(2½ Hours)

[Total Marks: 75]

N. B.: (1) All questions are compulsory.

(2) Make suitable assumptions wherever necessary and state the assumptions made.

(3) Answers to the same question must be written together.

(4) Numbers to the right indicate marks.

(5) Draw neat labeled diagrams wherever necessary.

(6) Use of Non-programmable calculators is allowed.

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Q. 1. Attempt any three of the following: **(15M)**

a)Convert:

i) (100011) _{2}= ( ? ) _{10} **(2M)**

ii) (2F)_{16} = ( ? )_{10} **(2M)**

iii) (011000)_{2} = ( ? )_{8} **(1M)**

b) Convert :

i) (62) _{10} = ( ? )_{excess3} **(2M)**

ii) (577)_{10} = ( ? )_{bcd }**(2M)**

iii) (100110000111) _{bcd} = ( ? )_{10} **(1M)**

c) Explain with an example to steps to find a two’s complement of a number and write

the rules of two’s complement subtraction in binary number system. **(5M)**

d) Solve :

i) (1000100)_{2} + (10010101)_{2} = ( ? )_{2} **(2M)**

ii) (10101010)_{2} – (10100010)_{2} = ( ? )_{2} (use direct method ) **(3M)**

e) Solve:

i) (122)_{10} = ( )_{2} = ( ? )_{8} **(3M)**

ii) (110101001)_{ 2} = ( ? )_{16} **(2M)**

f) Solve:

i) (AFD1)_{16} + (1292)16 = ( ? )_{16 }**(2M)**

ii) (AFD1 )_{16} – (129A)16 = ( ? )_{16 } **(3M)**

Q. 2. Attempt any three of the following: **(15M)**

a) Describe the NAND and the OR gate with the symbol, the logical statement , the Boolean expression and its logical circuit diagram

b) State and proof the commutative and associative law in Boolean algebra.

c) Prove the following

i) ???? + ????̅ ???? = ????̅ + ????

ii) (????̅ + ????)????̅ ???? ̅ ????̅ = ̅????̅̅+̅̅̅????̅̅̅+̅̅̅????̅

d) Simplify the expression and draw circuit diagram

???? = ( ???? + ????)(???? ̅ + ???? + ????)

e) Solve the SOP expression using Kmaps F(A,B,C,D) = Ʃ m (1,3,4,5,7,9,11,13,15)

f) Solve the POS expression using Kmaps

F(A,B,C,D) = ???? ????(4,6,8,9,10,12,13,14) + ????(0,2,5)

Q. 3. Attempt any three of the following: **(15M)**

a) Design a 4 -bit full adder using 3 Full adders.

b) With the help of K-Maps build a 2- bit half adder and describe it working.

c) Explain with an example code conversion from binary to gray.

d) Design a combinational circuit for the following description. The circuit had 4 inputs and 2 output. One of the output is true if the major inputs are true, the other output is true if there is a tie between the 4 input.

e) Describe the working of a comparator.

f) Describe the working a BCD subtractor.

Q. 4. Attempt any three of the following: **(15M)**

a) Draw the logical circuit diagram and describe the working of a 4:2 decoder.

b) Draw the logical circuit diagram and describe the working 4:1 multiplexer using 2:1 multiplexers.

c) Difference between multiplexer and demultiplexer,

d) Describe with a truth table the working of D-flip flop.

e) Describe with a truth table the working of T- flip flop.

f) Describe the working of the JK Flip Flop.

Q. 5. Attempt any three of the following: **(15M)**

a) Short note on synchronous counters.

b) Describe working of 4 bit binary counter.

c) Explain the terms bushing and per set of a counter.

d) Write a short note on Bidirectional shift registers.

e) Describe the working of the Johnson counter.

f) What are parallel and shift registers? Explain.

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