1. What is DeMorgan's theorem?
For N variables, DeMorgan’s theorems are expressed in the following formulas:
(ABC..N)' = A' + B' + C' + ... + N' -- The complement of the product is equivalent to the sum of the complements.
(A + B + C + ... + N)' = A'B'C'...N' -- The complement of the sum is equivalent to the product of the complements.
This relationship so induced is called DeMorgan's duality.
2. F'(A, B, C, D) = C'D + ABC' + ABCD + D. Express F in Product of Sum form.
Complementing both sides and applying DeMorgan's Theorem:
F(A, B, C, D) = (C + D')(A' + B' + C)(A' + B' + C' + D')(D')
3. How many squares/cells will be present in the k-map of F(A, B, C)?
F(A, B, C) has three variables/inputs.
Therefore, number of squares/cells in k-map of F = 2(Number of variables) = 23 = 8.
4. Simplify F(A, B, C, D) = Σ ( 0, 1, 4, 5, 7, 8, 9, 12, 13)
The four variable k-map of the given expression is:
The grouping is also shown in the diagram. Hence we get,
F(A, B, C, D) = C' + A'BD
5. Simplify F(A, B, C) = Σ (0, 2, 4, 5, 6) into Product of Sums.
The three variable k-map of the given expression is:
The 0's are grouped to get the F'.
F' = A'C + BC
Complementing both sides and using DeMorgan's theorem we get F,
F = (A + C')(B' + C')
6. The simplified expression obtained by using k-map method is unique. True or False. Explain your answer.
False. The simplest form obtained is not necessarily unique as grouping can be made in different ways.
7. Give the characteristic tables of RS, JK, D and T flip-flops.
8. Give excitation tables of RS, JK, D and T flip-flops.
9. Design a BCD counter with JK flip-flops
10. Design a counter with the following binary sequence 0, 1, 9, 3, 2, 8, 4 and repeat. Use T flip-flops.