26Which code is used to prevent errors during state transitions because only one bit changes at a time?
A.BCD
B.Excess-3
C.Gray Code
D.ASCII
Correct Answer: Gray Code
Explanation:Gray code is a unit-distance code where only one bit changes between successive values, minimizing error in switching applications.
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27What is the minimum number of 2-input NAND gates required to implement a 2-input AND gate?
A.1
B.2
C.3
D.4
Correct Answer: 2
Explanation:First NAND gives . Connecting this output to both inputs of a second NAND (acting as inverter) gives .
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28The range of signed decimal numbers that can be represented by 5-bit 2's complement arithmetic is:
A. to
B. to
C. to
D. to
Correct Answer: to
Explanation:The range is to . For : to , which is to .
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29In Boolean Algebra, is equal to:
A.$1$
B.
C.$0$
D.
Correct Answer: $0$
Explanation:The AND operation between a variable and its complement is always $0$ (Law of Contradiction).
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30Convert the Gray Code $1011$ to Binary.
A.1101
B.1001
C.1110
D.1010
Correct Answer: 1101
Explanation:MSB Binary = MSB Gray (1). Next Bin = Prev Bin Next Gray. . Next Bin = . Next Bin = . Result: $1101$.
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31The POS (Product of Sums) form represents the expression as a:
A.Sum of minterms
B.Product of maxterms
C.Product of minterms
D.Sum of maxterms
Correct Answer: Product of maxterms
Explanation:POS forms are written as the AND (product) of OR (sum) terms, which corresponds to the Product of Maxterms ().
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32Simplify the boolean expression using K-map if adjacent cells are all 1.
A.
B.
C.$1$
D.$0$
Correct Answer: $1$
Explanation:If all cells in a 2-variable map are 1, the function simplifies to constant logic High ($1$).
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33Which of the following is a self-complementing code?
A.BCD Code
B.Excess-3 Code
C.8421 Code
D.Gray Code
Correct Answer: Excess-3 Code
Explanation:Excess-3 is a self-complementing code. The 9's complement of a decimal number can be obtained by taking the 1's complement of its Excess-3 code.
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34Perform binary addition: .
A.110000
B.100100
C.110100
D.101110
Correct Answer: 110000
Explanation: (c1), (c1), (c1), (c1), (c1). Result including final carry: $110000$.
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35The XNOR gate is equivalent to:
A.
B.
C.
D.
Correct Answer:
Explanation:XNOR produces a high output when inputs are equal. The expression is (both 1) OR (both 0).
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36What is the radix of the Hexadecimal number system?
A.2
B.8
C.10
D.16
Correct Answer: 16
Explanation:Hexadecimal uses base (radix) 16.
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37In a 3-variable K-Map, the cell represented by binary $101$ corresponds to which decimal minterm?
A.3
B.5
C.6
D.7
Correct Answer: 5
Explanation:Binary $101$ converts to decimal: .
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38Using boolean algebra, simplified form of is:
A.
B.
C.
D.
Correct Answer:
Explanation:Distributive law: .
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39The symbol in Logic design indicates:
A.Sum of Products
B.Product of Sums
C.Division
D.XOR operation
Correct Answer: Product of Sums
Explanation:The capital Pi symbol is used to denote the Product of Maxterms, i.e., Product of Sums (POS).
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40Which law states ?
A.Associative Law
B.Commutative Law
C.Distributive Law
D.Absorption Law
Correct Answer: Associative Law
Explanation:The associative law allows the regrouping of terms in OR (and AND) operations.
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41Calculate using 4-bit 2's complement arithmetic. .
A.0111
B.1001
C.0011
D.0110
Correct Answer: 0111
Explanation:2's complement of 5 ($0101$) is $1011$. Add to 12: . Discard carry. Result $0111$ (Decimal 7).
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42What logic function is represented by ?
A.
B.
C.
D.
Correct Answer:
Explanation:Minterms: 000, 010, 100, 110. In all these, . Grouping these on a K-map covers the column where is low. Thus .
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43The maxterm designated as for 3 variables represents:
A.
B.
C.
D.
Correct Answer:
Explanation: corresponds to decimal 3 (binary 011). In Maxterms (Sum terms), 0 is the variable and 1 is the complement. So . Sum: .
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44The term 'Don't Care' in K-Maps is represented by:
A.0
B.1
C.X
D.Z
Correct Answer: X
Explanation:Don't care conditions are input combinations that never occur or where the output doesn't matter. They are marked with an 'X' (or 'd') and can be grouped as 1 or 0 to simplify logic.