Question:

Consider a combination of gates as shown:
Consider a combination of gates

Updated On: Jan 17, 2025
  • Consider a combination of gates

  • Consider a combination of gates

  • Consider a combination of gates

  • Consider a combination of gates

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The Correct Option is A

Solution and Explanation

Given Expression:

\[ y = (A'B') = A + B \]

In this expression, we have two components: A and B. The symbol ' represents the NOT operation, which inverts the value of the variable.

We begin by interpreting the term A'B' as the AND operation between the negation (NOT) of A and B. In Boolean algebra, the product (AND operation) of A' and B' can be represented as:

\[ A'B' \quad \text{(AND operation between the negations of A and B)} \]

Now, according to the given equation, the result y is also equal to the sum (OR operation) of A and B. The OR operation between A and B is written as:

\[ A + B \quad \text{(OR operation between A and B)} \]

Therefore, we conclude that the expression represents the behavior of an OR gate in digital logic. The OR gate will output 1 (True) if either of the inputs A or B is 1, and it will output 0 (False) only when both inputs are 0.

Conclusion: The given equation represents the logic of an OR gate. Hence, the correct option is (A) OR gate.

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Concepts Used:

Logic Gates

AND Gate

It is the gate, where a circuit performs an AND operation. It has n number of input where (n >= 2) and one output.

OR Gate

It is the gate, where a circuit performs an OR operation. It has n number of input where (n >= 2) and one output.

NOT Gate

An inverter is also called NOT Gate. It has one input and one output where the input is A and the output is Y.

NAND Gate

A NAND operation is also called a NOT-AND operation. It has n number of input where (n >= 2) and one output.

NOR Gate

A NOR operation is also called a NOT-OR operation. It has n number of input where (n >= 2) and one output.

XOR Gate

XOR or Ex-OR gate is a specific type of gate that can be used in the half adder, full adder, and subtractor. 

XNOR Gate

XNOR gate is a specific type of gate, which can be used in the half adder, full adder, and subtractor. The exclusive-NOR gate is flattened as an EX-NOR gate or sometimes as an X-NOR gate. It has n number of input (n >= 2) and one output.