Question 14: Semiconductors and Logic Gates

Question

$ 	ext { For the given logic gate circuit, which of the following is the correct truth table? } $
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1ml8w9dwt/0a71a29e-a35e-4038-b06c-a89b38de1249/60e985d0-0242-11f1-88dd-c7214e4b90e3/file-6y3zli1ml8w9dwu.png?format=png)

Accepted Answer

The gate I is OR Gate. It receives inputs n and m . Its output is $\mathrm{Y}_1=\mathrm{n}+\mathrm{m}$. $\$
Gate II is NAND Gate. It receives two inputs, the original input n and the output of the OR gate $\left(\mathrm{Y}_1ight)$. Its output z is the result of an AND operation followed by a NOT operation, $\mathrm{z}=\overline{\mathrm{n} \cdot(\mathrm{n}+\mathrm{m})}$. $\$
Using Boolean algebra laws : $\$
$ \mathrm{z}=\overline{\mathrm{n} \cdot(\mathrm{n}+\mathrm{m})} $
$\Rightarrow $ $ \mathrm{z}=\overline{(\mathrm{n} \cdot \mathrm{n})+(\mathrm{n} \cdot \mathrm{~m})} $ $\$
Since $\mathrm{n} \cdot \mathrm{n}=\mathrm{n}$, the expression simplifies to $\mathrm{z}=\overline{\mathrm{n}+(\mathrm{n} \cdot \mathrm{m})}=\overline{\mathrm{n}}$ $\$
$ \begin{array}{c|c|c|c} n & m & {Y}_1=n+m & 	ext {NAND Input } z=\overline{n+{Y}_1} \ 
\hline 0 & 0 & 0 & 1 \ 0 & 1 & 1 & 0 \ 1 & 1 & 1 & 0 \ 1 & 0 & 1 & 0 \end{array} $ $\$

The output z is purely the inverse of input n . When $\mathrm{n}=0, \mathrm{z}=1$. When $\mathrm{n}=1, \mathrm{z}=0$. $\$
$ \begin{array}{c|c|c} n & m & z \ \hline 0 & 0 & 1 \ 0 & 1 & 1 \ 1 & 1 & 0 \ 1 & 0 & 0 \end{array} $ $\$
Therefore, the correct option is (A).
![](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1mlahapen/97194d51-8487-4060-ae17-c8519be044f3/6df67af0-0321-11f1-ae98-255c285222ce/file-6y3zli1mlahapeo.png?format=png)

Answer

$ \begin{array}{c|c|c} n & m & z \ \hline 0 & 0 & 1 \ 0 & 1 & 1 \ 1 & 1 & 0 \ 1 & 0 & 0 \end{array} $

Answer

$ \begin{array}{c|c|c} n & m & z \ \hline 0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 1 & 1 \ 1 & 0 & 0 \end{array} $

Answer

$ \begin{array}{c|c|c} n & m & z \ \hline 0 & 0 & 0 \ 0 & 1 & 1 \ 1 & 1 & 0 \ 1 & 0 & 1 \end{array} $

Answer

$ \begin{array}{c|c|c} n & m & z \ \hline 0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 1 & 0 \ 1 & 0 & 0 \end{array} $

Semiconductors and Logic Gates

\text{ For the given logic gate circuit, which of the following is the correct truth table? }

Choose the correct answer: