermediate outputs when tracing cascaded gates.
  • Do not confuse an AND symbol with NAND; check for a bubble.
  • Use the exact input definitions when applying the rule to a context.
Common Mistakes
  • Outputting 1 for 1,0 or 0,1.
  • Drawing one three-input AND gate.
  • Adding an output bubble and accidentally creating NAND.
  • Treating AND as ordinary addition.
  • Ignoring brackets in a mixed expression.
Knowledge Check

1. When does AND output 1?

Answer: Only when both inputs are 1.

2. What is the output for 1 AND 0?

Answer: 0.

3. How many input rows are in a two-input truth table?

Answer: Four.

4. How can three conditions be ANDed in this syllabus?

Answer: Using two two-input AND gates in stages.

5. What does an AND output of 1 prove?

Answer: Both inputs were 1.
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