JEE MainPhysicsSemiconductors
A combinational logic circuit consists of three logic gates. Gate 1 is a NAND gate with inputs A and B . Gate 2 is an OR gate with the same inputs A and B . The outputs of Gate 1 and Gate 2 are fed as inputs into Gate 3, which is an AND gate. The output of Gate 3 is Y . The input waveforms for A and B over 6 distinct time intervals are given as sequences of logic levels: A = 0, 0, 1, 1, 0, 1 B = 0, 1, 0, 1, 1, 0 Iden
Options
- A0, 1, 1, 0, 1, 1
- B1, 0, 0, 1, 0, 0
- C1, 1, 1, 0, 1, 1
- D0, 1, 1, 1, 1, 1
Correct answer
A. 0, 1, 1, 0, 1, 1
Step-by-step solution
The Boolean expression for the output of Gate 1 (NAND) is A B . The Boolean expression for the output of Gate 2 (OR) is A + B . These outputs are fed into Gate 3 (AND), so the final output Y is given by: Y = ( A B ) (A + B) Using De Morgan's laws, A B = A + B . Substituting this into the expression for Y : Y = ( A + B ) (A + B) Y = A A + A B + B A + B B Since A A = 0 and B B = 0 , we get: Y = A B + A B This is the Boolean expression for an XOR gate. Now, we apply the XOR operation to the given input sequences inter