in Digital Logic retagged by
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15 votes
15 votes

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.

 

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5 Answers

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

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.

edited by
7 votes
7 votes

Option A is correct.

6 votes
6 votes

We can simplify this in this way :-

 

2 votes
2 votes

Option $(A)$ is the correct answer.

1 comment

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 ?
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