note on combinational logic circuit

1. CHAPTER 3
BASIC
&
COMBINATIONAL LOGIC CIRCUIT

3. 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

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

5. 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 2N for
an N-input truth table. For instance, for a 5-input truth
table, the input combinations will be 25 = 32.

6. TRUTH TABLE EXAMPLES

7. 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

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

9. 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

10. 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

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

12. AND gate EXERCISE
 Determine the AND gate output for the following figure.

13. 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

14. OR gate EXERCISE
 Determine the OR gate output for the following figure.

15. 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

16. NAND gate EXERCISE

17. NAND gate EXERCISE

18. 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

19. NOR gate EXERCISE

20. NOR gate EXERCISE

21. 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

22. XOR gate EXERCISE

23. XOR gate EXERCISE

24. 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

25. XNOR gate EXERCISE

26. XNOR gate EXERCISE

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

28. 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.

29. 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.

30. LAB 1

31. END OF PART 1

33. 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.

34. EXAMPLE 1: Boolean
Expression and Truth Table

35. STEP 1
STEP 2

36. STEP 3

37. STEP 4

38. STEP 5

39. EXAMPLE 2: Boolean Expression and
Truth Table
STEP 1

d  AB
e = B C

f = d +C
= (A B) +C

Z = e f
= (B C) (A B) +C

40.    
C
B
A
C
B 




Z
 The Boolean expression
 Truth table
STEP 2

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

42. 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

43. EXAMPLE 3 DESIGN A COMBINATIONAL
LOGIC CIRCUIT FROM BOOLEAN EXPRESSION
 From the Boolean expression
 Bracket the expression
BC
A
C
B
AC
y 


)
(
)
(
)
( BC
A
C
B
AC
y 


STEP 1
STEP 2

44. STEP 3

45. Exercise
 Draw the combinational circuit represented by the
Boolean expression below.
C
BC
C
B
A
Z 



48. 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.

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

50. 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.

51. 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.

52. END OF CHAP. 3