## Logic Design - Jun 2015

### 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)** Express the following Boolean function in canonical max term form:

F(A, B, C)= AB+C.(4 marks)
**1 (b)** Express the following Boolean function in canonical term form:

F(A, B, C, D)=AB+CD.(8 marks)
**1 (c)** Simplify the following Boolean function using four variable 'k' map. Realize the simplified expression using NAND gates.

F(A, B, C, D)= ∑m(1, 5, 6, 7, 11, 12, 13, 15).(8 marks)
**2 (a)** Simplify the following Boolean function using Quine-McClusky's minimization technique.

F(A, B, C, D)= ∑m(6, 7, 9, 10, 13) + d(1, 4, 5, 11, 15).(10 marks)
**2 (b)** Consider the following Boolean equation:

F(A, B, C, D) = ∑m(1, 3, 7, 11, 15) + ∑d(0, 2, 5).

Simplfy the function F using a 3 variable MEV k-map. Assign the variable D to be the MEV.(10 marks)
**3 (a)** Implement the Boolean functions:

F_{1}(x,y,z)=XY+YZ

F_{2}(x,y,z)=πm(0, 3, 5)

Using a 3-8 line decoder IC 74138 with active low outputs.(8 marks)
**3 (b)** Interface a 10 key keypad to a digital system using a IC 74147 which is a 10 line to BCD priority encoder. Draw the logic diagram and explain the operation with the truth table.(12 marks)
**4 (a)** Implement the Boolean function:

F(A, B,C, D)=∑m (0, 1, 2, 4, 5, 7, 8, 9)

Using a 8 to 1 multiplexer. Draw the logic diagram and explain the operation. Additional gates can be used if required.(8 marks)
**4 (b)** Explain the operation of a full subtractor with the help of a truth table and Boolean expression for the outputs. Implement the full subtractor using two number of

i) 4 to 1 multiplexers

ii) 2 to 1 multiplexers.

Additional gates if required can be used.(8 marks)
**4 (c)** Design a one bit binary comparator.(4 marks)
**5 (a)** Explain the operation of a gated SR latch with a logic diagram and a truth table.(6 marks)
**5 (b)** Explain the operation of a positive edge trigged 'D' flip-flop with the help of a logic diagram and truth table. Also draw the relevant waveforms.(4 marks)
**5 (c)** Draw the output waveforms Q_{M} and Q_{S} the outputs of the master and the slave respectively, if the inputs to a master slave JK flip-flop one as indicated below.

:!MAGE-(10 marks)
**6 (a)** Design a 4 bit binary ripple up counter using negative edge triggered JK flip-flops. Draw the timing diagram with respect to the input cock pulse. Explain the operation.(10 marks)
**6 (b)** Design a synchronous counter using clocked JK flip-flop for the counting sequence shown below:

Q_{2} | Q_{1} | Q_{0} |

0 | 0 | 0 |

0 | 1 | 0 |

0 | 1 | 1 |

1 | 1 | 0 |

1 | 0 | 1 |

0 | 0 | 1 |

0 | 0 | 0 |

**7 (a)**Explain mealy and Moore models of a clocked synchronous sequential circuit.(8 marks)

**7 (b)**Design a synchronous circuit using positive edge triggered JK flip-flop to generate the following sequence:

0-1-2-0 is input x=0 and

0-2-1-0 is input x=1

Provide an output which goes high to indicate the non-zero state in the 0-1-2-0 sequence.(12 marks)

**8**Construct the excitation table, transition table, state table and state diagram for the sequential circuit shown in Fig. Q8

:!MAGE-(20 marks)