NEETPhysicsSemiconductors
An oscilloscope monitoring a logic circuit shows that the output Y drops to a logic LOW ( 0 ) state if and only if both inputs A and B are simultaneously at a logic HIGH ( 1 ) state. At all other times, the output Y remains at a logic HIGH ( 1 ) state. Which of the following Boolean expressions correctly represents the relationship between the inputs and the output?
Options
- AY = A B
- BY = A B
- CY = A + B
- DY = A + B
Correct answer
C. Y = A + B
Step-by-step solution
From the given description, the output Y = 0 only when A = 1 and B = 1 . For all other combinations ( (0,0), (0,1), (1,0) ), the output Y = 1 . This behavior corresponds exactly to the truth table of a NAND gate. The Boolean expression for a NAND gate is Y = A B . According to De Morgan's theorem, the complement of a product is equal to the sum of the complements: A B = A + B Therefore, the correct Boolean expression is Y = A + B . Answer: Y = A + B