GATE CSE 2021 Set 2 | Question: 5

Question

Which one of the following circuits implements the Boolean function given below?

$f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6$, where $m_i$ is the $i^{\text{th}}$ minterm.

• A.
• B.
• C.
• D.

 

Comments

To element the options  write all minterms

${X}'{Y}'{Z}' + {X}'{Y}'Z + {X}'YZ + X{Y}'{Z}' + X{Y}'Z+ XY{Z}'$

now put values $Y=0,Z=0$ with the help of function we sholud get 1  elemenate option B & D   now put Values

$Y=1,Z=1$ we should get ${X}'$  now elemenate option C .

Answer 1

• $f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6$
• $S_1 = y,~S_0 = z$

Draw a small table as following and mark the min-terms in $f.$

$$\begin{array}{cccc}& \bf{I_0}    &\bf{I_1}&    \bf{I_2}&    \bf{I_3}\\
\bar{x}&    \color{Red} 0&    \color{Red} 1&    2  &  \color{Red} 3\\
x&    \color{Red} 4&    \color{Red} 5&    \color{Red} 6&    7 \end{array}$$

$\begin{array}{ll}I_0 = (\bar{x} + x ) = 1 &\text{(both rows are marked)} \\I_1 = (\bar{x} + x ) = 1 & \text{(both rows are marked)}\\I_2 = x&\text{(only row corresponding to $x$ is marked)}\\I_3 = \bar{x} & \text{(only row corresponding to $\bar{x}$ is marked)}\end{array}$

A is correct.

Comments

absolutely ingenuis

Answer 2

Option A is correct.

Answer 3

We can simplify this in this way :-

 

Answer 4

Option $(A)$ is the correct answer.

Comments

Bro can u explain table for  B C D, I get it for A as it is mentioned in the question only but others how ?