Fall 2007, Koç University

KU College of EngineeringElec 204: Digital Systems Design 1

Fall 2007, Koç University

Lecture 1

ELEC 204 Digital Systems Design

Serdar KozatCollege of EngineeringKoç University,Istanbul,[email protected]


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


• 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.


• 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/


• 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.


ELEC204Spring 2007 Calendar

Lab 1

Lab 2

Lab 3

Lab 4

Lab 5

M T W T F

Sep 17 Sep 18 Sep 19 Sep 20 Sep 21

Sep 24 Sep 25 Sep 26 Sep 27 Sep 28

Oct 1 Oct 2 Oct 3 Oct 4 Oct 5




Oct 29 Oct 30 Oct 31 Nov 1 Nov 2

Nov 5 Nov 6 Nov 7 Nov 8 Nov 9




Dec 3 Dec 4 Dec 5 Dec 6 Dec 7




Lectures on Tue & Thu (Eng Z16)

Lab Work

PS + Q on

Lab Midterm

Midterm

PS + Q

PS + Q


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.


• 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.


• 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.


Digital ComputerMemory: stores programs, i/o dataDatapath: perform arithmetic and other data-processing operationsControl Unit: supervises the flow of informationI/O: places program into memoryCPU: executes program from memory instruction by instruction. Control unit manipulates datapath to execute instructions.

Processor: contains CPU, FPU and MMUFPU (Floating Point Unit) : perform f-p operationsMMU (Memory Management Unit): layers of memory that helps instruction fetching and data I/O. Internal/external cache (very fast), RAM (between disk and cache)


Digital Devices

• Gates: The most basic digital devices

• Any digital function can be realized using just these three kinds of gates.


• 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.


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.


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


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


• 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

BZ

S


• Truth table: S A B Z

0 0 0 0

0 0 1 0

0 1 0 1

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 0

1 1 1 1

• Find the optimal equation:• Z = S’A + SB


• Gate level logic diagram (schematic):

A

B

S

Z


• HDL Program:

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 isbegin

Z <= A when S=‘0’ else B;end V1mux_arch

architecture V1mux_gate_arch of V1mux isbegin

U1: INV(S, SN);U2: AND2(A,SN,ASN);U3: AND2(S,B,SB);U4: OR2(ASN,SB,Z);

end V1mux_gate_arch;


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

ip

niirdD

1

MSB LSB


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.


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

ip

niirdD

1


• 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


Addition and Subtraction of Nondecimal Numbers

• Addition

101111000

X 190 10111110

Y 141 10001101

___+______________

X+Y 331 101001011

Cin/bin X Y Cout S Bout D

0 0 0 0 0 0 0

0 0 1 0 1 1 1

0 1 0 0 1 0 1

0 1 1 1 0 0 0

1 0 0 0 1 1 1

1 0 1 1 0 1 0

1 1 0 1 0 0 0

1 1 1 1 1 1 1


• 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.


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.

Lecture 2


• 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


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.


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)


One’s Complement Representation

• One’s complement of D-D = 2n - 1 – D

1710 = 000100012

111011102 = -1710


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).

01

2

7-8-7

-1-2

3

addsubt

00000001

0111

10001001

1111


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 sameand the sign of the sum is different from addends’ sign.


Binary Multiplication

• Unsigned binary multiplication– Shift and add multiplication

11 1011

x 13 1101

01011

00000

01011

1011

10001111


• 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-negated1 00001111


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


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 1 1

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

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