# Recent questions tagged canonical-normal-form

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What is the minimum number of $2$-input NOR gates required to implement a $4$ -variable function expressed in sum-of-minterms form as $f=\Sigma(0,2,5,7, 8, 10, 13, 15)?$ Assume that all the inputs and their complements are available. Answer: _______
1 vote
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Should we use Don't care terms while calculating POS expression?
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Are multiple SOP and POS expressions possible such that they all are unique ?
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Find the minimum product of sums of the following expression $f=ABC + \bar{A}\bar{B}\bar{C}$
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The simplified SOP (Sum of Product) from the Boolean expression $(P + \bar{Q} + \bar{R}) . (P + {Q} + R) . (P + Q +\bar{R})$ is $(\bar{P}.Q+\bar{R})$ $(P+{Q}.\bar{R})$ $({P}.\bar{Q}+R)$ $(P.Q+R)$
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The most simplified form of the Boolean function $x (A, B, C, D) = \sum (7, 8, 9, 10, 11, 12, 13, 14, 15)$ (expressed in sum of minterms) is? A + A'BCD AB + CD A + BCD ABC + D
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A Boolean expression is an expression made out of propositional letters (such as $p, q, r$) and operators $\wedge$, $\vee$ and $\neg$; e.g. $p\wedge \neg (q \vee \neg r)$. An expression is said to be in sum of product form ... operator. Every Boolean expression is equivalent to an expression without $\wedge$ operator. Every Boolean expression is equivalent to an expression without $\neg$ operator.
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Answer is 2 minimal and 2 canonical covers. Please give full explanation of how to solve.
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Given the function $F = P' +QR$, where $F$ is a function in three Boolean variables $P, Q$ and $R$ and $P'=!P$, consider the following statements. $(S1) F = \sum(4, 5, 6)$ $(S2) F = \sum(0, 1, 2, 3, 7)$ $(S3) F = \Pi (4, 5, 6)$ ... )-False (S1)-True, (S2)-False, (S3)-False, (S4)-True (S1)-False, (S2)-False, (S3)-True, (S4)-True (S1)-True, (S2)-True, (S3)-False, (S4)-False
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The total number of prime implicants of the function $f(w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is __________
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Kindly have a try .... IN canonical POS form following equation is written as F(A,B,C)=AB+BC+AC (A)&pi;M(0,1,2,4) (B)&pi;M(3,5,6,7) (C)&pi;M(0,1,2,3) (D)&pi;M(4,5,6,7)
The minterm expansion of $f(P,Q,R) = PQ +Q \bar{R}+P\bar{R}$ is $m_2+m_4+m_6+m_7$ $m_0+m_1+m_3+m_5$ $m_0+m_1+m_6+m_7$ $m_2+m_3+m_4+m_5$
Consider the following logic circuit whose inputs are functions $f_1, f_2, f_3$ and output is $f$ Given that $f_1(x,y,z) = \Sigma (0,1,3,5)$ $f_2(x,y,z) = \Sigma (6,7),$ and $f(x,y,z) = \Sigma (1,4,5).$ $f_3$ is $\Sigma (1,4,5)$ $\Sigma (6,7)$ $\Sigma (0,1,3,5)$ None of the above
Given $f_1$, $f_3$ and $f$ in canonical sum of products form (in decimal) for the circuit $f_1 = \Sigma m(4, 5, 6, 7, 8)$ $f_3 = \Sigma m(1, 6, 15)$ $f = \Sigma m(1, 6, 8, 15)$ then $f_2$ is $\Sigma m(4, 6)$ $\Sigma m(4, 8)$ $\Sigma m(6, 8)$ $\Sigma m(4, 6, 8)$