Question E7A08:
What logical operation does an OR gate perform?  

Choices:  
A: It produces a 1 at its output if any input is 1  
B: It produces a 0 at its output if all inputs are 1  
C: It produces a 0 at its output if some but not all inputs are 1  
D: It produces a 1 at its output if all inputs are 0    

Correct Answer is  A: It produces a 1 at its output if any input is 1  

To understand an OR gate, remember it’s the inclusive OR used in digital logic.

1) Why the correct answer is correct
- An OR gate outputs 1 if any input is 1.  
- Boolean expression: $$Y = A + B = A \lor B$$
- Two-input truth cases:
  - $0 \lor 0 \rightarrow 0$
  - $0 \lor 1 \rightarrow 1$
  - $1 \lor 0 \rightarrow 1$
  - $1 \lor 1 \rightarrow 1$

2) Why the other choices are incorrect
- B: “It produces a 0 at its output if all inputs are 1” describes a NAND gate. NAND is 0 only when all inputs are 1.
- C: “It produces a 0 at its output if some but not all inputs are 1” describes an XNOR gate (equivalence). XNOR is 0 for mixed inputs and 1 for equal inputs.
- D: “It produces a 1 at its output if all inputs are 0” describes a NOR gate. NOR is 1 only when all inputs are 0.

3) Useful formulas and rules of thumb
- OR is inclusive: “any one makes it true.”
- Boolean identities:
  - $A + 0 = A$
  - $A + 1 = 1$
  - $A + A = A$
  - Commutative: $A + B = B + A$
- De Morgan’s:
  - $\overline{A + B} = \overline{A}\,\overline{B}$
  - $A + B = \overline{\overline{A}\,\overline{B}}$
- Contrast with XOR (exclusive OR): $$A \oplus B = (A + B)\,\overline{AB}$$ which is 1 only for mixed inputs.