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Q1. What is Gate? State and prove De Morgan’s theorems.

Q2. Differentiate analog and digital signals.

Q3. Define (i) rise time (ii)fall time (iii)period (iv) frequency (v) duty cycle of a digital signal.

4. (i) Prove that duty cycle of a symmetrical waveform is 50%. (ii) What is the value of high

duty cycle (duty cycle H) if the frequency of a digital waveform is 5 MHz and the width of the

positive pulse is 0.05 μs? (iii) An asymmetrical signal waveform is high for 2ms and low for

3ms. Find Frequency, Period , Duty cycle low, Duty cycle high

Q5. Describe positive logic and negative logic. List the equivalences in positive and negative

logic.

Q6. Prove that (a) “Positive OR” logic is equal to “Negative AND” logic (b) “Positive AND”

logic is equal to “Negative OR” logic (c) “Positive NOR” logic is equal to “Negative NAND”

logic (d) “Positive NAND” logic is equal to “Negative NOR” logic

Q7. What is a universal gate? List the universal gates and prove their universalities.

Q8. Realize the XOR gate using (i) NAND gate (ii) NOR gate.

Q9. Implement the following functions using NAND gate only:

Q10. Implement the following functions using NOR gate only:

Q11. Define canonical Minterm form and canonical Maxterm form.

Q12. Express the function F=x+yz as the sum of its minterms and product of maxterms.

Q13. Express the function F=(x+yz) ́ as the sum of its minterms and product of maxterms.

Q14, Convert the following 3-variable SOP to POS form.

(i) Σm(3,5,6,7) (ii) Σm(0,2,5,6)

Q15. Convert the following 4-variable POS to SOP form.

(i) ΠM(1,3,4,7) (ii) ΠM(0,1,2,4,10,13,15)

Q16. Use K-Map to simplify the following functions:

Q17, Simplify the Product of Sum expression below and provide the result in POS form.

Q18. Simplify the Product Of Sum expression below and provide the result in SOP form.

Q19. Find the minimal SOP and minimal POS of the following Boolean function using K-Map.

Q20. Reduce the following Boolean function using K-Map and realize the simplified expression

using NAND gates.

Q21. Simplify the following expressions using Karnaugh map. Implement the simplified circuit

using the gates as indicated:

( ) ( , , , ) (1,5,7,9,10,13,15) (8,11,14) using NAND gates.

(ii) ( , , , ) (0,1,2,4,5,6,8,9,12,13,14) using NOR gates.

Q22. Simplify the following using Quine McClusky minimization technique:

Q23. What are static hazards? How to design a hazard free circuit? Explain with an example.

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Covers

Q1. What is Gate? State and prove De Morgan’s theorems.Q2. Differentiate analog and digital signals.

Q3. Define (i) rise time (ii)fall time (iii)period (iv) frequency (v) duty cycle of a digital signal.

4. (i) Prove that duty cycle of a symmetrical waveform is 50%. (ii) What is the value of high

duty cycle (duty cycle H) if the frequency of a digital waveform is 5 MHz and the width of the

positive pulse is 0.05 μs? (iii) An asymmetrical signal waveform is high for 2ms and low for

3ms. Find Frequency, Period , Duty cycle low, Duty cycle high

Q5. Describe positive logic and negative logic. List the equivalences in positive and negative

logic.

Q6. Prove that (a) “Positive OR” logic is equal to “Negative AND” logic (b) “Positive AND”

logic is equal to “Negative OR” logic (c) “Positive NOR” logic is equal to “Negative NAND”

logic (d) “Positive NAND” logic is equal to “Negative NOR” logic

Q7. What is a universal gate? List the universal gates and prove their universalities.

Q8. Realize the XOR gate using (i) NAND gate (ii) NOR gate.

Q9. Implement the following functions using NAND gate only:

Q10. Implement the following functions using NOR gate only:

Q11. Define canonical Minterm form and canonical Maxterm form.

Q12. Express the function F=x+yz as the sum of its minterms and product of maxterms.

Q13. Express the function F=(x+yz) ́ as the sum of its minterms and product of maxterms.

Q14, Convert the following 3-variable SOP to POS form.

(i) Σm(3,5,6,7) (ii) Σm(0,2,5,6)

Q15. Convert the following 4-variable POS to SOP form.

(i) ΠM(1,3,4,7) (ii) ΠM(0,1,2,4,10,13,15)

Q16. Use K-Map to simplify the following functions:

Q17, Simplify the Product of Sum expression below and provide the result in POS form.

Q18. Simplify the Product Of Sum expression below and provide the result in SOP form.

Q19. Find the minimal SOP and minimal POS of the following Boolean function using K-Map.

Q20. Reduce the following Boolean function using K-Map and realize the simplified expression

using NAND gates.

Q21. Simplify the following expressions using Karnaugh map. Implement the simplified circuit

using the gates as indicated:

( ) ( , , , ) (1,5,7,9,10,13,15) (8,11,14) using NAND gates.

(ii) ( , , , ) (0,1,2,4,5,6,8,9,12,13,14) using NOR gates.

Q22. Simplify the following using Quine McClusky minimization technique:

Q23. What are static hazards? How to design a hazard free circuit? Explain with an example.

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