Question

(~P ∧ ~Q) ∨ (~P ∧ ) ∨ (P ∧ ~Q),

For the circuit corresponding to the Boolean expression given above, there is an equivalent circuit with at most two logic gates. Construct such a circuit and explain the construction in detail.

Answer 1

The equivalent circuit can be constructed using two NAND gates. The NAND gate is universal and can be used to implement all other logic gates including AND, OR, NOT, etc.

Here's the construction of the equivalent circuit:

First NAND gate: The first NAND gate implements the expression (~P ∧ ~Q). The inputs to the gate are P and Q, and the output is connected to the first input of the second NAND gate.

Second NAND gate: The second NAND gate implements the expression (~P ∧ (output of first NAND gate)) ∨ (P ∧ ~Q). The second input of the second NAND gate is connected to the output of the first NAND gate. The output of the second NAND gate is the final output of the circuit.

This circuit implements the given Boolean expression and has at most two logic gates.