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)

Digital Systems Grade Policy Final Grade = 5% Notes + 11% Homework + 18% Quizzes + 28% Midterm Exam + 38% Final Exam + 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 collected after Quiz 3, and given back to you on the next class. Handwritten note contributes 5% of final grade. Homeworks will be given in fairly regular basis. The average of homework grades contributes 11% 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.

Digital Systems Grade Policy There will be 3 quizzes. Only the best 2 will be counted. The average of quiz grades contributes 18% of final grade. Midterm exam (28%) and final exam (38%) 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 0029202400058 21 March 2027 No.1. Answer: . . . . . . . . Heading of Written Homework Papers (Required)

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. http://zitompul.wordpress.com The use of internet for any purpose during class sessions is strictly forbidden.

Digital Systems Section 1 Introduction

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.

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

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.

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 2.67-3.33 GHz, with multiple cores.

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

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.

Digital Systems Section 2 Number Systems

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. ?

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 = 8·103 + 6·102 + 5·101 + 3·100 Formal notation for this number is (8653)10. Fraction representation: 97654.35 = 9·104 + 7·103 + 6·102 + 5·101 + 4·100 + 3·10–1 + 5·10–2 Formal notation: (97654.35)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.

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, (11001001)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.

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 = 2·163 + 10·162 + 15·161 + 3·160 = (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.

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

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

A Exercise Convert 18932 to binary and hexadecimal numbers. Lecture Digital Systems Exercise Convert 18932 to binary and hexadecimal numbers. (18932)10 = (100100111110100)2 (18932)10 = (49F4)16 A

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.

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.

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

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)

Binary-Coded Decimal (BCD) Lecture Digital Systems Binary-Coded Decimal (BCD) Binary coded decimal (BCD) represents each decimal digit with four bits. For example, 32910 = 0011 0010 1001 3 2 9 But, 32910 = 1010010012 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? ?

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.

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.

Homework 1 Convert (9522)10 to binary and to hexadecimal. Lecture Digital Systems Homework 1 Convert (9522)10 to binary and to hexadecimal. Convert (369.6875)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. Deadline: Tuesday, 13 September 2016.