Logic Design - Dec 2014

Electronics & Communication (Semester 3)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1(a) Design a combinational circuit which takes two,2-bit binary numbers as its input and generates an output equal to 1, when the sum of the two numbers is odd.(6 marks) 1(b) Convert the given boolean function into:
i) R=f(a,b.c) =$$(a^{-}-b)\left ( b+c^{-}\right )$$
ii)$$(a^{-}-b)\left ( b+c^{-}\right )$$ Minterm canonical form
ii) p=f(x,y,z)=x+$$=x+\overline{xy}(y+\overline z)$$(6 marks) 1(c) Distinguish prime implicant and essential prime implicant. Determine PI and EPI for the given function N-f(a,b,c,d)-π (0,1,4,5,8,9,11)+d(2,10),Simplify the given function and implement using logic gates.(8 marks) 2(a) Simplify the given Boolean function using Quine-McCluskey method;
Y=f(a,b,c,d)=∑(01,2,6,7,9,10,12)+d(3,5).Verify the result using k-map.(10 marks) 2(b) Find the minimal sum and product for the given Boolean function,using MEV technique : Solve by using 3-variable map and 2-variable map y=f(a,b,c,d)-&Sigma(2,3,4,5,13,15)-8,9,10,11).(10 marks) 3(a) Distinguish between a decoder and an encoder.Implement full adder using IC 74138.(8 marks) 3(b) Implement 3- bit binary a gray code conversion by IC74139.(6 marks) 3(c) Design a priority encoder for a system with a 3 inputs,the middle bit with highest priority encoding to 10,the MSB with next priority encoding to 11, while the LSB with least priority encoding to 01.(6 marks) 4(a) Realize the following Boolean function : p=f(w,x,y,z)-&sigma(0,1,5,6,7,10,15)using :
i) 16 to 1MUX ii) 8:1 MUX iii) 4:1 MUX(10 marks) 4(b) With a neat logic diagram,explain carry look ahead adder.(10 marks) 5(a) explain the working of a master-slave SR flip-flop with the help of a logic diagram, function table,logic symbol and timming diagram.(10 marks) 5(b) With a neat logic diagram,explain the working of positive edge triggered d flip-flop.(10 marks) 6(a) Obtain the characteristic equation for D and T flip-flop.(6 marks) 6(b) With a neat logic diagram,explain the operation of 4-bit SISO unidirectional shift register.(6 marks) 6(c) Explain the working of four-bit binary ripple up counter,configured using positive edge triggered flip-flop. Also draw the timing diagram.(8 marks) 7(a) Design synchronous mod-6 counter using D flip - flop to generate the sequence 0,2,3,6,5,1,0......(10 marks) 7(b) Compare Mealy and Moore sequential circuit models.(4 marks) 7(c) Analyze the sequential circuit shown in fig. q7(c).
write input and output equations table,static table and static diagram. (6 marks) 8(a) Write the basic recommended steps for the design of a clock synchronous sequential circuit.(6 marks) 8(b) Compare synchronous and asynchronous counter.(4 marks) 8(c) A sequential circuit has one input and one output.The state diagram is as shown in the fig.q8(c). design the sequential circuit with j-k flip - flop (10 marks)