Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech II Year DIGITAL LOGIC DESIGN Previous Question Paper (March - 2021 - R15)
Answer any five questions. All questions carry equal marks.
Main
Solve for x: i) (367)8=(x)2 ii) (378.93)10 = (x)8 iii) (B9F.AE)16 = (x)8 iv) (16)10 = (100)x.
Answer
i) To convert (367)8 to binary, replace each octal digit with its 3-bit binary equivalent: 3=011, 6=110, 7=111. Thus, (367)8 = (011110111)2.
ii) To convert (378.93)10 to octal, divide the integer 378 by 8 repeatedly: 378/8 = 47 remainder 2; 47/8 = 5 remainder 7; 5/8 = 0 remainder 5. Reading remainders upwards gives (572)8. For the fraction 0.93, multiply by 8: 0.93 * 8 = 7.44 (7); 0.44 * 8 = 3.52 (3); 0.52 * 8 = 4.16 (4). Thus, (378.93)10 ≈ (572.734)8.
iii) To convert (B9F.AE)16 to octal, first convert to binary: B=1011, 9=1001, F=1111, A=1010, E=1110. Binary is 101110011111.10101110. Grouping into 3 bits from the radix point: 101 110 011 111 . 101 011 100. Converting groups to octal: 5637.534. Thus, (B9F.AE)16 = (5637.534)8.
iv) For (16)10 = (100)x, the equation is 1*x2 + 0*x1 + 0*x0 = 16. Therefore, x2 = 16, which gives x = 4.
Convert (163.875)10 to binary, octal, hexadecimal.
Answer
For (163.875)10:
Binary: Integer 163 = 101000112. Fraction 0.875 * 2 = 1.75 (1); 0.75 * 2 = 1.5 (1); 0.5 * 2 = 1.0 (1). Thus, (163.875)10 = (10100011.111)2.
Octal: Group binary bits into sets of three from the radix point: 010 100 011 . 111. This results in (243.7)8.
Hexadecimal: Group binary bits into sets of four from the radix point: 1010 0011 . 1110. This results in (A3.E)16.
What are universal gates? Realize AND, OR, NOT, XOR gates using universal gates.
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Obtain the canonical SOP form of the following functions: i) Y(A,B) = A+B ii) Y(A,B,C,D) = AB+ACD
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Simplify the expression Y=Σ m(7,9,10,11,12,13,14,15) using the k-map method.
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Simplify the following Boolean function using K-map: F(A,B,C,D)= Σ m(1,3,7,11,15) + Σ d(0,2,5)
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Simplify the expression Y= Π (7, 9, 10, 11, 12, 13, 14, 15) using the k-map method.
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Simplify the expression Y= m1 + m5 + m10 + m11 + m12 + m13 + m15 using the k-map method.
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Draw the schematic diagram and truth table for half adder. Explain the design approach for half adder using universal gates. Draw the logic diagrams with relevant expressions.
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Design, draw and explain a 4-bit binary carry look ahead adder.
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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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Explain the operation of a 3-to-8 decoder 74LS138. Realize 4-to-16 decoder using two 3-to-8 decoders.
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Design, draw and explain a synchronous MOD-12 down-counter using j-k flip-flop.
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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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Give the logic implementation of a 32×4 bit ROM using decoder of suitable size.
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Implement the following Boolean function with PLA F(A,B,C) = Σ m(1,5,6,7).
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