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 Descriptian Language (Verilog and VHDL)

3. Digital Systems
Grade Policy
Final Grade = 10% Homework + 20% Quizzes % Midterm Exam + 40% Final Exam + Extra Points
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.
There will be 3 quizzes. Only the best 2 will be counted. The average of quiz grades contributes 20% of final grade.
The maximum lateness in coming to class is 25 minutes, otherwise attendance will not be counted.

4. Digital Systems
Grade Policy
Midterm and final exams follow the schedule released by AAB (Academic Administration Bureau).
Make up of quizzes 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.
Thermal Physics Homework 2 Emelie Raturandang March No.1. Answer:
Heading of Written Homework Papers (Required)

5. Digital Systems
Grade Policy
In order to maintain the integrity, the maximum score of a make up quiz or exam, upon discretion, can be set to 90.
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.
The use of internet for any purpose during class sessions is strictly forbidden.

6. Digital Systems
Section 1
Introduction

7. 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.

8. 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 (of/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

9. 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.

10. 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 2015, i7 cores work in GHz, with multiple cores.

11. 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

12. 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.

13. Digital Systems
Section 2
Number Systems

14. 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.
Convert C32A to decimal, to binary. ?

15. Lecture
Digital Systems
Decimal Numbers
Decimal numbers are made of decimal digits (0,1,2,3,4,5,6,7,8,9).
Number representation:
8653 = 8· · · ·100
Formal notation for this number is (8653)10.
Fraction representation:
= 9· · · · · ·10–1 + 5·10–2
Formal notation: ( )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.

16. 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).
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 are called a byte.
For example, ( )2.
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.

17. 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.

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

19. 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

20. 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

21. 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.

22. 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.

23. 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

24. 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)

25. Binary-Coded Decimal (BCD)
Lecture
Digital Systems
Binary-Coded Decimal (BCD)
Binary coded decimal (BCD) represents each decimal digit with four bits.
For example, =
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? ?

26. Lecture
Digital Systems
Register Transfer
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.

27. 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.

28. Homework 1 Convert (9522)10 to binary and to hexadecimal.
Lecture
First Law of Thermodynamics
Homework 1
Convert (9522)10 to binary and to hexadecimal.
Convert ( ) 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.
Deadline: Wednesday 16 September 2015.