combinational _logic_circuit_digital.pptx

note on combinational logic circuit

1. CHAPTER 3 BASIC & COMBINATIONAL LOGIC CIRCUIT

2. LEARNING OUTCOMES At the end of this chapter, you should be able to Describe the operation of NOT, AND, OR, NAND, NOR, XOR and XNOR gates and express them with Boolean expression Design a combinational logic circuit for a given Boolean output expression and truth table

3. BOOLEAN CONSTANT & VARIABLE Boolean variable is a quantity that may be equal to either or 1 at different times. Boolean variables represent only the state of a voltage variable in terms of and 1 , called the logic level . Different terms used to represent logic 0 and logic 1

4. TRUTH TABLE Truth tables list all possible input combinations and the corresponding output level. The number of input combination depends on the number of inputs. The number of input combinations will be equal to 2 N for an N -input truth table. For instance, for a 5-input truth table, the input combinations will be 2 5 = 32.

5. TRUTH TABLE EXAMPLES

6. BASIC GATES, FUNCTION AND PULSE WAVEFORMS There are 7 basic gates available: INVERTER gate AND gate OR gate NAND gate NOR gate XOR gate XNOR gate

7. INVERTER Also known as NOT gate It changes one logic level to the opposite level The symbol is Truth table

8. INVERTER Timing diagram A graph that accurately displays the relationship of two or more waveforms on time basis. Boolean expression of an Inverter with input A and output B is

9. AND gate AND gate can have two or more inputs but only 1 output. Operation: logical multiplication. Output is HIGH only when all the inputs are HIGH. The symbol is

10. AND gate EXERCISE Determine the AND gate output for the following figure.

11. AND gate EXERCISE Determine the AND gate output for the following figure.

12. OR gate OR gate can have two or more inputs but only 1 output. Operation: logical addition. Output is LOW only when all the inputs are LOW. The symbol is

13. OR gate EXERCISE Determine the OR gate output for the following figure.

14. NAND gate NAND gate can have two or more inputs but only 1 output. Operation: in combination AND, and INVERTER Output is LOW only when all the inputs are HIGH. The symbol is

15. NAND gate EXERCISE

16. NAND gate EXERCISE

17. NOR gate NOR gate can have two or more inputs but only 1 output. Operation: in combination OR and INVERTER Output is HIGH only when all the inputs are LOW. The symbol is

18. NOR gate EXERCISE

19. NOR gate EXERCISE

20. XOR gate XOR gate can have two or more inputs but only 1 output. Output is HIGH only when the inputs are at opposite logic levels. The symbol is

21. XOR gate EXERCISE

22. XOR gate EXERCISE

23. XNOR gate XNOR gate can have two or more inputs but only 1 output. Output is LOW only when the inputs are at opposite logic levels. The symbol is

24. XNOR gate EXERCISE

25. XNOR gate EXERCISE

26. EXAMPLES ON SIMPLE LOGIC DESIGN QUESTION UNDERSTAND THE QUESTION - DEVELOP THE TRUTH TABLE

27. EXAMPLE 1 Develop the truth table for a logic circuit with four input (A, B, C and D) that will produce a HIGH output whenever majority of the input are HIGH.

28. Quiz 2 Develop the truth table for a logic circuit to produce an output HIGH only if the inputs, represented by a 4-bit binary numbers, have an odd numbers of HIGH inputs.

29. LAB 1

30. END OF PART 1

31. ANALYSING A COMBINATIONAL LOGIC CIRCUIT In digital system, different gates are connected together to perform different function  combinational logic circuit Obtain the Boolean expression and analyse it to form the truth table for that particular combinational logic circuit.

32. EXAMPLE 1: Boolean Expression and Truth Table

33. STEP 1 STEP 2

34. STEP 3

35. STEP 4

36. STEP 5

37. EXAMPLE 2: Boolean Expression and Truth Table STEP 1

38. The Boolean expression Truth table STEP 2

39. Exercise For the combinational circuits given below, find its Boolean expression and truth table. (a) (b)

40. DESIGN A COMBINATIONAL LOGIC CIRCUIT FROM BOOLEAN EXPRESSION To draw a logic circuit, Step 1: Group the variables together in a bracket Step 2: Start to draw from either input or output

41. EXAMPLE 3 DESIGN A COMBINATIONAL LOGIC CIRCUIT FROM BOOLEAN EXPRESSION From the Boolean expression Bracket the expression STEP 1 STEP 2

42. STEP 3

43. Exercise Draw the combinational circuit represented by the Boolean expression below.

44. QUIZ 3 Design a logic circuit with four input (A, B, C and D) that will produce a HIGH output, Z whenever both A and C is HIGH as long as both B and D are either both HIGH or both LOW.

45. FOR A LONG AND COMPLICATED LOGIC DESIGN QUESTION..?? …..continued in CHAPTER 4 # BooleanTheorem #SOP #POS #K-Map

46. Exercise Design an electronic circuit that takes two 2-bit binary numbers X(x1, x0) and Y(y1, y0) and produces an output binary number Z(z3, z2, z1, z0) that is equal to the function Z = X*Y of the two input numbers.

47. Exercise Design an electronic circuit that takes two 2-bit binary numbers X(x1, x0) and Y(y1, y0) and produces an output binary number Z(z3, z2, z1, z0) that is equal to the function Z = X+2Y of the two input numbers.

48. END OF CHAP. 3