ECEN 248: INTRODUCTION TO DIGITAL SYSTEMS …dropzone.tamu.edu/~sshakkot/courses/ECEN248/week1.pdfECEN 248: INTRODUCTION TO DIGITAL SYSTEMS DESIGN Week 1 Dr. Srinivas Shakkottai Dept.

ECEN 248: INTRODUCTION TO DIGITAL SYSTEMS DESIGN

Week 1 Dr. Srinivas Shakkottai Dept. of Electrical and Computer Engineering

Instructor:

¨  Dr. Srinivas Shakkottai ! Office 332C WEB ! Office Hours: Wed 2:00PM-3:00 PM, Fri 2:00 PM – 3:00 PM ! Email: User: sshakkot at Domain: tamu.edu ! Lab Timings: check section ! No lab this week.

Required textbook:

¨  Brown and Vranesic (3rd Edition) Fundamentals of Digital Logic with Verilog

Design.

Reference textbook:

¨  "Digital Design: Principles and Practices" by John Wakerly.

¨  "Contemporary Logic Design” by Randy Katz.

Course info

¨  Mailing list: ! Emails will be sent periodically to tamu accounts ! Announcements:

n  Lecture cancellations n  Deadline extension n  Updates, etc.

¨  Course website !  http://cesg.tamu.edu/courses/ecen-248-digital-

systems-design/ ! All slides, labs, assignments, etc.

Grading Policy:

¨  5% Homework assignments. 10% Quizzes.

20% Laboratory. 20% Exam 1. 20% Exam 2. 25% Exam 3.

Grading scale

¨  A standard grading scale will be utilized. The tentative grading scale for the course is:  ¨  A       90-100% ¨  B         80-89% ¨  C        70-79% ¨  D         60-69% ¨  F        Below 59%

Course Goals

¨  Study methods for !  Representation, manipulation, and optimization for

both combinatorial and sequential logic !  Solving digital design problems !  Study HDL description language (Verilog)

Topics

¨  Number bases ¨  Logic gates and Boolean Algebra ¨  Gate–level minimization ¨  Combinational Logic ¨  Sequential logic (Latches, Flip-flops,

Registers, and Counters) ¨  Memory and Programmable Logic ¨  HDL language (Verilog)

Verilog

¨  Stands for Verify Logic. ¨  Verilog Hardware Description Language. ¨  Procedure is to use a compiler for

compiling source code written in Verilog. ¨  Subset of statements can be synthesized

using logic circuits.

The Evolution of Computer Hardware

¨  When was the first transistor invented? ● Modern-day electronics began with the invention in

1947 of the transfer resistor - the bi-polar transistor - by Bardeen et.al at Bell Laboratories

The Evolution of Computer Hardware

¨  When was the first IC (integrated circuit) invented?

●  In 1958 the IC was born when Jack Kilby at Texas Instruments successfully interconnected, by hand, several transistors, resistors and capacitors on a single substrate

The Underlying Technologies

Year Technology Relative Perf./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 PowerPC 750

¨  Introduced in 1999 ¨  3.65M transistors ¨  366 MHz clock rate ¨  40 mm2 die size ¨  250nm technology

ECEN 248

Layers of abstraction

I/O system Processor

Compiler Operating System (Mac OSX)

Application (ex: browser)

Digital Design Circuit Design

Instruction Set Architecture

Datapath & Control

transistors

Memory Hardware

Software Assembler

Year

Tran

sisto

rs

1000

10000

100000

1000000

10000000

100000000

1970 1975 1980 1985 1990 1995 2000

i80386

i4004

i8080

Pentium

i80486

i80286

i8086

Technology Trends: Microprocessor Complexity

2X transistors/Chip Every 1.5 years

Called “Moore’s Law”

Alpha 21264: 15 million Pentium Pro: 5.5 million PowerPC 620: 6.9 million Alpha 21164: 9.3 million Sparc Ultra: 5.2 million

Moore’s Law

Athlon (K7): 22 Million Itanium 2: 41 Million

NUMBER SYSTEMS

Overview

¨  Understanding decimal numbers ¨  Binary and octal numbers

! The basis of computers!

¨  Conversion between different number systems

Digital Computer Systems

¨  Digital systems consider discrete amounts of data. ¨  Examples

!  26 letters in the alphabet !  10 decimal digits

¨  Larger quantities can be built from discrete values: ! Words made of letters ! Numbers made of decimal digits (e.g. 239875.32)

¨  Computers operate on binary values (0 and 1) ¨  Easy to represent binary values electrically

! Voltages and currents. ! Can be implemented using circuits ! Create the building blocks of modern computers

Understanding Decimal Numbers

¨  Decimal numbers are made of decimal digits: (0,1,2,3,4,5,6,7,8,9)

¨  Number representation: !  8653 = 8x103 + 6x102 + 5x101 + 3x100

¨  What about fractions? !  97654.35 = 9x104 + 7x103 + 6x102 + 5x101 + 4x100 +

3x10-1 + 5x10-2

!  Informal notation à (97654.35)10

Understanding Octal Numbers

¨  Octal numbers are made of octal digits: (0,1,2,3,4,5,6,7)

¨  Number representation: !  (4536)8 = 4x83 + 5x82 + 3x81 + 6x80 = (2398)10

¨  What about fractions? !  (465.27)8 = 4x82 + 6x81 + 5x80 + 2x8-1 + 7x8-2

¨  Octal numbers don’t use digits 8 or 9

Understanding Binary Numbers

¨  Binary numbers are made of binary digits (bits): !  0 and 1

¨  Number representation: !  (1011)2 = 1x23 + 0x22 + 1x21 + 1x20 = (11)10

¨  What about fractions? !  (110.10)2 = 1x22 + 1x21 + 0x20 + 1x2-1 + 0x2-2

¨  Groups of eight bits are called a byte !  (11001001) 2

¨  Groups of four bits are called a nibble. !  (1101) 2

Why Use Binary Numbers?

°  Easy to represent 0 and 1 using electrical values.

°  Possible to tolerate noise.

°  Easy to transmit data

°  Easy to build binary circuits.

AND Gate

1

0 0

Conversion Between Number Bases

Decimal(base 10)!

Octal(base 8)!

Binary(base 2)!

Hexadecimal!(base16)!

Convert an Integer from Decimal to Another Base

1.  Divide decimal number by the base (e.g. 2)

2.  The remainder is the lowest-order digit

3.  Repeat first two steps until no divisor remains.

For each digit position:

Example for (13)10:

Integer Quotient

13/2 = 6 1 a0 = 1 6/2 = 3 0 a1 = 0 3/2 = 1 1 a2 = 1 1/2 = 0 1 a3 = 1

Remainder Coefficient

Answer (13)10 = (a3 a2 a1 a0)2 = (1101)2

Convert a Fraction from Decimal to Another Base

1.  Multiply decimal number by the base (e.g. 2)

2.  The integer is the highest-order digit

3.  Repeat first two steps until fraction becomes zero.

For each digit position:

Example for (0.625)10:

Integer

0.625 x 2 = 1 + 0.25 a-1 = 1 0.250 x 2 = 0 + 0.50 a-2 = 0 0.500 x 2 = 1 + 0 a-3 = 1

Fraction Coefficient

Answer (0.625)10 = (0.a-1 a-2 a-3 )2 = (0.101)2

The Growth of Binary Numbers n 2n

0 20=1

1 21=2

2 22=4

3 23=8

4 24=16

5 25=32

6 26=64

7 27=128

n 2n

8 28=256

9 29=512

10 210=1024

11 211=2048

12 212=4096

20 220=1M

30 230=1G

40 240=1T

Mega

Giga

Tera

Kilo

Binary Arithmetic

Binary Addition

¨  Binary addition is very simple. ¨  This is best shown in an example of adding two binary

numbers…

1 1 1 1 0 1 + 1 0 1 1 1 ---------------------

0

1

0

1

1

1 1 1 1

1 1 0 0

carries

Binary Subtraction

°  We can also perform subtraction (with borrows in place of carries).

°  Let’s subtract (10111)2 from (1001101)2…

1 10 0 10 10 0 0 10

1 0 0 1 1 0 1

- 1 0 1 1 1 ------------------------ 1 1 0 1 1 0

borrows

Binary Multiplication

¨  Binary multiplication is much the same as decimal multiplication, except that the multiplication operations are much simpler…

1 0 1 1 1 X 1 0 1 0 ----------------------- 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 1 1 ----------------------- 1 1 1 0 0 1 1 0

Digital Systems

Binary Data Storage

•  Binary cells store individual bits of data

•  Multiple cells form a register.

•  Data in registers can indicate different values

•  Hex (decimal)

•  BCD

•  ASCII

Binary Cell

0 0 1 0 1 0 1 1

Register Transfer

¨  Data can move from register to register. ¨  Digital logic used to process data. ¨  We will learn to design this logic.

Register A Register B

Register C

Digital Logic Circuits

Digital Systems

¨  Analysis problem:

!  Determine binary outputs for each combination of inputs

¨  Design problem: given a task, develop a circuit that accomplishes the task !  Many possible implementations. !  Try to develop “best” circuit based on some criterion (size, power,

performance, etc.)

· ·

· ·

Logic Circuit Inputs Outputs

Toll Booth Controller

¨  Consider the design of a toll booth controller. ¨  Inputs: quarter, car sensor. ¨  Outputs: gate lift signal, gate close signal

¨  If driver pitches in quarter, raise gate. ¨  When car has cleared gate, close gate.

Logic Circuit

$·25

Car?

Raise gate

Close gate

Gates

Describing Circuit Functionality: Inverter

¨  Basic logic functions have symbols. ¨  The same functionality can be represented with truth

tables·∙ !  Truth table completely specifies outputs for all input

combinations. ¨  The above circuit is an inverter.

!  An input of 0 is inverted to a 1. !  An input of 1 is inverted to a 0.

A Y

0 1

1 0

Input Output

A Y

Symbol

Truth Table

The AND Gate

¨  This is an AND gate. ¨  So, if the two inputs signals

are asserted (high) the output will also be asserted. Otherwise, the output will be deasserted (low).

A B Y

0 0 0

0 1 0

1 0 0

1 1 1

A

B Y

Truth Table

The OR Gate

¨  This is an OR gate. ¨  So, if either of the two

input signals are asserted, or both of them are, the output will be asserted.

A B Y

0 0 0

0 1 1

1 0 1

1 1 1

A B

Y

The NAND Gate

¨  This is a NAND gate. It is a combination of an AND gate followed by an inverter. Its truth table shows this. A B Y

0 0 1 0 1 1 1 0 1 1 1 0

A B

Y

The NOR Gate

¨  This is a NOR gate. It is a combination of an OR gate followed by an inverter. It’s truth table shows this A B Y

0 0 1 0 1 0 1 0 0 1 1 0

A B

Y

The XOR Gate (Exclusive-OR)

¨  This is a XOR gate. ¨  XOR gates assert their output

when exactly one of the inputs is asserted, hence the name.

¨  The switching algebra symbol for this operation is ⊕, i.e. 1 ⊕ 1 = 0 and 1 ⊕ 0 = 1.

A B Y 0 0 0 0 1 1 1 0 1 1 1 0

A B

Y

Describing Circuit Functionality: Waveforms

¨  Waveforms provide another approach for representing functionality.

¨  Values are either high (logic 1) or low (logic 0). ¨  Can you create a truth table from the waveforms?

A B Y 0 0 0 0 1 0 1 0 0 1 1 1

AND Gate

Consider three-input gates

3 Input OR Gate

Ordering Boolean Functions

¨  How to interpret A ·∙ B+C? !  Is it A ·∙ B ORed with C ? !  Is it A ANDed with B+C ?

¨  Order of precedence for Boolean algebra: AND before OR.

¨  Note that parentheses are needed here :