search
Log In
1 vote
344 views

GATE CSE 2021 Set 2 | Question-5.8

  1. GATE CSE 2021 Set 2 | Question-25
  2. GATE CSE 2021 Set 2 | Question-25
  3. GATE CSE 2021 Set 2 | Question-25
  4. GATE CSE 2021 Set 2 | Question-25

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.

 

in Digital Logic
edited by
344 views

3 Answers

1 vote

Option $(A)$ is the correct answer.

1 vote

Option A is correct.

1 vote

A

 

While solving I would suggest to go along with your intuition mechanisms but for the sake of completeness I’m choosing the time consuming one to better understand how to build and solve one.


Most of the times while using MUX to implement boolean functions people tend to use the less significant variables as their select lines. We use Variable Entrant Map for such problems.

The min-terns are designated to the VEM by choosing the variables for LSBs to represent the select lines here, two bits are used which is used to designate min-term under which box(in VEM) it appears, all of them are pooled to together and the optimal gate logic is found out functions under their boxes.

 

Here,
$m_0\ \&\ m_4$ under $\overline{y}\overline{z}$
$m_1\ \&\ m_5$ under $\overline{y}z$
$m_6$ under $y\overline{z}$ and.
$m_3$ under $yz$
$\hspace{170pt} \begin{array}{cc} \begin{array}{c}\\\bar{y}\\ y\end{array} \begin{array}{c}\bar{z}\hspace{11pt}z\\ \begin{array}{|c|c|}\hline 1 &1\\\hline x&\bar{x}\\\hline\end{array} \end{array}\end{array} $

                                                                                             Voilà


Now for using the above table, design the MUX which should look like this.

                                                                                 

Which resembles Option A(can’t go wrong copied it :P)


edited by
Answer:

Related questions

1 vote
2 answers
1
355 views
The format of the single-precision floating point representation of a real number as per the $\text{IEEE 754}$ ... $=00000000$ and mantissa $=0000000000000000000000001$ exponent $=00000001$ and mantissa $=0000000000000000000000000$ exponent $=00000001$ and mantissa $=0000000000000000000000001$
asked Feb 18 in Digital Logic Arjun 355 views
2 votes
2 answers
2
0 votes
4 answers
3
1.8k views
If the numerical value of a $2$-byte unsigned integer on a little endian computer is $255$ more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer? $0\text{x}6665$ $0\text{x} 0001$ $0\text{x} 4243$ $0\text{x} 0100$
asked Feb 18 in Digital Logic Arjun 1.8k views
0 votes
1 answer
4
330 views
Consider a Boolean function $f(w,x,y,z)$ such that $\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}$ The number of literals in the minimal sum-of-products expression of $f$ is _________
asked Feb 18 in Digital Logic Arjun 330 views
...