Logic Design - Dec 2013

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 three-input one-output minimal tow level gate combinational circuit which has an output equal to 1 when majority of its inputs are at logic 1 and has an output equal to 0 when majority of its inputs are at logic 0.(8 marks) 1 (b) Minimize the expression: $$ \overline{Y}= \overline{A}B\overline{C}\ \overline{D} + \overline{A} B\overline{C}D+ A B \overline{C} \ \overline{D}+AB\overline{C}D+A\overline{B}\ \overline{C}D+\overline{A} \ \overline{B}C\overline{D} $$(6 marks) 1 (c) Reduce the following functions using K-map technique.
f{A, B, C, D}=Π M(0, 3, 4, 7, 8, 10, 12, 14) + d(2,6).(6 marks) 2 (a) Obtain all the prime implicants of the following Boolean function using Quine-McCluskey method.
f(a,b,c,d)=∑(0,2,3,5,8,10,11)
verify the result using K-map technique.(10 marks) 2 (b) Simplify the given function using MEV technique taking the least significant variable as the map entered variable.
f(a,b,c,d,e)=∑(1,3,4,6,9,11,12,14,17,19,20,22,25,27,28,30)+∑d(8,10,24,26).(10 marks) 3 (a) Implement the multiple functions:
f₁(a,b,c,d)=∑(0,48,10,14,15) and
f₂(a,b,c,d)=∑(3,7,9,13) using two 3 to 8 decoder.(6 marks) 3 (b) Implement the following with a suitable decoder with active to enable input and active high output: f(w,x,y,z)=∑(3,7,9)
g(a,b,c)=Π(2,4,7).(6 marks) 3 (c) Draw the interfacing diagram of ten key keypad interface to a digital system using decimal to BCD encoder.(6 marks) 4 (a) Configure a 16 to 1 MUX using 4 to 1 MUX.(6 marks) 4 (b) Implement the following Boolean function with 8:1 multiplexer f(A, B, C, D)=∑_m(0, 2, 6, 10, 11, 12, 13)+d(3, 8, 14).(6 marks) 4 (c) Write a truth table for two-bit magnitude comparator. With the K-map for each output of two-bit magnitude for two-bit magnitude comparator. Write the K-Map for each output of two-bit magnitude comparator and the resulting equation.(8 marks) 5 (a) What do you mean by sequential circuit? Explain with the help of block diagram?(4 marks) 5 (b) Explain with timing diagram, the working of SR latch as a switch debouncer.(6 marks) 5 (c) Explain the working of a master-slave JK flip-flop with the help of logic diagram, function table, logic symbol and timing diagram.(10 marks) 6 (a) Obtain the characteristic equation for a SR flip-flop.(4 marks) 6 (b) Design a 4-bit register using positive edge triggered D flip-flops to operate as indicated in the table below:

7 (b) Analyse the synchronous sequential circuit shown in Fig. Q7(b). (12 marks)

8 (b) Construct the excitation table, transmission table, state table and state diagram for the Moore sequential circuit shown in Fig. Q8(b). (14 marks)