10.5 The OR Gate

Learning Objectives

Define the function of a two-input OR gate.
Complete and interpret the OR truth table.
Distinguish inclusive OR from XOR.
Use two-input OR gates in multi-stage circuits.

Key Terms

OR gate: A two-input gate that outputs 1 when at least one input is 1.
At least one: One input, the other input, or both inputs.
Inclusive OR: The OR rule in which input combination 1,1 also produces 1.
Alternative condition: A condition that can independently make the output true.
Combined result: The output formed by joining alternatives using OR.

Summary diagram — Summary Of The Main Ideas In This Lesson

Function Of OR

A two-input OR gate outputs 1 if A is 1, B is 1, or both are 1. It outputs 0 only when both inputs are 0.

The symbol has a curved input side and a pointed curved output side. It has two inputs, one output and no inversion bubble.

The expression can be written X = A OR B.

Truth Table For OR

A	B	X = A OR B
0	0	0
0	1	1
1	0	1
1	1	1

Inclusive Meaning Of OR

Cambridge OR is inclusive. The combination A = 1 and B = 1 produces output 1. This is different from XOR, which produces 0 when both inputs are 1.

Ordinary language can sometimes use either/or to imply only one choice. A logic question that means exactly one true input is likely to use words such as either A or B but not both, indicating XOR.

When the statement simply says A or B, the standard OR gate normally includes the case where both are true.

Language That Indicates OR

Phrases such as at least one, one or both, any of the conditions, A or B, or if either condition is true often indicate OR.

For example, a building alarm sounds if smoke is detected or heat is detected. Let S = 1 for smoke and H = 1 for heat. Then X = S OR H. The alarm also sounds when both are detected.

A statement can contain several alternatives. Under the two-input gate rule, combine them in stages.

Three Inputs Using Two-Input Gates

For A OR B OR C, first calculate P = A OR B and then X = P OR C. The final output is 0 only when all three inputs are 0.

Do not draw one three-input OR gate. Use two ordinary two-input OR gates.

If the statement groups inputs differently, preserve that structure when drawing the circuit even where the final truth table could be the same.

OR In A Mixed Circuit

For X = (A AND B) OR C, calculate A AND B first. Then OR the intermediate result with C.

C = 1 is sufficient to make X = 1, regardless of A and B. When C = 0, X follows the result of A AND B.

A useful truth table can include P = A AND B followed by X = P OR C.

Interpreting Outputs

If OR outputs 0, both inputs must be 0. If OR outputs 1, at least one input is 1, but the output alone does not reveal whether the input combination was 01, 10 or 11.

This reverse reasoning can be used to complete missing values when other parts of a circuit are known.

Practical Decision Example

A ventilation fan starts if a temperature sensor is high or a manual override switch is active. T = 1 indicates high temperature and M = 1 indicates override active. F = T OR M.

The fan starts for either cause and remains started if both causes are present.

Worked Examples

Simple OR

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

OR looks for at least one input equal to 1.
B is 1.

Answer: X = 1.

Distinguishing OR From XOR

Question: Which gate outputs 1 for inputs 1,1: OR or XOR?

Recall that OR is inclusive.
Recall that XOR requires exactly one input to be 1.

Answer: OR outputs 1; XOR outputs 0.

Examination Guidance

State that OR outputs 1 when at least one input is 1.
Include the 1,1 row as output 1.
Look for phrases such as at least one or one or both.
Use two OR gates for three alternatives.
Check whether the wording excludes the both-true case before choosing XOR.

Common Mistakes

Treating OR as exactly one input true.
Writing 0 for the 1,1 row.
Drawing a three-input OR gate.
Confusing the OR symbol with XOR and forgetting the extra curve.
Ignoring the order of operations in a mixed circuit.

Knowledge Check

1. When does OR output 0?

Answer: Only when both inputs are 0.

2. What is 1 OR 1?

Answer: 1.

3. What phrase describes the OR condition?

Answer: At least one input is 1.

4. How does OR differ from XOR for 1,1?