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The correct OPTION is (a) XY’

The best explanation: Given: Y’ (X’ + Y’) (X + X’Y)

= Y’(X’ + Y’)(X + Y)

= (X’Y’ + Y’)(X + Y)

= (XX’Y’ + X’Y’Y + XY’ + YY’)

= XY’.

Correct ANSWER is (a) DFA

Easiest explanation: A Deterministic Finite automaton SYSTEM is USED in the lexical ANALYSIS of the compiler.

The correct ANSWER is (a) two automata accept the same set of INPUT strings

Easy explanation: The formal definition is if two automata J and K are EQUIVALENT then if there is a path from the start state of J to a final state of J and there is a path from the start state of k to a final state of K as WELL as if there is a path from the start state of K to a final state of K, where there is a path from the start state of J to a final state of J. Two automata J and K are said to be equivalent if both automata accept exactly the same set of input strings.

Right choice is (a) exactly one

To explain: In a DETERMINISTIC automaton, for each possible input every state has exactly one transition. In a non-deterministic automaton, an input can have one, more than one, or no transition for a given state. In the study of computation, a transition system is used and it can be MADE of states and TRANSITIONS between states, which MAY be labeled with labels chosen from a set.

The correct option is (b) superset construction

Explanation: For every N-DFA there is a corresponding DFA for every N-DFA, and the basic technique is DESCRIBED as subset construction because each STATE in the DFA CORRESPONDS to some subset of STATES of the NDFA.

Right option is (b) HUFFMAN encoding scheme

Explanation: The job of FASTEST known algorithm, hopcroft minimization algorithm is to optimize and FSM SYSTEM that means FINDING a machine with the minimum number of states which can have the same function to perform. Acyclic FSAs can be minimized in linear TIME.

Right answer is (a) ASM method

The best I can explain: An abstract state machine (ASM) has its operations on states that are arbitrary data structures as well as it can BRIDGE the gap between the two ends of the SYSTEM development. This method builds upon three basic concepts such as ASM, GROUND model and refinement.

Correct option is (b) initial state

To explain I would say: A deterministic finite state MACHINE or acceptor deterministic finite state machine is a quintuple (Σ, G, s1, δ, F), where: Σ is the input ALPHABET (a finite, non-empty SET of symbols), G is a finite, non-empty set of states, s1 is an initial state, an element of S, δ is the state-transition function: δ: G × Σ → G.

Correct answer is (b) 2

To elaborate: In cyclic prime IMPLICANT, min terms will be (1, 3, 5, 7, 9, 11). Hence, either we can have [(1,3), (7,11), (5,9)] or [(1,5), (11,9), (3.7)]. So, there can be 2 minimal forms.

Correct CHOICE is (b) Dynamic programming

The best EXPLANATION: The powerset construction algorithm is a powerful algorithm that can TRANSFORM any non-deterministic automaton into a more complex deterministic automaton with IDENTICAL functionality.

Right choice is (c) 1

To elaborate: As an FSM’s memory is limited by the number of states, it cannot PERFORM the COMPUTATIONAL TASKS that a TURING machine can do. A “Combinatorial FSM” is defined as a FINITE state machine with only one state and it allows actions based upon transition into a state.

Right answer is (b) 2

Easy EXPLANATION: There are two essential PRIME implicants such as (B+C) and (B+C’) for the given FUNCTION. HENCE, the REQUIRED answer is 2.

Right option is (b) 1

Easy explanation: By, solving the minimization EXPRESSION USING K-Map, there is only 1 essential PRIME IMPLICANT exist as it is not covered by any other input variable.

The CORRECT choice is (b) 0

To explain: There are no ESSENTIAL prime implicants for this SWITCHING FUNCTION. We can get this solution by using K-Map.

Correct option is (c) 3

To explain: An IMPLICANT of a FUNCTION is a product TERM which is included in the function.

Hence, for the given function, y’z’, xy and X’z all are PRIME implicants.

The correct choice is (c) 256

To EXPLAIN: Any Boolean expression or a function COMPRISING of 8 VARIABLES can be SOLVED using an 8-variable K-Map. So, an 8-variable K-Map must contain 2^8 = 256.

The CORRECT ANSWER is (C) 2^33

To EXPLAIN: For n-variable K Map, we have = 2^n-1 PRIME implicants. In this case, n=34 and the maximum number of prime implicants will be 2^34-1 = 2^33.

The correct ANSWER is (d) IMPLY gate

For explanation I would SAY: The IMPLY gate is a digital logic gate that is used to implements logical conditional. Two SYMBOLS are used to represent the IMPLY gates → the traditional SYMBOL and the IEEE symbol. IMPLY gate can be made by two memristors.

Right choice is (B) 213

Easiest explanation: OR gate works in a WAY such that if any of the INPUT is BINARY low(or 0), the output of the gate is binary 1(or high). Here, the NUMBER of stage possible = 2^n = 2^13.

The CORRECT choice is (b) Apollo GUIDANCE Computer

Easiest explanation: The first embedded system is the Apollo Guidance Computer which was built EXCLUSIVELY from NOR gates. A LOGICALLY inverted OR gate is a NOR gate and it can have two or more inputs.

The correct CHOICE is (a) NOT gate

To explain: NOT gate is the SIMPLEST digital logic circuit which is ALSO called an inverter because it takes the input in 0 or 1 form and gives the OUTPUT as the complement of the input.

The correct CHOICE is (a) selector BIT, DATA bit

Easy explanation: In MULTIPLEXER gate for selecting the inputs say, for 3 input bits, ONE bit is required as selector bit and two other bits are required as data bits.

Right answer is (C) 4

Easiest explanation: An XOR gate is created by USING four NAND gates. This construction gives a propagation DELAY three times to that of a single NAND gate.

Correct option is (d) flip-flop

The best explanation: A shift register, in digital circuitry, is a COMBINATION of two or more flip-flops to share the bits of information by using the same CLOCK. A shift register can have both parallel and serial inputs and OUTPUTS.

Right CHOICE is (a) 0 and 1

Explanation: The DATA, in boolean algebra MUST be in a bit-representation FORM which can be in between two values 0 and 1.

The correct option is (b) NAND GATE

Explanation: The NAND gate CONSISTS of TWO inputs and if both of them are high the output is LOW. A luggage security ALARM circuit is a system which is based on the NAND gate. It is used to generate an alarm when any authorized person tries to steal the luggage.

Correct CHOICE is (a) single bit

For explanation: In Gray coding, the adjacent code values differ only by a single bit. If the GIVEN code-word is 01, then the previous and the next code-words are to be 11 or 00 but cannot be 10 in any case. Each cell within a K-map has a definite place-value which is obtained by using this encoding technique. The rows and the columns of the table USE Gray code-labeling which in turn represents the values of the corresponding input variables and each K-map cell can be addressed using a unique Gray Code-Word.

Correct CHOICE is (a) Maurice Karnaugh

To EXPLAIN: The Karnaugh MAP (KM or K-map) is INVENTED by Maurice Karnaugh in 1953 that is a method of simplifying Boolean expressions.

Correct option is (d) yz+xy+xy’z

Explanation: F = x’yz + xyz + xy z’ + xy’z’ is the canonical FORM for the FUNCTION. Now, USING k-map the MINIMAL form must be: yz+xy+xy’z.

The correct option is (a) (x+y)(y+z)(x+z)(x’+z’)

To ELABORATE: By solving the given EXPRESSION, the MAXTERMS are: (x+y), (x’+y), (x+z) and (x’+z’). Hence, we can get REQUIRED expression (x+y)(x’+y)(x+z)(x’+z’).

The correct ANSWER is (b) 2

To EXPLAIN I would say: Addition of bits requires carry-in and carry-out bits. Addition of TWO terms (bits) a and b, and a carry-in BIT Cin is required to compute a sum bit S and a carry-out bit Cout. Hence, two bits are produced in general.

The CORRECT choice is (b) AB+C

The explanation is: By solving the GIVEN EXPRESSION, the minterms are: C and AB. HENCE, we can get the required expression C+AB.

Right choice is (a) k-map

Easy explanation: A Karnaugh map can be used to build the appropriate POS expression for DESIGNING a circuit to form the truth table. Karnaugh maps are not LIMITED to SOP expressions only for minimizing boolean FUNCTIONS.

Correct OPTION is (c) A’D+BCD+A’BC+AB’C’

The best explanation: By solving the GIVEN EXPRESSION we have minterms such as A’D+BCD+A’BC+AB’C’. So, we can GET the required expression A’D+BCD+A’BC+AB’C’.

The correct option is (a) logic minimization

To explain I WOULD say: K-map(Maurice Karnaugh of Bell labs in 1953) is defined as a diagrammatic method for logic minimization and it is a PICTORIAL view of TRUTH table which shows the relationship between inputs and output. It is more EFFICIENT than Boolean algebra. K-map is a diagram made up of squares in which each square represents a minterm or MAXTERM of the logic function.

Correct OPTION is (c) X + Z

The best explanation: We have, x+x’y’z+yz

= x+y’z+yz [SINCE, x+x’y’z=x+y’z]

= x+z(y’+y)

= x + z.

The correct answer is (c) (XY)’

Easy explanation: GIVEN XY’+X’+Y’X’ = Y’(X+X’) + X’ = Y’.1 + X’ = X’ + Y’ = (XY)’ [De Morgan’s law].

The CORRECT option is (B) MN+M’N’

Easy explanation: Given: MN(M + N’) + M(N + N’)

= MN(M+N’) + M.1

= MNM + MNN’ + M

= MN + 0 +M

= M(N + 1)

= M.

The correct ANSWER is (d) X+Y

For explanation: (X + Z)(X + XZ’) + XY + Y[ORIGINAL EXPRESSION]

= (x + z)X(1 + Z’) + XY + Y[Distributive]

= (X + Z)X + XY + Y[Complement, IDENTITY]

= (X+Z)X + Y(X+1)[ Distributive]

= (X+Z)X + Y[Idempotent]

= XX + XZ + Y[Distributive]

= X + XZ + Y[Identity]

= X(1+Z) + Y

= X + Y[Idempotent].

The correct choice is (B) (A’B+C’)

To elaborate: Given:A’(A + BC) + (AC + B’C)

= A’A + A’BC + AC + B’C

= A’BC + C(A + B’)

= C(A’B + A + B’)

= C(A + B + B’)

= C(A + 1)

= AC.

The CORRECT answer is (c) sum-of-products

The BEST I can EXPLAIN: The sum of MINTERMS that represents the function is called the sum-of-products expansion or the disjunctive normal form. A Boolean sum of minterms has the value 1 when exactly one of the minterms in the sum has the value 1. It has the value 0 for all other combinations of values of the variables.

Correct choice is (a) (a+b)(a`+b`)

For EXPLANATION: a ⊕ b

= a`b + AB`

= a`b+aa` + bb` + ab` [As, a*a` = 0 and b*b` = 0]

= a`(a+b) + b`(a+b)

= (a+b)(a`+b`).