## 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)