# Questions & Answers of Minimization

## Weightage of Minimization

Total 8 Questions have been asked from Minimization topic of Digital Logic subject in previous GATE papers. Average marks 1.38.

Consider the Karnaugh map given below, where X represents "don't care" and blank represents 0.

Assume for all inputs (a, b, c, d), the respective complements  $\style{font-family:'Times New Roman'}{\left(\overline a,\;\overline b,\;\overline c,\;\overline d\right)}$  are also available. The above logic is implemented using 2-input NOR gets only. The minimum number of gates required is _____________.

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Given $\style{font-family:'Times New Roman'}{f(w,\;x,\;y,\;z)=\sum\nolimits_m(0,\;1,\;2,\;3,\;7,\;8,\;10)+\sum\nolimits_d(5,\;6,\;11,\;15)}$ where d represents the don't-care condition in Karnaugh maps. Which of the following is a minimum product-of-sums (POS) form of $f\left(w,x,y,z\right)$ ?

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Consider the following minterm expression for F:

$F\left(P,Q,R,S\right)=\sum 0,2,5,7,8,10,13,15$

The minterms 2, 7, 8 and 13 are ‘do not care’ terms. The minimal sum-of-products form for F is

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What is the minimal form of the Karnaugh map shown below? Assume that X denotes a don’t care term.

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The minterm expansion of $f\left(P,Q,R\right)=PQ+Q\overline{)R}+P\overline{)R}$ is

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In the Karnaugh map shown below, X denotes a don’t care term. What is the minimal form of the function represented by the Karnaugh map?

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Consider the following Boolean function of four variables:

$f\left(w,x,y,z\right)=\sum \left(1,3,4,6,9,11,12,14\right)$

The function is

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Let $f\left(w,x,y,z\right)=\sum \left(0,4,5,7,8,9,13,15\right)$. Which of the following expressions are NOT equivalent to f ?

(P) x'y'z' + w'xy' + wy'z + xz
(Q) w'y'z' + wx'y' + xz
(R) w'y'z' + wx'y' + xyz + xy'z
(S) x'y'z' + wx'y' + w'y