1. Digital Systems, Principles and Applications, 10th Edition
Digital Electronics
Digital Systems, Principles and Applications, 10th Edition
R.J Tocci, N. S. Windmer, G. L. Moss, 2007.
Applications:
Computers
Telecommunication
Automation
Medical Science and Technology
Transportation
Space Exploration
Entertainment
Home Appliances
Others

2. Course Summary Overview of Electronics
Digital Electronics Number systems, decimal, binary, hexadecimal
Combinational logic circuits
Sequential logic circuits
Computer Systems

3. Combinational Logic Systems
Course Summary (cont.)
Combinational Logic Systems
Number systems: Binary, decimal and hexadecimal conversions and calculations
Basic logic gates: AND, OR, NOT and Ex-OR
Truth tables, Boolean equations.
Combinational logic circuit design: General hierarchical logic design methodology
Minimisation using Karnaugh maps and Boolean algebra, De-Morgan’s laws.
Simulation of gates and combinational logic designs
Implementation and testing of designs using a suitable version of TTL series ICs.
Practical aspects of using logic ICs: data sheets, current and voltage characteristics, timing issues, output types, compatibility, families etc..

4. Course Summary (cont.) Sequential logic design
Flip-flops: SR, JK, D, T types, truth tables, excitation tables and device operation.
Flip-flop applications: Registers and counters (asynchronous); MSI and LSI devices
Synchronous counter and sequence generator design method

5. Course Summary (cont.) Introduction to Microprocessor Systems
Overview of computer systems architectures, a simple microprocessor-based system, the stored programme concept.
Design of a microprocessor based system
Differences between microprocessors and microcontrollers.
Brief history of microprocessors and microcontrollers.

6. Overview of Electronics
Analogue electronics
Power electronics
Physical electronics
Differences between digital and other types of electronics
Numerical Presentation

7. In 1947, Transistor was invented in Bell labs in the USA.
It was as tall as the face of wristwatch.
In November 2001, another Bell lab team has built a transistor from a single Molecule - small enough to fit about 10 million transistors on the head of a pin.

8. Numerical Representation
There is two ways to represent numerical values.
1- Analogue
In analogue representation one quantity is represented by another quantity which is directly proportional to the first quantity.
Analogue = Continuous
2- Digital
In digital representation the quantities are not represented by proportional quantities but symbols called digits. The digital representation is in discrete steps.
Digital = Discrete
Logic Level in digital representation, 0 – 0.8 logic 0 and 2 – 5 logic 1.
Voltage between 0.8 V and 2 V are unacceptable and are never used.

9. Converting decimal to binary and Converting decimal to hexadecimal
Number systems
Type of Numbers
Decimal, Binary, Octal and Hexadecimal
Converting decimal to binary and
Converting decimal to hexadecimal
Converting binary to hexadecimal

10. Number Systems g Decimal Binary Hexadecimal 0000 1 0001 2 0010 3 0011
Base of 10
Binary
Base 0f 2
Hexadecimal
Base of 16
0000 1
0001 2
0010 3
0011 4
0100 5
0101 6
0110 7
0111 8
1000 9
1001 10
1010 A 11
1011 B 12
1100 C 13
1101 D 14
1110 E 15
1111 F g

11. Converting Decimal to Binary
Convert Therefore, = (1000)2
LSB, Less Significant Bit
MSB, Most significant Bit
To examine
(0 X 2 0) + (0 X 2 1) + (0 X 2 2) + (1 X 2 3) = 8 decimal into binary

12. 2nd Example Convert 624 decimal into binary
624 decimal = in binary.
To examine the result
(1 X 2 4) + (1 X 2 5) + (1 X 2 6) + (1 X 2 9) = 624

13. Converting Decimal to Hex
Find the Hex equivalent of (3875)
(3875) = (F23)H
To examine
(15 X 162) + (2 X 161) + (3 X 160) = 3875

14. Converting Hex to Decimal
Convert (AF16B)16 to decimal.
(AF16B)16 = [(10 X 164) + (15 X 163) + (1 X 162) + (6 X 161) + (11 X 160)]
= ( )
= (717163)10

15. Converting Binary to Hex
To convert Binary into Hex, simply group them in four and write down the Hex equivalent for each group.
Example:
( ) 2 = (1011)2 (0011)2 = (11)10 (3)10 = B316

16. Main Points Digital Electronics use many exciting applications
Introduction to digital electronics
Number systems: Decimal, binary and hex
Converting from one number system into another

17. The End Thank you for your attention. Any questions?
Good luck and have fun!

18. Digital Electronics
Lecture 2
Logic Gates

19. Lecture 2 outline Logic Gates AND, OR, NOT, EX-OR, NAND, NOR
Announcement:
Review of last Lecture
Logic Gates
AND, OR, NOT, EX-OR, NAND, NOR
Truth Tables
Boolean equations

20. Review of Last Lecture
Introduction to electronics
Digital Electronics use many exciting applications
Introduction to digital electronics
Number systems: Decimal, binary and hex
Converting from one number system into another

21. The AND gate
The logical function of this gate may be expressed in words as follows:
Y = A.B
The Output, Y, of this gate is True only if all inputs to the gate are TRUE

22. IC, AND gate

23. The OR gate
The logical function of this gate may be expressed in words as follows:
Y = A+B+C
The Output, Y, of this gate is True if any of the inputs to the gate are TRUE

24. Overview of Electronics
The logical function of this gate may be expressed in words as follows:
B=A_
The Output, A, of this gate is True the input signal B is False

25. NAND, NOR

26. EX-OR gate
The logical function of this gate may be expressed in words as follows:
Y = A. B_ + A_.B

27. INTEGRATED CIRCUIT (IC) LOGIC GATES
7408 AND gate
7432 OR gate
7404 NOT gate or Inverter
7400 NAND gate
7402 NOR gate
7486 XOR gate

28. Turning equations into circuits
It is always possible to produce a logic circuit which corresponds to a particular boolean expression, although it may contain many gates if the expression is a large, complicated one

29. Circuit diagram

30. BOOLEAN ALGEBRA
The mathematical system of binary logic is called Boolean algebra or switching algebra.
Boolean Theorems
A- Single variable Theorems
1- A . 0 = 0
2- A . 1 = A
3- A . A = A
4- A . A_ = 0
5- A + 0 = A
6- A + 1 = 1
7- A + A = A
8- A + A_ =1

31. BOOLEAN ALGEBRA (cont.)
B- Multi Variable Theorems
9- A + B = B + A
Commutative Laws
10- A . B = B . A
11- A + (B + C) = (A + B) +C
Associative Laws
12- A. (B . C) = (A . B) .C
13- A . (B + C) = A . B + A . C
Theorems 9 to 13 are similar to ordinary algebra.
14- A + AB = A
A.(1 + B) = A .1 = A
15- A + A_ B = A + B
Equations 14 and 15 can be proved by truth table

32. Main Points Logic gates AND, OR, NOT, Ex-OR, NAND, NOR Truth Tables
Boolean Algebra

33. The End
Thank you for your attention.

34. DeMorgan Theorem, Computer Simulation Exercises
Digital Electronics
Lecture 3
DeMorgan Theorem, Computer Simulation Exercises

35. Lecture 3 outline DeMorgan theorems Simulation of Logic Gates
Review of last Lecture
DeMorgan theorems
Simulation of Logic Gates
Introduction to combinational logic circuits

36. Review of Last Lecture Logic gates AND, OR, NOT, Ex-OR, NAND, NOR
Truth Tables
Boolean Algebra

37. DeMorgan Theorems
DeMorgan theorems provide mathematical verification of the equivalency of the NOR and negative-AND gates and the equivalency of the NAND and negative-OR gates.
16- A + B = A_ . B_
17- (A . B) = A_ + B_
To use DeMorgan theorem in simplifying Boolean expressions, the following algorithm is needed.
1- Negate each variable.
2- Replace dots with pluses and vice versa
3- Negate the whole Boolean expression.

38. Examples Consider the following F = A_ + B = A + B_ step 1
F = A . B_ step 3
Example 2
F = A_ B + AB_
= A_ B + AB_ Step 1
=A_ B . AB_ Step 2
=A_ B . AB_ Step 3
DeMorgan therem can also be applied to expressions with more than two variables.

39. Simplification using Boolean Algebra
In the application of Boolean algebra, we have to reduce a particular expression to its simplest form and then use the simplified expression to implement our digital circuit.
For Example: Simplify the following expression.
AB + A(B + C) + B (B + C)

40. Circuit diagram using original expression

41. Circuit diagram using simplified expression

42. Simulation exercises
Use Multisim and draw the circuit shown in Figure 1.
Simulate the circuit and produce a complete truth table for this AND gate.

43. More exercises
Replace the AND gate in figure 1 by OR (74LS32), NAND (74LS00), Ex-OR (74LS86) and NOT (74LS04) gates and then produce the truth tables for such gates using Multisim.

44. Main Points DeMorag Theorem Simplification using Boolean Algebra
Simulation of AND, OR, NOT, Ex-OR, NAND gates

45. The End
Thank you for your attention.

46. Digital Electronics Lecture 4
Simplification using Boolean Algebra, Combinational Logic Circuit Design

47. Lecture 4 outline Karnough Map
Review of last Lecture
Simplification using Boolean Algebra
More simulation
Karnough Map
Introduction to combinational logic circuits

48. Review of Last Lecture DeMorag Theorem
Introduction to simulation of digital circuits
Simulation of AND, OR, NOT, Ex-OR, NAND gates

49. Simplification using Boolean Algebra
In the application of Boolean algebra, we have to reduce a particular expression to its simplest form and then use the simplified expression to implement our digital circuit.
For Example: Simplify the following expression.
AB + A(B + C) + B (B + C)

50. Circuit diagram using original expression

51. Circuit diagram using simplified expression

52. Another Example
Simplify the following,
AB + AC + A_ B_ C

53. Main Points Simplification using Boolean Algebra
Continuation of simulation for OR, NOT, Ex-OR, NAND gates

54. The End
Thank you for your attention.

55. Digital Electronics Lecture 5
Simplification using Karnough Map, Combinational Logic Circuit Design

56. Lecture 5 outline Combinational logic circuits Review of last Lecture
Simplification using Karnough Map
Simplification using logic converter in MULTISIM
Combinational logic circuits

57. Review of Last Lecture Simplification using Boolean Algebra
Continuation of simulation for OR, NOT, Ex-OR, NAND gates

58. Simplification using Karnough Map
This technique is used for minimizing Boolean functions. This technique enables the mapping of every on of 2n input combinations for "n" variables.

59. Example 1 Simplify the following using K-map. F = AB_ + AB + A_B
= AB_ + AB + AB + A_B Using theorem 7
= A(B_ + B) + B(A + A_) Using theorem 8
= A(1) + B(1) Using theorem 2
= A + B

60. Example 2 Simplify the following using K- map.
F = A_ B_ C_ + A_BC + A_BC_ + AB_ C _+ ABC_Circuit diagram using original expression

61. Using Boolean Algebra F = A_ B_ C_ + A_BC + A_BC_ + AB_ C _+ ABC_
F = A_B +B_ C_ +BC_
F = A_B + C_ (B + B_)
F = A_B + C_

62. Decimal
Binary
A B C D 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

63. Example – 4 Variables Simplify the following using K-map.
F= A_ B_ C_ D_ + A_ B_ C_ D+ A_ B_ C D_ + A_ B C_ D + A_ BCD + A B C_ D_ + ABC_D + ABCD + ABCD_ + AB_ C_ D_ + AB_ C_ D

64. Main Points Simplification using K-map
Simplification using logic converter in Multisim

65. The End
Thank you for your attention.

66. Digital Electronics
Lecture 6
Combinational Logic Circuit Design

67. Lecture 6 outline
Review of last Lecture
Design procedure for simple combinational logic circuits
Continuation of Simulation exercises

68. Review of Last Lecture Simplification using K-map
Simplification using logic converter in Multisim

69. DESIGN PROCEDURE FOR SIMPLE COMBINATIONAL LOGIC CIRCUIT
1- Write out the truth table for the required function.
2- From the truth table, write down the Boolean equation for the output.
3- Minimize the equation if appropriate. (using Karnough map).
4- Apply DeMorgan theorem as appropriate.
5- Draw out the circuit using NAND (or NOR) gates. Apply rules 4 and 5 if the circuit is restricted to one type of gates only.

70. Example 1
Design a NAND gate Implementation of the following truth table.
A B C F
Starting Point

71. Using Boolean Algebra 2- F = A_BC + AB_C + ABC_ +ABC
3- Adding redundant term ABC many times.
F = BC (A_ + A) + AC(B_ +B) + AB (C_ +C)
F = BC + AC + AB
4- Apply DeMorgan theorem
F = BC . AC . AB

73. Example 2
This circuit is one of many employed in the arithmetic logic unit of a digital computer. It basically generates a Sum and a Carry simultaneously whilst adding a pair of one bit numbers.
A B Sum Carry
Sum = A_B + AB_
Carry = A.B

74. FULL ADDER

75. Truth table
A B Cin Sum Carry

76. S = A_B_C + A_BC_ +AB_C_ + ABC
S = C (A_B_ +AB) + C_ ( A_B + AB_)
S = C (A+B) + C_ ( A + B)
S = A + B + C
Co = A_BC + AB_C + ABC_ + ABC
Co = C ( A_B + AB_) + AB
C = C(A + B) + AB

77. MULTIPLEXER
A multiplexer (MUX) is a device that allows digital information from several sources to be routed onto a single line for transmission over the line to a common destination.

78. -------------------------------------------------------------------
Data Select Inputs Input Selected
S1 S0
0 0 S_1 S_0 A A
0 1 S_1 S0 B B
1 0 S1 S_0 C C
1 1 S1 S0 D D
X = S_1 S_0 A + S_1 S0 B + S1 S_0 C + S1 S0 D
X = S_1 S_0 A + S_1 S0 B + S1 S_0 C + S1 S0 D

79. Main Points Design procedure for combinational logic circuits. Adders
Multiplexer
Simulation exercises using logic converter

80. The End
Thank you for your attention.

81. Digital Electronics
Lecture 7
Sequential Logic Circuit Design

82. Announcements
Books, CD
Exam and further teaching of electronics
Digital Systems, Principles and Applications, 10th Edition
R.J Tocci, N. S. Windmer, G. L. Moss, 2007.
Kleitz, W., Digital Electronics, Pearson Education Inc, 2005.
Clements, A, Microproscessor System Design, PWS-Kent publishing Copany, 1992.

83. Lecture 6 outline Sequential Logic Circuits Basic Latch Flip-Flops
Review of last Lecture
Sequential Logic Circuits
Basic Latch
Flip-Flops

84. Review of Last Lecture
Design procedure for combinational logic circuits.
Adders
Multiplexer
Simulation exercises using logic converter

85. Sequential Logic Circuits
Any sequential logic system can be broken down into two sections:
Memory part
combinational part
The combinational part will comprise the usual AND, OR gates etc.
The memory part is usually implemented with bistable devices.
Two basic types: latches and flip-flops.

86. Sequential Logic Circuits
Any sequential logic system can be broken down into two sections:
Memory part
combinational part
The combinational part will comprise the usual AND, OR gates etc.
The memory part is usually implemented with bistable devices.
Two basic types: latches and flip-flops.

87. A latch changes state when the input states change
A latch changes state when the input states change. This property is known as transparency. Data is stored by the latch when an enable input (if provided) is valid.
A flip-flop however can only change state on the application of a clock pulse.
A purely sequential system is one in which the output is determined by the order in which the input signals are applied.
Sequential circuits are classified as asynchronous (unclocked) or synchronous (clocked).

88. The Basic Latch
The basic latch has two stable states that correspond to a logic 1 and logic 0. The output changes from one state to another depending on the inputs.
Consider the simple latch shown below.
Truth table as shown below: A B X Y 1

89. This is the basis of the SR (or RS) latch , where A=R, B=S, X=Q and Y=/Q. The circuit symbol is shown below.
This is the basis of the SR (or RS) latch , where A=R, B=S, X=Q and Y=/Q. The circuit symbol is shown below.

90. The Gated SR Latch The Gated SR Latch
The inputs to a gated Latch are controlled by a gate/enable/clock input which allows the latch inputs A and B to be active only when a logic 1 is present on the clock input. This therefore is a level activated device.
The Gated SR Latch
The truth table is now: R S
Clk Q /Q X
Same as A = B = 1 1
The function of the RS gated latch can be illustrated with a waveform diagram as shown below.

91. The truth table is now: Symbol The truth table is now: R S Clk Q /Q XX
Same as A = B = 1 1
The function of the RS gated latch can be illustrated with a waveform diagram as shown below.

92. The JK Flip-Flop
The JK flip-flop is basically an SR gated latch with modifications to eliminate the problems of the final indeterminate state. When the two inputs J and K are both 1 then the output Q changes state. It is said to toggle under these conditions.
Circuit Symbol:

93. J K
Qn+1 Qn 1
/Qn

94. Truth table Qn
Qn+1 J K X 1
Truth table:

95. Excitation table Qn
Qn+1 J K X 1
Truth table:

96. The D-Type Flip-Flop
The D (data) type flip-flop is basically a single-bit storage device. It can be constructed by connecting an inverter between the J and K inputs of a JK flip-flop as shown overleaf. D
Qn+1 1

97. Data appearing on the data input D is simply clocked through to the output Q on the application of a clock pulse.
Symbol:

98. The T-Type Flip-Flop
The T (toggle) type flip-flop also has a single input. It too can be implemented using a JK flip-flop; the inputs are simply connected together as shown below T
Qn+1 Qn 1
/Qn

99. PR ESET and Clear inputs
Positive and negative edged triggered devices

100. Main Points Sequential Logic Circuits. Latch J-K flip-flop
D – Type flip-flop
T-type flip-flop
Counters
Shift register

101. The End
Thank you for your attention.