combinational-logic-circuit_with_Proper_Diagrams.pptx

Combinational Logic Circuits

1. Combinational Logic circuit 18 Marks Course Outcome: Build simple combinational circuits

2. Contents Types of digital circuit Combinational circuit Block diagram of combinational circuit Sum of product form Product of sum form Standard SOP form Standard POS form Conversion of non standard SOP to standard SOP Conversion of non standard POS to standard POS Minterm and Maxterm

3. Types of circuits In digital Electronics Two types of circuits 1. combinational circuit 2. sequential circuit

4. Introduction of Combinational circuit a circuit whose output is dependent only on the state of its inputs The output of combinational circuit at any instant of time, depends only on the levels present at input terminals. The combinational circuit do not use any memory. The previous state of input does not have any effect on the present state of the circuit. A combinational circuit can have an n number of inputs and m number of outputs. for example: Adder, subtractor,encoder , decoder, multiplexer and demultiplexer .

5. Block Diagram of Combinational Logic Circuit

6. 3.1 Standard Boolean representation Sum of Product (SOP) & Product of Sum (POS), Maxterm and Minterm , Conversion between SOP and POS forms, Realization using NAND/NOR gates. Unit outcome: Develop logic circuits in standard SOP/POS form for the given logical expression.

7. Standard Any logical expression can be expressed in the following two forms: Sum of Product (SOP) Form Product of Sum (POS) Form

8. Sum of product form ( SOP form) of logical expression

9. Product of Sum form(POS form) of logical expression

10. Standard or canonical form means? A logic expression is said to be in the standard (or canonical) SOP or POS form if each product term (for SOP) and sum term (for POS) consists of all the literals in their complemented or uncomplemented form. std. SOP form std. POS form

11. Example:

12. Conversion of non standard SOP form to Standard SOP Steps: 1. Write down all the terms. 2. If one or more variables are missing in any product term, expand the term by multiplying it with the sum of each one of the missing variable and its complement . 3. Drop out the redundant terms

13. Conversion of non standard SOP expression in to standard SOP form

14. Continued---

15. Example: convert the following expression into canonical SOP form A+BCD ABC+BD

16. Convert the expression into canonical POS form 1. Y=(A+B)(A+C)(B+C) 2. Y=(A+B)(A+C)

17. Conversion of POS form to Standard POS Steps: 1. Write down all the terms. 2. If one or more variables are missing in any sum term, expand the term by adding the products of each one of the missing variable and its complement . 3. Drop out the redundant terms

18. Example

19. Continued--

20. minterm and Maxterm

21. minterm and Maxterm A  minterm  is a Boolean expression resulting in  1  for the output of a single cell, and  s for all other cells in a Karnaugh map, or truth table. If a minterm has a single  1  and the remaining cells as  s, it would appear to cover a minimum area of  1 s. minterm ABC a single product term, as a single 1 in a map A  Maxterm  is a Boolean expression resulting in a   for the output of a single cell expression, and  1 s for all other cells in the Karnaugh map, or truth table. Maxterm   (A+B+C) , a single sum term, as a single   in a map

22. Minterm

23. Maxterm

24. Minterm & Maxterm

25. Minterm

26. Maxterm

27. K-Map Reduction Technique

28. K-map reduction technique for the Boolean expression

29. K-map

30. Cell number assignment

31. K-map

32. K-map

33. K-map

34. K-map

35. K-map

36. K-map

37. K-map

38. K-map

39. Representation of Standard SOP form expression on K-map

40. Simplification of K-map

41. Simplification of K-map

42. Simplification of K-map

43. Grouping of Two Adjacent 1’s : Pair

44. Grouping of Two Adjacent 1’s : Pair

45. Grouping of Two Adjacent 1’s : Pair