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Recent questions tagged booleanalgebra
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GateBook Test Series: Digital Logic  Boolean Algebra
What is the time complexity for checking whether an assignment of truth values to variables $x_1,\dots ,x_n$ satisfies a given formula $f(x_1\dots,x_n)$? $O(2^n)$ $O(g(n))$ where $g$ is a polynomial $O(log(n))$ None of the above
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May 15
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Digital Logic
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Boolean algebradigital logic
$(a) A = 101010$ and $B = 011101$ are $1’s$ complement numbers. Perform the following operations and indicate whether overflow occurs. $(i) A + B$ $(ii) A − B$ $(b)$ Repeat part $(a)$ assuming the numbers are $2’s$ complement numbers.
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May 11
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Digital Logic
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Boolean algebra expression Floyd Digital Logic
Simplify the following expression AB’C + A’BC + A’B’C Solution given is A’C + B’C can someone show me how?
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May 2
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Digital Logic
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Testbook Test Series Question
f(A,B,C,D)=∏M(0,1,3,4,5,7,9,11,12,13,14,15) is a maxterm representation of a Boolean function f(A,B,C,D) where A is the MSB and D is the LSB. The equivalent minimized representation of this function is (A+C¯+D)(A¯+B+D)(A+C¯+D)(A¯+B+D) AC¯D+A¯BD+A¯BC A¯CD¯+AB¯CD¯+AB¯C¯D¯ (B+C¯+D)(A+B¯+C¯+D)(A¯+B+C+D)
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Apr 18
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Morris Mano Edition 3 Exercise 4 Question 25 (Page No. 151)
prove that $ x’ \oplus y = x \oplus y’ = (x \oplus y)’ = xy+x’y’$
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Apr 2
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Digital Logic
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Morris Mano Edition 3 Exercise 4 Question 26 (Page No. 151)
Prove that $x \oplus 1$ = x’ and $x \oplus 0$ = x.
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Apr 2
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Digital Logic
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Morris Mano Edition 3 Exercise 4 Question 27 (Page No. 151)
Show that if xy = 0, then $x\oplus y$ = x + y.
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Apr 2
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Digital Logic
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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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Apr 2
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Digital Logic
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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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Apr 2
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Digital Logic
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ajaysoni1924
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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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Apr 2
in
Digital Logic
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ajaysoni1924
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digitallogic
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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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Apr 2
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Digital Logic
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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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Apr 2
in
Digital Logic
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ajaysoni1924
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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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Apr 2
in
Digital Logic
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ajaysoni1924
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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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Apr 2
in
Digital Logic
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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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Apr 2
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Digital Logic
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Morris Mano Edition 3 Exercise 3 Question 18 (Page No. 112)
Give three possible ways to express the function F with eight or fewer literals. F(A,B,C,D) = $\sum(0,2,5,7,10,13)$
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Apr 2
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Digital Logic
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ajaysoni1924
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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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Apr 1
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Digital Logic
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18
Morris Mano Edition 3 Exercise 3 Question 14 (Page No. 112)
Draw a logic diagram using only two input NAND gate to implement the following expression: (AB + A’B’)(CD’ + C’D)
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Apr 1
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Digital Logic
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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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Apr 1
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Digital Logic
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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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Apr 1
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Digital Logic
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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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Apr 1
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Digital Logic
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ajaysoni1924
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22
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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Apr 1
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Digital Logic
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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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Apr 1
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Digital Logic
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ajaysoni1924
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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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Digital Logic
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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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Apr 1
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Digital Logic
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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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Apr 1
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Digital Logic
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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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Apr 1
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Digital Logic
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28
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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Apr 1
in
Digital Logic
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ajaysoni1924
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29
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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Apr 1
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Digital Logic
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ajaysoni1924
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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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Digital Logic
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