JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech II Year DIGITAL SYSTEM DESIGN Previous Question Paper (August/September -2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
State and prove Boolean Theorems: i) Commutative ii) Associative iii) Distributive
Answer
Boolean theorems are fundamental identities used to simplify logic expressions:
- Commutative Law: A + B = B + A and A · B = B · A. This states that the order of operands does not affect the result of OR or AND operations.
- Associative Law: A + (B + C) = (A + B) + C and A · (B · C) = (A · B) · C. This allows grouping of variables in multi-input operations without changing the output.
- Distributive Law: A · (B + C) = (A · B) + (A · C) and A + (B · C) = (A + B) · (A + C). This allows the distribution of an AND operation over an OR operation and vice versa.
These are proven using truth tables by demonstrating that for all possible combinations of inputs (0,0,0 to 1,1,1), the outputs of the left-hand side and right-hand side expressions are identical.
Expand
Answer
Given expression: F = A + (A + B)(A + B + C). Using the absorption law (A + AB = A), the expression simplifies to F = A. To expand into minterms and maxterms for three variables (A, B, C):
Minterms: F = A(B + B')(C + C') = ABC + ABC' + AB'C + AB'C' = Σm(4, 5, 6, 7).
Maxterms: F = (A + B · B')(A + C · C') = (A + B)(A + B')(A + C)(A + C') = ΠM(0, 1, 2, 3).
i) Add 6E16 and C516
ii) Add 5D16 from 3A16
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Reduce the following function using K-Map:
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Design and explain a 4-bit binary parallel Adder/Substractor.
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Explain the differences between a MUX and a DEMUX. Realize 16-input multiplexer by cascading of two 8-input multiplexers.
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Describe the operations performed by the following logic circuits with an example: (i) Comparator (ii) Decoder (iii) Encoder.
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With the block diagram, Truth table, describe the principle operation of edge triggered negative SR flip flop.
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Explain the operation of 4-stage twisted ring counter with circuit diagram and timing diagram.
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Differentiate combinational and sequential circuits.
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Write differences between Mealy and Moore machines.
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Write the limitations of finite state machines?
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Design, draw and explain a 4-bit ring counter using D-flip flops with relevant timing diagrams.
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Explain the operation J-K master slave flip flop. Explain its truth table.
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Draw a state diagram of a sequence detector which can detect 101.
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How to interface TTL and CMOS and also CMOS to TTL.
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Discuss about RTL logic family in detail, with one example.
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Realize 2-input NAND using TTL logic.
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