Three Input NOR Gate Output Analysis

Understanding NOR Gates

A NOR gate is a fundamental digital logic gate. It produces a high output (logic 1) only when all of its inputs are low (logic 0). Otherwise, its output is low.

For a three-input NOR gate, let the inputs be A, B, and C. The output Y can be represented by the Boolean expression:

\( Y = \overline{A \lor B \lor C} \)

Here, '\(\lor\)' represents the OR operation, and the overline represents the NOT (inversion) operation.

Determining High Output Condition

The NOR gate's output (Y) is high (1) only if the expression inside the inversion is low (0).

• The OR expression \(A \lor B \lor C\) evaluates to 0 if and only if all individual inputs are 0.
• Therefore, for \(A \lor B \lor C = 0\), we must have \(A=0\), \(B=0\), and \(C=0\).
• Substituting these values into the NOR gate equation: \(Y = \overline{0 \lor 0 \lor 0} = \overline{0} = 1\).
• Thus, a high output occurs exclusively when all inputs are low.

Conclusion

The condition for a three-input NOR gate to produce a high output is that all its inputs must be low.

Correct Option: all I/P are low