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Morris Mano Edition 3 Exercise 3 Question 27 (Page No. 113)
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) = $\sum(6,9,13,18,19,25,27,29,41,45,57,61)$
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Morris Mano Edition 3 Exercise 3 Question 25 (Page No. 112)
Implement the following boolean function F together with the don’tcare 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) $ $d(A,B,C,D) = \sum(8,10,14,15)$
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Morris Mano Edition 3 Exercise 3 Question 24 (Page No. 112)
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'tcare conditions.
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Morris Mano Edition 3 Exercise 3 Question 23 (Page No. 113)
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) $F(A,B,C,D) = \sum (3,4,13,15)$ $d(A,B,C,D) =\sum(1,2,5,6,8,10,12,14)$
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Morris Mano Edition 3 Exercise 3 Question 22 (Page No. 112113)
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) $F(A,B,C,D) = \sum(1,3,5,7,9,15)$ $d(A,B,C,D)= \sum(4,6,12,13)$
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Morris Mano Edition 3 Exercise 3 Question 21 (Page No. 112)
List the Eight degenerate 2 level forms and show that they reduce to the single operation. Explain how the degenerate twolevel forms can be used to extend the number of inputs to a gate.
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Morris Mano Edition 3 Exercise 3 Question 20 (Page No. 112)
Implement the function F with the Following two level Forms: NANDAND, ANDNOR, ORNAND, AND NOROR. F(A,B,C,D) = $\sum(0,1,2,3,4,8,9,12)$
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Morris Mano Edition 3 Exercise 3 Question 19 (Page No. 112)
Find the eight different twolevel gate circuit to implement F = xy’z + x’yz + w.
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Morris Mano Edition 3 Exercise 3 Question 15,16 (Page No. 112)
Simplify the following functions and implement them with (15) two level NOR gate circuits (16) threelevel NOR gate circuits. F = wx’ + y’z’ + w’yz’ F(w,x,y,z) = $\sum(5,6,9,10)$
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Morris Mano Edition 3 Exercise 3 Question 13 (Page No. 112)
Draw the NAND gate logic diagram that implements the complement of the following funcions: F(A,B,C,D) = $\sum ( 0,1,2,3,4,8,9,12)$
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Morris Mano Edition 3 Exercise 3 Question 12,17 (Page No. 112)
Simplify the following expressions and implement them with (12)twolevel NAND gate circuits (17) threelevel NAND gate circuits (a) AB’ + ABD + ABD’ + A’C’D + A’BC’ (b) BD + BCD’ + AB’C’D’
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Morris Mano Edition 3 Exercise 3 Question 11 (Page No. 112)
Draw the ANDOR gate implementation of the following function after simplifying it in (a) sum of products and (b) product of sums. F= (A,B,C,D) = $\sum (0,2,5,6,7,8,10)$
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Morris Mano Edition 3 Exercise 3 Question 10 (Page No. 112)
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’)
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Morris Mano Edition 3 Exercise 3 Question 9 (Page No. 111)
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) = $\prod(0,1,2,3,4,10,11)$
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Morris Mano Edition 3 Exercise 3 Question 8 (Page No. 111)
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’
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Morris Mano Edition 3 Exercise 3 Question 7 (Page No. 111)
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) = $\sum (1,3,4,5,10,11,12,13,14,15)$
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Morris Mano Edition 3 Exercise 3 Question 6 (Page No. 111)
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
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Morris Mano Edition 3 Exercise 3 Question 5 (Page No. 111)
Simplify the following boolean expressions using Four variable Kmaps. 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
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Morris Mano Edition 3 Exercise 3 Question 4 (Page No. 111)
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) = $\sum (2,3,10,11,12,13,14,15)$
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Morris Mano Edition 3 Exercise 3 Question 3 (Page No. 111)
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) = $\sum (3,7,11,13,14,15)$
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Morris Mano Edition 3 Exercise 3 Question 2 (Page No. 111)
Simplify the Following Boolean Expressions using threevariable kmap. xy + x’y’z’ + x’yz’ x’y’ + yz + x’yz ’ A’B + BC’ + B’C’
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Morris Mano Edition 3 Exercise 3 Question 1 (Page No. 111)
Simplify the following Boolean functions using ThreeVariable 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) = $\sum (0,2,3,4,6)$
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Morris Mano Edition 3 Exercise 2 Question 12 (Page No. 70)
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)
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Morris Mano Edition 3 Exercise 2 Question 5 (Page No. 69)
Find the complement of X + YZ; then show that F.F’=0 and F + F’ = 1
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Morris Mano Edition 3 Exercise 2 Question 4 (Page No. 69)
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
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Morris Mano Edition 3 Exercise 2 Question 3 (Page No. 69)
Simplify the Boolean expression to the minimum numbers of the literals. $ABC + A’B + ABC’$ $X’YZ + XZ$ $( X+ Y)’(X’ + Y’)$ $XY + X(WZ + WZ’)$ $(BC’ + A’D)(AB’ + CD’)$
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Morris Mano Edition 3 Exercise 2 Question 2 (Page No. 69)
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’
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Peter Linz Edition 4 Exercise 6.1 Question 13 (Page No. 162)
Consider the grammar G with Productions $S \rightarrow AB,$ $A \rightarrow λ,$ $B \rightarrow aBb,$ $B \rightarrow b$. Construct a Grammar $\hat{G}$ by applying the algorithm in Theorem 6.3.
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Removal of Null production
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?
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Automata: Conversion from CFG to CNF
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?
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