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Fall 2007, Koç University

ELEC 204 Digital Systems Design Serdar Kozat College of Engineering Ko ç University ,Istanbul,Turkey skozat@ku.edu.tr. Fall 2007, Koç University. Lecture 1. Elec 204: Digital Systems Design.

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Fall 2007, Koç University

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  1. ELEC 204 Digital Systems DesignSerdar KozatCollege of EngineeringKoç University,Istanbul,Turkeyskozat@ku.edu.tr Fall 2007, Koç University KU College of Engineering Elec 204: Digital Systems Design Lecture 1

  2. Elec 204: Digital Systems Design • Text Book: M.M. Mano and C. R. Kime, Logic and Computer Design Fundamentals, 3rd Edition Updated, Prentice Hall. • Reference Book: J.F. Wakerly, Digital Design Principles & Practices, Prentice Hall. • Teaching Assistants: • Burak Gorkemli, Osman Nuri Yogurtcu, Yasemin Demir KU College of Engineering Elec 204: Digital Systems Design

  3. Course Objectives: • ELEC204 is a course targeting electrical and computer engineering students to build the fundamental digital design and experimentation concepts. • In this course we will study • combinational logic circuit design techniques, sequential logic circuits, registers and counters, memory, and state machines. • In parallel to lectures we will develop experimental skills studying various digital design techniques during our laboratory hours. • Our experimental setup will be based on Field Programmable Gate Array (FPGA) structure, and we'll experience various design tools. KU College of Engineering Elec 204: Digital Systems Design

  4. Grading: • Lecture Part: • In class quizes (20%), midterm exam (35%), final exam (45%). • Lab Work Part: • Bi-weekly lab assignments (50%), lab midterm (20%), lab project (30%). • Elec 204 is a 4-credit course with the lecture part having 3 credits and the lab work part having 1 credit. The lecture and lab work parts of the Elec 204 will be graded separately. A passing final letter grade requires passing grades from both the lecture and lab work parts. The lecture and lab work letter grades will be combined (3 credits for the lecture and 1 credit for the lab work) for the final letter grade. • Lab Work: • We have two hours assigned each week to perform our experimental work in digital design lab. However student should do their preliminary study on their lab assignments before hand so they can complete the experimental work during the assigned lab hours. After completing the fundamental experiments in the first half of the semester, each student will be required to pick a term digital design project. Possible design projects will be announced by the instructor. Students must attend all Lab works, missing 1/3 of the Lab work will yield a fail grade for the Elec-204 course. • Web page: http://courses.eng.ku.edu.tr/elec204/ KU College of Engineering Elec 204: Digital Systems Design

  5. Academic Dishonesty • The students taking this course are expected to submit their own work in all midterms, projects, homeworks and in class quizes. Please be aware that, being a part of a dishonest plot intentionally (for example, helping others cheat, doing others' homeworks or lab work, giving your reports to others) will also be considered as cheating. Disciplinary acts will be taken for the students who are involved in academic dishonesties, and they will not be offered any voluntary compensation. • Lecture Regulations • Students should attend all lectures. There will not be any form of make-ups for in-class quizes.  • Students who are late more than 15 minutes will not take in-class quizes. • Disruptive talking, cell phone use, walking in&out during the lecture, eating&drinking and any kind of distraction to the lecture will not be allowed during the lecture. KU College of Engineering Elec 204: Digital Systems Design

  6. ELEC204 Spring 2007 Calendar Lab 1 PS + Q Lab 2 PS + Q Lectures on Tue & Thu(Eng Z16) Lab Work PS + Q on Lab 3 Midterm Lab 4 Lab Midterm Lab 5 KU College of Engineering Elec 204: Digital Systems Design

  7. 0. Introduction • Analog vs Digital • Analog devices: process time varying signals that can take on any value across a continuous range of voltage, current or another metric. • Digital devices: so do they! But we can pretend that they don’t!! • Digital signal model: two discrete values 0 or 1, (LOW/HIGH, FALSE/TRUE, negated/asserted, etc) • They have been around since 1940s and in commercial use since 1960s. KU College of Engineering Elec 204: Digital Systems Design

  8. One-analog gone digital systems: • Still pictures • Audio/Video recordings • Automobile carburetors • Telephone system • Advantages of digital systems: • Reproducibility of results • Ease of design (Logic design vs complex characteristics of capacitors, transistors, etc) • Flexibility and functionality (eg: scrambling code) • Programmability: Digital design is carried out today with Hardware Description Languages (HDLs). HDL also comes with simulation and synthesis tools. KU College of Engineering Elec 204: Digital Systems Design

  9. Advantages of digital systems: • Speed: today’s digital devices are fast. Switch in less than 10 picoseconds (10-12). Note: in vacuum light travels ~1cm in 33 ps, the speed of light delay between transistors has became a limiting factor. • Economy: Lots of functionality in a small space • Steadily advancing technology: you should consider that in a few years there will be a faster, a cheaper or otherwise a better technology. KU College of Engineering Elec 204: Digital Systems Design

  10. Digital Computer Memory: stores programs, i/o data Datapath: perform arithmetic and other data-processing operations Control Unit: supervises the flow of information I/O: places program into memory CPU: executes program from memory instruction by instruction. Control unit manipulates datapath to execute instructions. Processor: contains CPU, FPU and MMU FPU (Floating Point Unit): perform f-p operations MMU (Memory Management Unit): layers of memory that helps instruction fetching and data I/O. Internal/external cache (very fast), RAM (between disk and cache) KU College of Engineering Elec 204: Digital Systems Design

  11. Digital Devices • Gates: The most basic digital devices • Any digital function can be realized using just these three kinds of gates. KU College of Engineering Elec 204: Digital Systems Design

  12. Flip-flop: stores either 0 or 1, the states can be changed only at certain times determined by a “clock” input • Combinational circuits: contain only AND, OR and NOT gates • Sequential circuits: contain gates and flip-flops • The output depends on not only inputs but also the past sequence of inputs that have been applied to it. KU College of Engineering Elec 204: Digital Systems Design

  13. Electronic Aspects • Digital circuits deal with voltages and currents and are built with analog components. We perform digital abstraction only. • Electronic circuit design ensures that logic gates produce and recognize logic signals that are within the appropriate range. KU College of Engineering Elec 204: Digital Systems Design

  14. Software Aspects • In computer-aided design (CAD) various tools are available today to improve productivity, correctness and the quality of designs. • Ways of digital design in CAD: • Schematic entry: schematic diagrams to be drawn on screen. • HDLs : Hardware description languages • Simulators: debug and check KU College of Engineering Elec 204: Digital Systems Design

  15. Integrated Circuits • IC: a collection of one or more gates fabricated on a single silicon chip • Small-scale integration (SSI) 1-20 gates • Medium-scale integration (MSI) 20-200 gates • Typically contain a functional building block, such as encoder, counter, … • Large-scale integration (LSI) 200-200,000 gates • Include memories, microprocessors, etc. • Very large-scale integration (VLSI) • Ics with over 1,000,000 transistors KU College of Engineering Elec 204: Digital Systems Design

  16. Programmable Logic Devices • ICs that can have their logic function programmed into them after they are manufactured. • Digital Design Levels • A simple design example: two input multiplexer A Z B S KU College of Engineering Elec 204: Digital Systems Design

  17. Truth table: • Find the optimal equation: • Z = S’A + SB KU College of Engineering Elec 204: Digital Systems Design

  18. Gate level logic diagram (schematic): A Z S B KU College of Engineering Elec 204: Digital Systems Design

  19. Library IEEE; Use IEEE.std_logic_1164.all; entity V1mux is port (A,B,S : in STD_LOGIC; Z : out STD_LOGIC); end V1mux; architecture V1mux_arch of V1mux is begin Z <= A when S=‘0’ else B; end V1mux_arch architecture V1mux_gate_arch of V1mux is begin U1: INV(S, SN); U2: AND2(A,SN,ASN); U3: AND2(S,B,SB); U4: OR2(ASN,SB,Z); end V1mux_gate_arch; • HDL Program: KU College of Engineering Elec 204: Digital Systems Design

  20. 1. Digital Information: Number Systems • Positional number systems: • D = d1 d0 . d-1 d-2 = d1101 + d0100 + d-110-1 + d-210-2 • Here 10 is called base or radix. • General form: (r>1 integer) • 100112 = 1*16 + 0*8 + 0*4 +1*2 + 1*1 = 1910 LSB MSB KU College of Engineering Elec 204: Digital Systems Design

  21. Octal and Hexadecimal Numbers • Base 8 and 16 provide convenient shorthand representation for multi-bit numbers in a digital system. • Octal digit  3-bit string (0-7) • Hexadecimal digit  4-bit string (0-9, A-F) • 1000110011102 = 43168 = 8CE16 • 10.10110010112 = 010.101 100 101 1002 = 2.54548 • = 0010.1011 0010 11002 = 2.B2C16 • In hexadecimal systems 2 digits represent an 8-bit byte. KU College of Engineering Elec 204: Digital Systems Design

  22. Positional Number System Conversions • Base-r-to-decimal conversions: • r: base/radix • p: digits to the left of radix point • n: digits to the right of radix point • Eg: • 436.58 = 4*82 + 3*81 + 6*80 + 5*8-1 = 286.62510 KU College of Engineering Elec 204: Digital Systems Design

  23. Decimal-to-base-r conversion: • 179 / 2 = 89 remainder 1 (LSB) / 2 = 44 rem 1 / 2 = 22 rem 0 / 2 = 11 rem 0 / 2 = 5 rem 1 / 2 = 2 rem 1 / 2 = 1 rem 0 / 2 = 0 rem 1 (MSB) • Hence, 17910 = 101100112 KU College of Engineering Elec 204: Digital Systems Design

  24. Addition and Subtraction of Nondecimal Numbers • Addition 101111000 X 190 10111110 Y 141 10001101 ___+______________ X+Y 331 101001011 KU College of Engineering Elec 204: Digital Systems Design

  25. Binary subtraction: (borrow, difference bits) Bout 001111100 Minuend X 229 11100101 Subtrahend Y 46 00101110 _____________-_________________ Difference X-Y 183 10110111 • Use binary subtraction to compare numbers. If X-Y produces a borrow out at the most significant bit, then X is less than Y. KU College of Engineering Elec 204: Digital Systems Design

  26. Lecture 2 Representation of Negative Numbers • Signed-Magnitude System/Representation: • MSB: sign bit, 0: plus, 1: minus 010101012 = +8510 110101012 = -8510 011111112 = +12710 111111112 = -12710 000000002 = +010 100000002 = -010 • n-bit signed integer lies within –(2n-1-1) through +(2n-1-1) with two representations of zero. KU College of Engineering Elec 204: Digital Systems Design

  27. Signed-magnitude adder • If signs are same add magnitudes, sign is same else compare magnitudes subtract smaller from the larger sign is sign of larger • Signed-magnitude subtractor • Change the sign of subtrahend, perform addition KU College of Engineering Elec 204: Digital Systems Design

  28. Complement Number Systems • Taking the complement is more difficult than changing the sign, but in complement system add/subt are easier. • Radix complement: rn – D where D is an n-digit number • If D is between 1 and rn-1 then D complement is between rn-1 and rn- (rn-1) = 1 • When D=0, D complement id rn (n+1) digits, hence D complement is also 0. KU College of Engineering Elec 204: Digital Systems Design

  29. Two’s Complement • Radix complement for binary numbers D: n bit binary number (– D) = 2n – D = (2n-1) – D + 1 1710 = 000100012 00002 11101110 1111 +_______1 +___1 111011112 = -1710 100002 • The range of representable numbers: -(2n-1) – (2n-1-1) • A number is negative iff MSB is 1. • Zero (0) is positive, one extra negative number. • Decimal equivalent of two’s complement number is computed in the same way for unsigned except MSB is (-2n-1), not (2n-1). • Sign extension property: extend MSB for (n+1) bit number from n bit number • 0110 = 00110 (5 bit), 1010 = 11010 (5 bit) KU College of Engineering Elec 204: Digital Systems Design

  30. One’s Complement Representation • One’s complement of D -D = 2n - 1 – D 1710 = 000100012 111011102 = -1710 KU College of Engineering Elec 204: Digital Systems Design

  31. Two’s complement addition -3 1101 -2 1110 -1 1111 +1 0001+1 0001+1 0001 -2 1110 -1 1111 0 10000 • Subtract n (add –n) • Add 16-n • Surprisingly (?) 16-n is 4-bit two’s complement of n, that is (-n). 0000 0001 1111 0 subt -1 1 add -2 2 3 7 -7 -8 0111 1001 1000 KU College of Engineering Elec 204: Digital Systems Design

  32. Two’s complement subtraction 1 cin 1 +4 0100 0100 +3 0011 0011 - +3 0011 1100- -4 1100 0011 +1 10001 +7 0111 • Overflow • If the result exceeds the range of the number system +5 0101 + +6 0110 +11 1011 = -5 Overflow rule: Addn: if the sign of the addends’ are same and the sign of the sum is different from addends’ sign. KU College of Engineering Elec 204: Digital Systems Design

  33. Binary Multiplication • Unsigned binary multiplication • Shift and add multiplication 11 1011 x 13 1101 01011 00000 01011 1011 10001111 KU College of Engineering Elec 204: Digital Systems Design

  34. Two’s complement multiplication • Shift and two’s complement addition except for the last step. Remember MSB represent (-2n-1) -5 1011 x –3 1101 0000 initial partial product, which is zero. 1011 11011 partial product 0000 111011 partial product 1011 11100111 0101 shifted-and-negated 1 00001111 KU College of Engineering Elec 204: Digital Systems Design

  35. Binary division • Shift and subtract with unsigned numbers • No other easy way. • So for signed numbers, take care of signs and perform shift-and-subtract KU College of Engineering Elec 204: Digital Systems Design

  36. BCD: Binary-Coded Decimal • 0-9 encoded with their 4-bit unsigned binary representation (0000 – 1001). The codewords (1010 – 1111) are not used. • 8-bit byte represent values from 0 to 99. • BCD Addition: Carry 11 448 0100 0100 1000 + 489 0100 1000 1001 937 Sum 1001 1101 10001 Add 6 + 0110+ 0110 BCD sum 1 0011 1 0111 BCD result 1001 0011 0111 KU College of Engineering Elec 204: Digital Systems Design

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