Sol_HA12

8/12/2019 Sol_HA12

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Department of Electrical Engineering, IIT Kanpur ESc 201: Introduction to Electronics

4th November, 2013

Home Assignment – 12

1. In a certain chemical process control application, a particular relay must operate for

certain input conditions. There are three input variables A, B and C, where A is the MSBand C is the LSB. The requirements are as follows:

Relay must be ON for 010, 011 and 100. Relay must be OFF for 000, 001 and 110. The

remaining input condition will never occur.

(a) Obtain a minimum expression for the above relay function using K-map.(b) Realize the above expression using NAND gates only.

2. A 4-input NAND gate is defined by the function z y xw z y xw f ...),,,( . Design a 4-input

NAND gate using 2-input NAND gates only.

3. A combinational circuit has 3 outputs F 1, F 2 and F 3 as follows:

y x z y x F

y x z y x F

z x z y x F

...3

...2

...1

Design the circuit with decoder and external gates.

4. BCD (binary coded decimal) is a representation of decimal digits using four bits. The

decimal digit can have values within 0 to 9. The four bit binary number represents a

decimal number N , where 0

0

1

1

2

2

3

3 2222 bbbb N , and 0123 bbbb is binary number

having four bits. We want to use a seven-segment display as shown below to display the

decimal number corresponding to 4-bit BCD input. Each segment of display is an LEDwhich glows when logic is 1. Determine the Boolean expression representing logic for

each element of display. Minimize the expression using K-map.

a

e

c

f

g

b

d

5. The four bit binary number represents a decimal number A, where

0

0

1

1

2

2

3

3 2222 aaaa A , and 0123 aaaa is binary number having four bits. Design a

circuit using 16 to 1 MUX to check whether A is prime number or not. Recall that a

number A is prime number if it is a natural number greater than 1 that has no other

divisors except 1 and the number itself.

8/12/2019 Sol_HA12


Department of Electrical Engineering, IIT Kanpur ESc 201: Introduction to Electronics

6. Construct an 8-to-1 MUX using minimum number of 4-to-1 and 2-to-1 MUXs as

building blocks.

7. Design the circuit using an 8 x 1 Multiplexer to implement the logic function

)14,13,11,10,9,8,6,5,2(),,,( m DC B A f .

8. Implement half-adder using 2-input NOR gates only.

9. Implement full adder using two 4 x 1 Multiplexers.

8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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8/12/2019 Sol_HA12


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t.o the "rnutttplexeY.

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-$= ?t

Cor,tf * )l

5=iCoul = \

5=:t

Cout = I

8/12/2019 Sol_HA12


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Sol_HA12