2. Textbook and Syllabus Textbook: Topics:
Digital Systems
Textbook and Syllabus
Textbook:
“Fundamentals of Digital Logic with VHDL Design”, Brown and Vranesic, McGraw-Hill, 3rd Edition, 2009.
Topics:
Introduction
Number Systems
Logic Gates and Boolean Algebra
Gate-level Minimization
Combinatorial Logic
Sequential Logic (Latches, Flip-Flops, Registers, and Counters)
Memory and Programmable Logic
Hardware Description Language (Verilog and VHDL)

3. Textbook and Syllabus Textbook: Topics:
Digital Systems
Textbook and Syllabus
Textbook:
“Digital Systems, Principles and Applications”, Tocci, Widmer, and Moss, Pearson Education, 11th Edition, 2010.
Topics:
Introductory Concepts
Number Systems and Codes
Describing Logic Circuits
Combinational Logic Circuits
Flip-Flops and Related Devices
Digital Arithmetic: Operations and Circuits
Counters and Registers

4. Digital Systems
Grade Policy
Final Grade = 5% Notes + 10% Homework + 16% Quizzes % Midterm Exam + 34% Final Exam % Core Values + Extra Points
You are expected to write a note along the lectures to record your own conclusions or materials which are not covered by the lecture slides.
Your handwritten note will be checked in Final Exam.
Handwritten note contributes 5% of final grade.
Homeworks will be given in fairly regular basis. The average of homework grades contributes 10% of final grade.
Written homeworks are to be submitted on A4 papers, otherwise they will not be graded.
Homeworks must be submitted on time, one day before the next lecture. Late submission will be penalized by point deduction of –10·n, where n is the total number of lateness made.

5. Digital Systems
Grade Policy
There will be 3 quizzes. Only the best 2 will be counted. The average of quiz grades contributes 16% of final grade.
Midterm exam (25%) and final exam (34%) follow the schedule released by AAB (Academic Administration Bureau).
Make up of quiz must be requested within one week after the schedule of the respective quiz.
Make up for mid exam and final exam must be requested directly to AAB.
Digital Systems Homework 2 Emelie Raturandang March No.1. Answer:
Heading of Written Homework Papers (Required)

6. Digital Systems
Grade Policy
Extra points will be given if you solve a problem in front of the class. You will earn 1 or 2.
Lecture slides can be copied during class session. It is also available on internet. Please check the course homepage regularly.

7. Digital Systems
Section 1
Introduction

8. The Evolution of Computer Hardware
Lecture
Digital Systems
The Evolution of Computer Hardware
Modern-day electronics began with the invention of the transfer resistor (transistor) in 1947.
By John Bardeen, Walter Brattain, and William Shockley at Bell Laboratories.
A transistor is a semiconductor device used to amplify and switch electronic signals and electronic power.

9. The Evolution of Computer Hardware
Lecture
Digital Systems
The Evolution of Computer Hardware
In digital circuits, transistors are arranged to function as logical switch.
Logical switch has only 2 values: 1 (on/high) and 0 (off/low).
In general, a switch has three parts: source input, control input, and output.
The control input is represented by a voltage that will decide whether current can flow through the switch or not.
“off”
“on”
output
source
input
control
As the size of transistor shrinks, the size of electronic devises also shrinks.
relay
vacuum tube
discrete
transistor
integrated circuit

10. The Evolution of Computer Hardware
Lecture
Digital Systems
The Evolution of Computer Hardware
In 1958 the first integrated-circuit (IC) was born when Jack Kilby at Texas Instruments successfully interconnected, by hand, several transistors, resistors and capacitors on a single substrate.
Interconnection between components are not integrated.
Low connectivity between components.

11. The Evolution of Computer Hardware
Lecture
Digital Systems
The Evolution of Computer Hardware
In 1999, PowerPC 750L was introduced.
In contains 3.65 millions of transistors, with die size of 40 mm2.
The clock rate is 300–533 MHz, with power consumption of 6 W at 500 MHz.
As in 2017, i9 cores work in GHz, with multiple cores and multiple threads.

12. The Evolution of Computer Hardware
Lecture
Digital Systems
The Evolution of Computer Hardware
Advances in technology increase the performance of computer hardware and decrease the production cost enormously.
Year
Technology
Relative Performance/ Unit Cost
1951
Vacuum Tube 1
1965
Transistor 35
1975
Integrated Circuit (IC)
900
1995
Very Large Scale IC (VLSI)
2,400,000
2005
Ultra VLSI
6,200,000,000

13. The Evolution of Computer Hardware
Lecture
Digital Systems
The Evolution of Computer Hardware

14. The Evolution of Computer Hardware
Lecture
Digital Systems
The Evolution of Computer Hardware
Compiler
Operating System
Application
Digital Design
Circuit Design
Data Path and Control
Transistors
Hardware
Software
Assembler
Processor | Memory | I/O System
The scope of this lecture is the theory and implementation of digital design, in the hardware layer.

15. Numerical Representations
Lecture
Digital Systems
Numerical Representations
Analog representations:
A quantity is represented by a continuously variable, proportional indicator.
Physical quantities are coupled to an indicator by purely mechanical means or proportional voltage or current.
Digital representations:
A quantity is represented by symbols called digits.
The quantity changes in discrete steps.

16. Digital Techniques Advantages:
Lecture
Digital Systems
Digital Techniques
Advantages:
Digital systems are generally easier to design.
Information storage is easy.
Accuracy and precision are easier to maintain throughout the system.
Operation can be programmed.
Digital circuits are less affected by noise.
More digital circuitry can be fabricated on IC chips.
Limitations:
The real world is analog.
Processing digitized signals takes time.

17. Digital and Analog Systems
Lecture
Digital Systems
Digital and Analog Systems
To take advantage of digital techniques when dealing with analog inputs and outputs, four steps must be followed:
Convert the physical variable to an electric signal (analog).
Convert the electric signal (analog into digital form).
Process (operate on) the digital information.
Convert the digital outputs back to real-world analog form.

18. Digital Systems
Section 2
Number Systems

19. Overview of Number Systems
Lecture
Digital Systems
Overview of Number Systems
Decimal: 0, 1, 2, 3, ..., 8, 9, 10, 11, ..., 123, 456, ...
Binary: 0, 1, 10, 11, 100, 101, ...
Unary: 1, 11, 111, 1111, 11111, ...
Duodecimal (base 12)
Hexadecimal (base 16): 0, 9, 31, 2F, C32A
Sexagesimal (base 60): 2:30:55, 6°12’36”
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

20. Lecture
Digital Systems
Decimal Numbers
Decimal numbers are made of decimal digits (0,1,2,3,4,5,6,7,8,9).
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.
MSD : Most Significant Digit LSD : Least Significant Digit

21. Decimal Numbers Number representation:
Lecture
Digital Systems
Decimal Numbers
Number representation:
8653 = 8· · · ·100
Formal notation for this number is (8653)10.
Fraction representation:
= 9· · · · · ·10–1 + 5·10–2
Formal notation: ( )10.

22. Binary Numbers Binary numbers are made of binary digits or bits (0,1).
Lecture
Digital Systems
Binary Numbers
Binary numbers are made of binary digits or bits (0,1).
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.
MSB : Most Significant Bit LSB : Least Significant Bit

23. ? Binary Numbers Number representation:
Lecture
Digital Systems
Binary Numbers
Number representation:
(1011)2 = 1·23 + 0·22 + 1·21 + 1·20 = (11)10.
Fraction representation:
(100.10)2 = 1·22 + 0·21 + 0·20 + 1·2–1 + 0·2–2 = (4.5)10.
A group of eight bits is called a byte.
For example, ( )2.
What is the decimal equivalent of ? ?
What is the next binary number following ?

24. Binary Counting vs. Decimal Counting
Lecture
Digital Systems
Binary Counting vs. Decimal Counting

25. Octal and Hexadecimal Numbers
Lecture
Digital Systems
Octal and Hexadecimal Numbers
Octal numbers are made of eight distinct symbols (0,1,2,3,4,5,6,7).
Number representation:
(217)8 = 2·82 + 1·81 + 7·80 = (143)10.
Hexadecimal numbers are made of sixteen distinct symbols (0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F).
Number representation:
(2AF3)16 = 2· · · ·160 = (10995)10.
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.
Each hexadecimal digit represents four bits.
Convert C32A to decimal, to binary. ?

26. Conversion between Number Bases
Lecture
Digital Systems
Conversion between Number Bases
Decimal (base 10)
Octal (base 8)
Binary (base 2)
Hexadecimal
(base16)

27. Converting Integer Decimal to Binary
Lecture
Digital Systems
Converting Integer Decimal to Binary
Divide the decimal number by the base (2, 8, or 16).
The remainder is the lowest-order digit.
Divide the result from Step 2 by the base again.
The remainder is the next higher-order digit.
Repeat Step 3 and Step 4 until the result is zero.
Decimal
Result
Remainder
13/2 6 1
= a0
6/2 3
= a1
3/2
= a2
1/2
= a3
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.
(13)10 = (a3 a2 a1 a0)2 = (1101)2

28. A Exercise Convert 18932 to binary and hexadecimal numbers.
Lecture
Digital Systems
Exercise
Convert to binary and hexadecimal numbers.
(18932)10 = ( )2
(18932)10 = (49F4)16 A

29. Digital Computer System
Lecture
Digital Systems
Digital Computer System
Digital systems consider discrete amounts of data. For example, consisting characters built by 26 letters in the alphabet and 10 decimal digits.
Larger quantities can be constructed from these discrete values: word is made of letter, sentence is made of words, and so on. Numbers are made of more and more digits.
Computers operate on binary value (0 and 1).
It is easy to represent binary values electrically, through voltage or current.
We can assign: high = 1, low = 0; on = 1, off = 0.
The logical operations can be implemented using circuits, which are the building blocks of modern computers.
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

30. Why is Binary Number Used?
Lecture
Digital Systems
Why is Binary Number Used?
It is easy to represent 0 and 1 using electrical values (voltages or currents).
It is possible to tolerate noise (by assigning a certain range for each signal).
It is easy to transmit the data.
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

31. The Growth of Binary Numbers
Lecture
Digital Systems
The Growth of Binary Numbers n 2n
20 =1 1
21 =2 2
22 =4 3 8 4 16 5 32 6 64 7
128
256 9
512 10
1024 n 2n 11
2048 12
4096 20
1.04 M 30
1.07 G 40
1.1 T 50
1.1 P

32. Binary Data Storage and Representation
Lecture
Digital Systems
Binary Data Storage and Representation
Binary cells store individual bits of data.
Multiple cells form a register.
Data in registers can indicate different values, such as:
Hexadecimals
Binary-Coded Decimal (BCD)
ASCII (American Standard Code for Information Interchange)
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.
A binary cell
The data above can be interpreted as
4F (hexadecimal)
4 15 (for BCD)
Letter O (for ASCII)

33. Binary-Coded Decimal (BCD)
Lecture
Digital Systems
Binary-Coded Decimal (BCD)
Binary coded decimal (BCD) represents each decimal digit with four bits.
For example, = BCD
But, =
Digit
BCD Code
0000 5
0101 1
0001 6
0110 2
0010 7
0111 3
0011 8
1000 4
0100 9
1001
BCD is not efficient, commonly used in early computers.
It is still in some applications, such as to encode numbers for seven-segment (by using a BCD to 7 Segment Decoder).
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.
A BCD clock
What time is it? ?

34. Parallel and Serial Transmission
Lecture
Digital Systems
Parallel and Serial Transmission
Parallel Transmission
Serial Transmission

35. Memory and Register Transfer
Lecture
Digital Systems
Memory and Register Transfer
A circuit which retains a response to a momentary input is displaying memory. Memory is important because it provides a way to store binary numbers temporarily or permanently, which is called data.
Data can be moved from register to register, for a certain meaning or purpose.
Digital logic is used to process the data. The overall system is called a digital system.
We will learn about digital logic and how it is used to design a digital system.
Register A
Register B
Register C
Digital Logic
Circuits
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

36. Digital Systems Logic Circuit .
Lecture
Digital Systems
Digital Systems
In any problem design and analysis, we need to determine the binary outputs for each combination of inputs.
For a given task, we must develop a circuit that accomplishes the task.
Many ways of implementations are thus possible.
We should try to develop the “best” circuit based on some criterion (size, power consumption, performance, price, etc.)
Logic
Circuit
Inputs
Outputs .
credential:
bring a computer
die photo
wafer :
This can be an hidden slide. I just want to use this to do my own planning.
I have rearranged Culler’s lecture slides slightly and add more slides. This covers everything he covers in his first lecture (and more) but may
We will save the fun part, “ Levels of Organization,” at the end (so student can stay awake): I will show the internal stricture of the SS10/20.
Notes to Patterson: You may want to edit the slides in your section or add extra slides to taylor your needs.

37. Lecture
Digital Systems
Digital Computers
In simplest terms, a computer is an electronic device for storing and processing data, typically in binary form, according to instructions given to it in a variable program.

38. Major Parts of Digital Computers
Lecture
Digital Systems
Major Parts of Digital Computers
Input unit—Processes instructions and data into the memory.
Memory unit—Stores data and instructions.
Control unit—Interprets instructions and sends appropriate signals to other units as instructed.
Arithmetic/logic unit—arithmetic calculations and logical decisions are performed.
Output unit—presents information from the memory to the operator or process.

39. Lecture
Digital Systems
Types of Computers
Microprocessor—a central processing unit (CPU) in an integrated circuit that can be connected to the other blocks of a computer system. Example: AMD, Intel.
Microcomputer—a small computer (compared to big supercomputers) that uses a microprocessor as its CPU. Example: PC, PDA, smartphone.
Microcontroller—a computer that performs an intended control task. A microcontroller generally has all the elements of a complete computer (CPU with low clock speed, memory, and input/output port). Example: Game console, electronic clock.

40. Homework 1 Convert (9522)10 to binary and to hexadecimal.
Lecture
Digital Systems
Homework 1
Convert (9522)10 to binary and to hexadecimal.
Convert ( )10 to binary and to octal.
Convert (3F67A)16 to decimal and to binary.
One grain of rice is put on the first square of a chessboard, two on the second, four on the third, and so on (the number of grain is doubled from one square to the next). (a) How many grain of rice would be on the last square?; (b) Assuming that one grain weigh 20 mg, determine the weight of the rice on that last square (in tons).
Deadline: 1 day before class.
Monday, 11 September 2017 (Class 2).
Tuesday, 12 September 2017 (Class 1).