Q. Find the value of radix r, with the following equality is matached.

√(21)ᵣ = (11)ᵣ

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Q. How many bits are needed to represent 20 digit decimal number in binary?

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Q. Consider the following subtraction and Identify the correct answer.

(C012.25)₄ – (10111001110.101)₈

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Q. Let A = 11111010 and B = 00001010 be two 8 – bit 2's complement numbers. Their product in 2's complement is

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Q. The range of integers that can be represented by an n – bit 2's complement number system is

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Q. The switching expression corresponding to f(A, B,C, D) = Σ (1, 4, 5, 9, 11,12) is

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Q. What is the maximum number of different Boolean functions involving n boolean variables?

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Q. How many Boolean functions are possible with 2 trinary variables?

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Q. How many minimum 2-input nor gates are needed to realize A+BC?

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Q. Which of the following statement is true regarding ‘HAZARD’?

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Q. The min term expansion of f(P,Q,R) = PQ + QR̅ + PR̅ is

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Q. How many Boolean functions are possible with 3 Boolean variables such that the number of min terms are either one or two?

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Q. Which of the following statement is FALSE regarding functionally completeness, (FC).

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Q. Which of the following is the minimization expression for A+A'B+A'B'C+A'B'C'D?

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Q. Consider a hypothetical k-map in which essential prime implicants covering all the min – terms except two. Each of the left over min – term is covered by 3 different redundant prime implicants. What would be the no of minimal expressions denoted by the map?

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Q. The literal count of a Boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of (x y + x z) is 4. What are the minimum possible literal counts of the product – of – sum and sum – of – product representations respectively of the function given by the following karnaugh map? Here, x denotes “don’t care”.

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Q. What are the essential prime implicants of the following Boolean functions?

F (a, b, c) = a'c + ac' + b'c

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Q. A 4-bit carry look ahead adder, which adds two 4-bit numbers, is designed using AND, OR, NOT, NAND, NOR gates only. Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit, what is the overall propagation delay of the adder? Assume that the carry network has been implemented using two-level AND-OR logic.

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Q. Consider a Boolean function f(w,x,y,z). Suppose that exactly one of its inputs is allowed to change at a time. If the function happens to be true for two input vectors i₁=⟨w₁,x₁,y₁,z₁⟩ and i₂=⟨w₂,x₂,y₂,z₂⟩ , we would like the function to remain true as the input changes from i₁ to i₂ (i₁ and i₂ differ in exactly one bit position) without becoming false momentarily. Let f(w,x,y,z)=∑(5,7,11,12,13,15) . Which of the following cube covers of f will ensure that the required property is satisfied?

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Q. Define the connective * for the Boolean variable X and Y as :

X * Y = XY + X'Y'.

Let Z = X * Z.Consider the following expression P, Q and R.
P : X = Y * Z
q : Y = X * Z
R : X * Y * Z = 1

Which of the following is true?

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