Truth table for system of four `NAND` gates as shown in figure is :
.

Options

A. `|{:(A,B,Y),(0,0,0),(0,1,1),(1,0,1),(1,1,0):}:|`
B. `|{:(A,B,Y),(0,0,0),(0,1,0),(1,0,1),(1,1,1):}:|`
C. `|{:(A,B,Y),(0,0,1),(0,1,1),(1,0,0),(1,1,0):}:|`
D. `|{:(A,B,Y),(0,0,1),(0,1,0),(1,0,0),(1,1,1):}:|`

Answer

A

Explanation

Refer figure shown below,

From Boolean algebra
`y_(1)=bar(A.B), y_(2)=bar(A.y_(1))`,
`y_(3)=bar(y_(1).B), y=bar(y_(2).y_(3))`
The truth table for the various stages will be as given below:
`|{:(A,B,y_(1)=bar(A+B),y_(2)=bar(A.y_(1)),y_(3)=bar(B.y_(1)),y=bar(y_(2).y_(3))),(0,0,1,1,1,0),(0,1,1,1,0,1),(1,0,1,0,1,1),(1,1,0,1,1,0):}:|`