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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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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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Morris Mano Edition 3 Exercise 2 Question 15 (Page No. 71)
Convert the following Expressions into the sum of Products and Product of sums. (AB + C)(B + C’D) X’ + X(X + Y’)(Y + Z’)
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Apr 1
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Digital Logic
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Morris Mano Edition 3 Exercise 2 Question 17 (Page No. 71)
Draw the Logic Diagram corresponding to the following Operation without simplifying them. BC’ + AB + ACD (A + B)(C + D)(A’ + B + D) (AB + A’B’)(CD’ + C’D)
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Apr 1
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Morris Mano Edition 3 Exercise 2 Question 18 (Page No. 71)
Show that the Dual of the Exclusive OR is equal to its complement.
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Apr 1
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Morris Mano Edition 3 Exercise 2 Question 19 (Page No. 71)
by substituting the boolean expression equivalent of the binary operation defined in the below table, show the following. The inhibition operation is neither commutative nor associative. The ExclusiveOR operation is commutative and Associative.
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Apr 1
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Digital Logic
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7
Morris Mano Edition 3 Exercise 2 Question 20 (Page No. 71)
Verify the truth table for three Variable ExclusiveOR function. Do that By listing all the eight combinations of X, Y and Z than Evaluate A = X $\bigoplus$ Y. also Evaluate F = A $\bigoplus Z = X \bigoplus Y\bigoplus Z$
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Apr 1
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Morris Mano Edition 3 Exercise 2 Question 21 (Page No. 71)
TTL SSI comes mostly in 14pin packets. two pins are reserved for power and the other 12 pins are for inputoutput terminals. Determine the number of gates that can be enclosed in one package if it contains the following ... two input exclusiveOR gate three input AND gates Four input NAND Gates FIveinput NOR gates Eight input NAND gates
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Apr 1
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Digital Logic
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digitallogic
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Morris Mano Edition 3 Exercise 2 Question 22 (Page No. 71)
Show that a positive logic NAND gate is a negative Logic Nor Gate and vice versa.
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Apr 1
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Digital Logic
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Morris Mano Edition 3 Exercise 2 Question 23 (Page No. 71)
An integratedcircuit Logic Family has NAND Gates having Fan out 5 and Buffer gates with fan out 10. Show how the output signal of a Single NAND gate can be applied to 50 other NAND gate without overloading the output gate.use the buffer to satisfy the fanout requirement
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Apr 1
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Digital Logic
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1
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Morris Mano Edition 3 Exercise 2 Question 15 (Page No. 71)
The sum of all the minterms of the boolean function of the n variable is 1. Prove the above statement with n = 3. give a Procedure for a general proof
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Mar 31
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Digital Logic
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Morris Mano Edition 3 Exercise 2 Question 14 (Page No. 71)
Convert the following to the other canonical Form $(a) F(A,B,C,D) = \prod(0,1,2,3,4,6,12)$ $(b) F(x,y,z) = \sum(1,3,7)$
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Mar 31
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Digital Logic
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Morris Mano Edition 3 Exercise 2 Question 13 (Page No. 71)
Express the complement of the following function in the sum of minterms. $(a) F(A,B,C,D) = \sum(0,2,6,11,13,14)$ $(b) F(x,y,z) = \prod(0,3,6,7)$
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Mar 31
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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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Mar 31
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Digital Logic
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digitallogic
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1
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15
Morris Mano Edition 3 Exercise 2 Question 11 (Page No. 70)
Given the Following Boolean Function: F = xy'z + x'y'z + w'xy + wx'y + wxy Obtain the truth table of the function. Draw the logic diagram using the original Boolean Expression. Simplify the function to the minimum ... Draw the logic diagram of the simplified function and Compare the total number of gates with the logic diagram in part 2.
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Mar 31
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Digital Logic
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Morris Mano Edition 3 Exercise 2 Question 10 (Page No. 70)
For the Boolean Function F Given in the Truth Table, Find the following. x y z F 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 List the Minterm of F’.and F Express F in the sum of Minterm in algebraic form. simplify the function to an Expression with the minimum number of the literals.
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Mar 31
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Digital Logic
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Morris Mano Edition 3 Exercise 2 Question 9 (Page No. 70)
Obtain the truth tables of the following Boolean Functions. Express Each Function in Sum of minterm And Product of Maxterm. (xy + z)((y + xz) (A’ + B)(B’ + C) y’z + wxy’ +wxz’ + w’x’z
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Mar 31
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18
Morris Mano Edition 3 Exercise 2 Question 8 (Page No. 70)
Using DeMorgan’ s theorem, Convert the following Boolean Expressions to the Equivalent Expressions that have only AND and Complement Operation. Show that the function can be implemented with the logic diagram that have AND gate and inverter Only. (a) F = x’y’ + x’z + y’z (b) F = (y + z’)(x + y)(y’ + z)
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Mar 31
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19
Morris Mano Edition 3 Exercise 2 Question 7 (Page No. 70)
Using DeMorgan’ s theorem, Convert the following Boolean Expressions to the Equivalent Expressions that have only OR and Complement Operation. Show that the function can be implemented with the logic diagram that have OR gate and inverter Only. (a) F = x’y’ + x’z + y’z (b) F = (y + z’)(x + y)(y’ + z)
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Mar 31
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Digital Logic
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digitallogic
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2
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20
Morris Mano Edition 3 Exercise 2 Question 6 (Page No. 70)
Find the complement of the following boolean expressions x’y + xy’ (AB’ + C)D’ + E AB(CD’ + C’D) + A’B’(C + D’)(C’ + D) (X + Y’ + Z)(X’ + Z’)(X + Y)
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Mar 31
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32
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vote
2
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21
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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Mar 31
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22
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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Mar 31
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23
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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Mar 31
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24
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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Mar 31
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Digital Logic
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25
Morris Mano Edition 3 Exercise 2 Question 1 (Page No. 69)
Demonstrate the validity of the Following identities by means of the truth tables. DeMorgan’s theorem for three variables (xyz)’= x’ + y’ + z’. the second Distributive Law x + yz = (x+y)(x+z). The Consensus Theorem xy+x’z + yz = xy + x’z.
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Mar 31
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Digital Logic
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digitallogic
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+3
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4
answers
26
GATE20196
Which one of the following is NOT a valid identity? $(x \oplus y) \oplus z = x \oplus (y \oplus z)$ $(x + y) \oplus z = x \oplus (y+z)$ $x \oplus y = x+y, \text{ if } xy=0$ $x \oplus y = (xy+x’y’)’$
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Feb 7
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Digital Logic
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gate2019
digitallogic
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27
GATEBOOK2019 Mock Test122
Which of the following conditions can be expressed by a Boolean formula in the Boolean variables $p1,p2,p3,p4$ and the connectives ∧ ∨, (without ¬ )? At least three of $p1,p2,p3,p4$ are true. Exactly three of $p1,p2,p3,p4$ are true. An even number of $p1,p2,p3,p4$ are true. I only II only III only I and III
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Jan 19
in
Digital Logic
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GATEBOOK
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gb2019mock1
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kmap
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votes
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28
Boolean Algebra
The function f(a,b,q,g)=$\prod m(1,2,4,6,8,9)$. Can f(a,b,q,g) be written as f(q,g,b,a) + $\sum m(5,10)$? If not, what would be the correct equation?
asked
Dec 30, 2018
in
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Jay Bhutada 1
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173
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87
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digitallogic
booleanalgebra
0
votes
1
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29
Digital electronics Morris Mano
Please provide, how to make the truth table of such type of questions
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Nov 14, 2018
in
Digital Logic
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kd.....
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digitallogic
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combinational
digitalcircuits
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30
Self Doubt
What is DUAL for Function F = AB + C Fd = (A + B).C Or Fd = A + (B.C) OR>AND and AND>OR but what about precedence ??
asked
Nov 4, 2018
in
Digital Logic
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