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51.

(X+Y`)(X+Z) can be represented by _____(a) (X+Y`Z)(b) (Y+X`)(c) XY`(d) (X+Z`)I got this question in an online quiz.This is a very interesting question from Boolean Functions topic in section Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer» CORRECT option is (a) (X+Y`Z)

The EXPLANATION is: (X+Y`) (X+Z)

= XX + XZ + XY`+ Y`Z

= X + XZ + XY`+ Y`Z

= X (1+Z) + XY`+ Y`Z

= X.1 + XY`+ Y`Z

= X (1+Y`) + Y`Z

= X + Y`Z.
Discussion
52.

The set for which the Boolean function is functionally complete is __________(a) {*, %, /}(b) {., +, -}(c) {^, +, -}(d) {%, +, *}I got this question during an interview for a job.This question is from Boolean Functions in section Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»
Discussion
53.

Minimization of function F(A,B,C) = A*B*(B+C) is _________(a) AC(b) B+C(c) B`(d) ABThis question was addressed to me by my school principal while I was bunking the class.My enquiry is from Boolean Functions topic in section Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»
Discussion
54.

A _________ is a Boolean variable.(a) Literal(b) String(c) Keyword(d) IdentifierI have been asked this question during an interview.This is a very interesting question from Boolean Functions topic in chapter Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

Correct choice is (a) Literal

For EXPLANATION: A literal is a BOOLEAN variable or its COMPLEMENT. A MAXTERM is a sum of n literals and a MINTERM is a product of n literals.
Discussion
55.

There are _________ numbers of Boolean functions of degree n.(a) n(b) 2^(2*n)(c) n^3(d) n^(n*2)The question was asked in unit test.My question is based upon Boolean Functions topic in section Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

Correct choice is (b) 2^(2*n)

The explanation: There are 2n DIFFERENT n-tuples of 0’s and 1’s. A BOOLEAN function is an ASSIGNMENT of 0’s or 1’s to each of these 2 n different n-tuples. HENCE, there are 2^(2*n) different Boolean functions.
Discussion
56.

Inversion of single bit input to a single bit output using _________(a) NOT gate(b) NOR gate(c) AND gate(d) NAND gateI got this question in a national level competition.The doubt is from Boolean Functions in section Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

Correct CHOICE is (a) NOT GATE

The explanation: A NOT gate is USED to invert a SINGLE bit INPUT (say A) to a single bit of output (~A).
Discussion
57.

_________ is used to implement the Boolean functions.(a) Logical notations(b) Arithmetic logics(c) Logic gates(d) ExpressionsThis question was posed to me in an internship interview.Enquiry is from Boolean Functions in portion Boolean Algebra and Modeling Computations of Discrete Mathematics

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Discussion
58.

What is the use of Boolean identities?(a) Minimizing the Boolean expression(b) Maximizing the Boolean expression(c) To evaluate a logical identity(d) Searching of an algebraic expressionThis question was posed to me by my college professor while I was bunking the class.My enquiry is from Boolean Functions topic in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer» CORRECT answer is (a) Minimizing the BOOLEAN expression

Easy explanation: Boolean IDENTITIES are used for minimizing the Boolean expression and TRANSFORMING into an equivalent expression.
Discussion
59.

The ___________ of all the variables in direct or complemented from is a maxterm.(a) addition(b) product(c) moduler(d) subtractionThe question was asked in a job interview.This key question is from Boolean Algebra topic in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

Correct CHOICE is (a) addition

For explanation I WOULD say: The BOOLEAN function is expressed as a sum of the 1-minterms and the INVERSE of function is represented as 0-minterms.
Discussion
60.

The logic gate that provides high output for same inputs ____________(a) NOT(b) X-NOR(c) AND(d) XORThe question was asked in quiz.My doubt is from Boolean Algebra in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

The correct OPTION is (B) X-NOR

The explanation: The logic gate which GIVES high output for the same inputs, otherwise LOW output is KNOWN as X-NOR or Exclusive NOR gate.
Discussion
61.

Which of the following is/are the universal logic gates?(a) OR and NOR(b) AND(c) NAND and NOR(d) NOTI have been asked this question during an internship interview.This is a very interesting question from Boolean Algebra topic in chapter Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

The correct option is (c) NAND and NOR

Explanation: NAND and NOR gates are known as the UNIVERSAL logic gates. A universal GATE is a gate which can implement any Boolean FUNCTION without the help of 3 basic gate TYPES.
Discussion
62.

What are the canonical forms of Boolean Expressions?(a) OR and XOR(b) NOR and XNOR(c) MAX and MIN(d) SOM and POMThis question was posed to me in an online quiz.My question comes from Boolean Algebra in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

Correct choice is (d) SOM and POM

For explanation I would say: There are two kinds of CANONICAL forms for a BOOLEAN expression-> 1)sum of minterms(SOM) form and

2)product of maxterms(SOM) form.
Discussion
63.

Which of the following is a Simplification law?(a) M.(~M+N) = M.N(b) M+(N.O) = (M+N)(M+O)(c) ~(M+N) = ~M.~N(d) M.(N.O) = (M.N).OI had been asked this question during an interview for a job.Query is from Boolean Algebra topic in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

Right CHOICE is (a) M.(~M+N) = M.N

The best I can EXPLAIN: By SIMPLIFICATION Law we can have X.(~X+Y) = X.Y and X+(~X.Y) = X+Y. By, De’ Morgan’s law ~(X+Y) = ~X.~Y. By commutative law we can say that A.(B.C) = (A.B).C.
Discussion
64.

A ________ value is represented by a Boolean expression.(a) Positive(b) Recursive(c) Negative(d) BooleanI got this question at a job interview.This intriguing question comes from Boolean Algebra topic in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

Correct choice is (d) Boolean

Explanation: A Boolean value is given by a Boolean expression which is formed by COMBINING Boolean variables and LOGICAL connectives.
Discussion
65.

F(X,Y,Z,M) = X`Y`Z`M`. The degree of the function is ________(a) 2(b) 5(c) 4(d) 1I had been asked this question in a job interview.Question is from Boolean Algebra topic in portion Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

Correct option is (c) 4

To EXPLAIN I WOULD SAY: This is a function of DEGREE 4 from the set of ordered pairs of Boolean variables to the set {0,1}.
Discussion
66.

What is the definition of Boolean functions?(a) An arithmetic function with k degrees such that f:Y–>Y^k(b) A special mathematical function with n degrees such that f:Y^n–>Y(c) An algebraic function with n degrees such that f:X^n–>X(d) A polynomial function with k degrees such that f:X^2–>X^nI had been asked this question in examination.My doubt stems from Boolean Algebra in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

The correct OPTION is (b) A SPECIAL mathematical FUNCTION with n degrees such that f:Y^n–>Y

Explanation: A Boolean function is a special mathematical function with n degrees and where Y = {0,1} is the Boolean domain with being a non-negative integer. It helps in describing the way in which the Boolean output is derived from Boolean inputs.
Discussion
67.

Boolean algebra can be used ____________(a) For designing of the digital computers(b) In building logic symbols(c) Circuit theory(d) Building algebraic functionsI got this question in class test.I would like to ask this question from Boolean Algebra topic in division Boolean Algebra and Modeling Computations of Discrete Mathematics

Answer»

Correct option is (a) For designing of the digital computers

The explanation is: For designing digital computers and building different electronic circuits BOOLEAN algebra is accepted WIDELY.
Discussion
68.

Algebra of logic is termed as ______________(a) Numerical logic(b) Boolean algebra(c) Arithmetic logic(d) Boolean numberI got this question in an online interview.Asked question is from Boolean Algebra topic in section Boolean Algebra and Modeling Computations of Discrete Mathematics

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Correct ANSWER is (C) ARITHMETIC logic

Easy EXPLANATION: The variables that can have two discrete values False(0) and True(1) and the operations of logical significance are dealt with Boolean algebra.
Discussion