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Recent questions tagged simplification

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1
Simplify the Following boolean function by means of the tabulation method. (a) P(A,B,C,D,E,F,G)=$\sum(20,28,52,60)$ (b) P(A,B,C,D,E,F,G)= $\sum(20,28,38,39,52,60,102,103,127)$ (C) P(A,B,C,D,E,F) = $\sum(6,9,13,18,19,25,27,29,41,45,57,61)$
asked Apr 2, 2019 in Digital Logic ajaysoni1924 176 views
2 votes
1 answer
2
Implement the following boolean function F together with the don’t-care conditions d using no more than two NOR gates. Assume both normal and the compliment inputs are available. F(A,B,C,D) = $\sum(0,1,2,9,11) $ $d(A,B,C,D) = \sum(8,10,14,15)$
asked Apr 2, 2019 in Digital Logic ajaysoni1924 191 views
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1 answer
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A logic circuit implements the following Boolean function: F = A’C + AC’D’ it is found that the circuit input combination A=C=1 can never occur. Find a simpler expression for F using the proper don't-care conditions.
asked Apr 2, 2019 in Digital Logic ajaysoni1924 322 views
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4
Simplify the boolean function F together with the don’t care conditions d in (1) sum of products and (2)product of sums. (A) $F(w,x,y,z) = \sum(0,1,2,3,7,8,10)$ $d(w,x,y,z) = \sum(5,6,11,15)$ (b) $F(A,B,C,D) = \sum (3,4,13,15)$ $d(A,B,C,D) =\sum(1,2,5,6,8,10,12,14)$
asked Apr 2, 2019 in Digital Logic ajaysoni1924 94 views
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5
Simplify the following boolean function F together with the don’t care condition d; then express the simplified function in the sum of minterms. (a)$F(x,y,z)=\sum(0,1,2,4,5) $ $d(x,y,z)= \sum(3,6,7)$ (b) $F(A,B,C,D) = \sum(0,6,8,13,14)$ $d(A,B,C,D) = \sum(2,4,10)$ (C) $F(A,B,C,D) = \sum(1,3,5,7,9,15)$ $d(A,B,C,D)= \sum(4,6,12,13)$
asked Apr 2, 2019 in Digital Logic ajaysoni1924 86 views
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List the Eight degenerate 2 level forms and show that they reduce to the single operation. Explain how the degenerate two-level forms can be used to extend the number of inputs to a gate.
asked Apr 2, 2019 in Digital Logic ajaysoni1924 61 views
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Simplify the following functions and implement them with (15) two- level NOR gate circuits (16) three-level NOR gate circuits. F = wx’ + y’z’ + w’yz’ F(w,x,y,z) = $\sum(5,6,9,10)$
asked Apr 1, 2019 in Digital Logic ajaysoni1924 176 views
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Simplify the following expressions and implement them with (12)two-level NAND gate circuits (17) three-level NAND gate circuits (a) AB’ + ABD + ABD’ + A’C’D + A’BC’ (b) BD + BCD’ + AB’C’D’
asked Apr 1, 2019 in Digital Logic ajaysoni1924 62 views
1 vote
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12
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13
Simplify the following boolean expressions into (1) Product of sums (2) sum of products. x’z’ + y’z’ + yz’ + xy AC’ + B’D + A’CD + ABCD (A’ + B’ + D’)(A + B’ + C’)(A’ + B + D’)(B + C’ + D’)
asked Apr 1, 2019 in Digital Logic ajaysoni1924 79 views
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Simplify the following boolean functions in product of sums: F(w,x,y,z) = $\sum(0,2,5,6,7,8,10)$ F(A,B,C,D) = $\prod(1,3,5,7,13,15)$ F(x,y,z) = $\sum(2,3,6,7)$ F(A,B,C,D) = $\prod(0,1,2,3,4,10,11)$
asked Apr 1, 2019 in Digital Logic ajaysoni1924 60 views
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Simplify the following boolean function using five variable maps. F(A,B,C,D,E) = $\sum (0,1,4,5,16,17,25,21,29)$ F(A,B,C,D,E) = $\sum (0,2,3,4,5,6,7,11,15,16,18,19,23,27,31)$ F= A’B’CE’ + A’B’C’D + B’D’E’ + B’CD’ + CDE’ + BDE’
asked Apr 1, 2019 in Digital Logic ajaysoni1924 92 views
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16
Simplify the following boolean functions by first finding the essential prime implicants. F(w,x,y,z) = $\sum (0,2,4,5,6,7,8,10.13,15)$ F(A,B,C,D) = $\sum (0,2,3,5,7,8,10,11,14,15)$ F(A,B,C,D) = $\sum (1,3,4,5,10,11,12,13,14,15)$
asked Apr 1, 2019 in Digital Logic ajaysoni1924 48 views
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17
Find the Minterms of the each of the following expression by first plotting each function in the map. xy + yz + xy’z C’D + ABC’ +ABD’ + A’B’D wxy + x’z’ + w’xz
asked Apr 1, 2019 in Digital Logic ajaysoni1924 54 views
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Simplify the following boolean expressions using Four variable K-maps. w’z + xz + x’y + wx’z B’D + A’BC’ + AB’C + ABC’ AB’C + B’C’D’ + BCD + ACD’ + A’B’C + A’BC’D wxy + yz + xy’z + x’y
asked Apr 1, 2019 in Digital Logic ajaysoni1924 36 views
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Simplify the following boolean functions using four variable K- maps F(A,B,C,D) = $\sum (0,1,2,4,5,7,11,15)$ F(w,x,y,z) = $\sum (1,4,5,6,12,14,15)$ F(A,B,C,D) = $\sum (0,2,4,5,6,7,8,10,13,15)$ F(w,x,y,z) = $\sum (2,3,10,11,12,13,14,15)$
asked Apr 1, 2019 in Digital Logic ajaysoni1924 38 views
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Simplify the following boolean functions using four variable K- maps F(A,B,C,D) = $\sum (4,6,7,15)$ F(w,x,y,z) = $\sum (2,3,12,13,14,15)$ F(A,B,C,D) = $\sum (3,7,11,13,14,15)$
asked Apr 1, 2019 in Digital Logic ajaysoni1924 91 views
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21
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22
Simplify the following Boolean functions using Three-Variable maps. F(x,y,z) = $\sum (0,1,5,7)$ F(x,y,z) = $\sum (1,2,3,6,7)$ F(x,y,z) = $\sum (3,5,6,7)$ F(A,B,C) = $\sum (0,2,3,4,6)$
asked Apr 1, 2019 in Digital Logic ajaysoni1924 45 views
1 vote
2 answers
23
Express the following function in the sum of minterms and The product of the maxterms. (a) F(A,B,C,D) = B’D + A’D + BD (b)F(x,y,z)=(xy + z)(xz + y)
asked Mar 31, 2019 in Digital Logic ajaysoni1924 305 views
0 votes
1 answer
25
Reduce the Following Boolean Expressions to the indicated numbers of the literals A’C’ + ABC +AC’ to three literals (X’Y’ + Z’)’ + Z + XY + WZ to three literals A’B(D’ + C’D) + B(A + A’CD) to one literals (A’ + C)(A’ + C’)(A+ B + C’D) to four literals
asked Mar 31, 2019 in Digital Logic ajaysoni1924 139 views
1 vote
1 answer
26
Simplify the Boolean expression to the minimum numbers of the literals. $ABC + A’B + ABC’$ $X’YZ + XZ$ $( X+ Y)’(X’ + Y’)$ $XY + X(WZ + WZ’)$ $(BC’ + A’D)(AB’ + CD’)$
asked Mar 31, 2019 in Digital Logic ajaysoni1924 70 views
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Simplify the following boolean Expressions to the minimum number of Literals x’y’ + xy + x’y (x + y)(x + y’) x’y + xy’ + xy + x’y’ x’ + xy + xz’ + xy’z’ xy’ + y’z’ + x’z’
asked Mar 31, 2019 in Digital Logic ajaysoni1924 171 views
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Consider the grammar G with Productions $S \rightarrow A|B,$ $A \rightarrow λ,$ $B \rightarrow aBb,$ $B \rightarrow b$. Construct a Grammar $\hat{G}$ by applying the algorithm in Theorem 6.3.
asked Mar 23, 2018 in Theory of Computation Mk Utkarsh 204 views
1 vote
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S -> AB A -> aBB | epsilon B -> bAA | epsilon What will be the CFG after removal of NULL production My doubt is in this grammer epsilon is also accepted So we cant remove it right else the equivalent grammer will not be same as this grammer so What should be the answer of such problem if said to get rid of null productions?
asked Nov 1, 2017 in Theory of Computation Na462 1.1k views
1 vote
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Convert the following context free grammar into Chomsky Normal Form: $S \rightarrow ASA | aB$ $A \rightarrow B | S$ $B \rightarrow b | \epsilon$ Does the appearance of starting symbol S at RHS impacts the conversion from CFG to CNF?
asked Oct 14, 2017 in Theory of Computation Manu Thakur 1.5k views
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