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IB JIO Grade-2 Tech 2023 part-2: 16
Q.16 Simplify the Boolean expression. \[ Y=A B+A(B+C)+B(B+C) \] Ans 1. $Y=B+A C$ 2. $Y=A+B C$ 3. $Y=C+A B$ 4. $Y=A C$ Question ID : 630680278458 Option 1 ID : 6306801082190 Option 2 ID : 6306801082189 Option 3 ID : 6306801082191 Option 4 ID : 6306801082192 Status : Answered Chosen Option : 2

admin asked in Digital Logic Jul 31, 2023

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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) = $\sum(6,9,13,18,19,25,27,29,41,45,57,61)$

ajaysoni1924 asked in Digital Logic Apr 2, 2019

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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’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) $ $d(A,B,C,D) = \sum(8,10,14,15)$

ajaysoni1924 asked in Digital Logic Apr 2, 2019

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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't-care conditions.

ajaysoni1924 asked in Digital Logic Apr 2, 2019

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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) $F(A,B,C,D) = \sum (3,4,13,15)$ $d(A,B,C,D) =\sum(1,2,5,6,8,10,12,14)$

ajaysoni1924 asked in Digital Logic Apr 2, 2019

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Morris Mano Edition 3 Exercise 3 Question 22 (Page No. 112-113)
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) $F(A,B,C,D) = \sum(1,3,5,7,9,15)$ $d(A,B,C,D)= \sum(4,6,12,13)$

ajaysoni1924 asked in Digital Logic Apr 2, 2019

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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 two-level forms can be used to extend the number of inputs to a gate.

ajaysoni1924 asked in Digital Logic Apr 2, 2019

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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: NAND-AND, AND-NOR, OR-NAND, AND NOR-OR. F(A,B,C,D) = $\sum(0,1,2,3,4,8,9,12)$

ajaysoni1924 asked in Digital Logic Apr 2, 2019

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Morris Mano Edition 3 Exercise 3 Question 19 (Page No. 112)
Find the eight different two-level gate circuit to implement F = xy’z + x’yz + w.

ajaysoni1924 asked in Digital Logic Apr 2, 2019

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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) three-level NOR gate circuits. F = wx’ + y’z’ + w’yz’ F(w,x,y,z) = $\sum(5,6,9,10)$

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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) = $\sum ( 0,1,2,3,4,8,9,12)$

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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)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’

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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’)

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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) = $\prod(0,1,2,3,4,10,11)$

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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’

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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) = $\sum (1,3,4,5,10,11,12,13,14,15)$

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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Morris Mano Edition 3 Exercise 3 Question 5 (Page No. 111)
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

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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) = $\sum (2,3,10,11,12,13,14,15)$

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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) = $\sum (3,7,11,13,14,15)$

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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Morris Mano Edition 3 Exercise 3 Question 2 (Page No. 111)
Simplify the Following Boolean Expressions using three-variable k-map. xy + x’y’z’ + x’yz’ x’y’ + yz + x’yz ’ A’B + BC’ + B’C’

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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Morris Mano Edition 3 Exercise 3 Question 1 (Page No. 111)
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) = $\sum (0,2,3,4,6)$

ajaysoni1924 asked in Digital Logic Apr 1, 2019

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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)

ajaysoni1924 asked in Digital Logic Mar 31, 2019

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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

ajaysoni1924 asked in Digital Logic Mar 31, 2019

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25

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

ajaysoni1924 asked in Digital Logic Mar 31, 2019

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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. $ABC + A’B + ABC’$ $X’YZ + XZ$ $( X+ Y)’(X’ + Y’)$ $XY + X(WZ + WZ’)$ $(BC’ + A’D)(AB’ + CD’)$

ajaysoni1924 asked in Digital Logic Mar 31, 2019

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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’

ajaysoni1924 asked in Digital Logic Mar 31, 2019

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Peter Linz Edition 4 Exercise 6.1 Question 13 (Page No. 162)
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.

Mk Utkarsh asked in Theory of Computation Mar 23, 2018

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Stuck in Recurrence Relation in Algorithm
How to find log of the first n natural numbers? $T(n)= \log 1+ \log 2+ \log 3+\ldots + \log n$ // How to proceed from here?

iarnav asked in Quantitative Aptitude Jan 11, 2018

by iarnav

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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?

Na462 asked in Theory of Computation Nov 1, 2017

by Na462

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