question_answer

To get an output 1 from the circuit shown in the figure, the input must be

A) \[A=0,\,\,B=1,\,\,C=0\]

B) \[A=1,\,\,B=0,\,\,C=0\]

C) \[A=1,\,\,B=0,\,\,C=1\]

D)  \[A=1,\,\,B=1,\,\,C=0\]

Correct Answer: C

Solution :

We can realize the gate circuit as Output of gate\[1,\,\,{{Y}_{1}}=A+B\] Output of gate\[2,\,\,{{Y}_{2}}={{Y}_{1}}\cdot C\]                                                                 \[=(A+B)\cdot C\] [a] If\[A=0,\,\,B=1,\,\,C=0\], then                 \[{{Y}_{2}}=(0+1)\cdot 0=1\cdot 0=0\] [b] If\[A=1,\,\,B=0,\,\,C=0\], then                 \[{{Y}_{2}}=(1+0)\cdot 0=1\cdot 0=0\] [c] If\[A=1,\,\,B=0,\,\,C=1\], then                 \[{{Y}_{2}}=(1+0)\cdot 1=1\cdot 1=0\] [d] If\[A=1,\,\,B=1,\,\,C=0\], then                 \[{{Y}_{2}}=(1+1)\cdot 0=1\cdot 0=0\]