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 M

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+\[=x+\overline{xy}(y+\overline z)\]

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 M

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 M

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.

Y=f(a,b,c,d)=∑(01,2,6,7,9,10,12)+d(3,5).Verify the result using k-map.

10 M

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 M

3(a)
Distinguish between a decoder and an encoder.Implement full adder using IC 74138.

8 M

3(b)
Implement 3- bit binary a gray code conversion by IC74139.

6 M

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 M

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

i) 16 to 1MUX ii) 8:1 MUX iii) 4:1 MUX

10 M

4(b)
With a neat logic diagram,explain carry look ahead adder.

10 M

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 M

5(b)
With a neat logic diagram,explain the working of positive edge triggered d flip-flop.

10 M

6(a)
Obtain the characteristic equation for D and T flip-flop.

6 M

6(b)
With a neat logic diagram,explain the operation of 4-bit SISO unidirectional shift register.

6 M

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 M

7(a)
Design synchronous mod-6 counter using D flip - flop to generate the sequence 0,2,3,6,5,1,0......

10 M

7(b)
Compare Mealy and Moore sequential circuit models.

4 M

7(c)
Analyze the sequential circuit shown in fig. q7(c).

write input and output equations table,static table and static diagram.

write input and output equations table,static table and static diagram.

6 M

8(a)
Write the basic recommended steps for the design of a clock synchronous sequential circuit.

6 M

8(b)
Compare synchronous and asynchronous counter.

4 M

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 M

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