ENGR 303 – Introduction to Logic Design Lecture 1

Dr. Chuck BrownEngineering and Computer Information Science

Folsom Lake College

<2>

• Objective of the course

• Course Material / Policies

• Course Outline

• Number Systems

• Logic Gates

Outline for Todays Lecture

ENGR 303

<3> ENGR 303

Examples of Digital Logic Design

• Digital Logic is the basis of electronic systems, such as computers, cell phones, and numerous other high-tech systems.

• Digital Logic is rooted in binary code, a series of zeroes and ones each having an opposite value.

• Digital Logic facilitates computing, robotics and other electronic applications.

• Digital Logic Design is used to develop hardware, such as circuit boards and microchip processors.

<4>

• Identify common digital components such as – logic gates, flip-flops, counters, registers, state

machines, and programmable logic devices (PLDs)

• Analyze a digital design problem using – combinational logic, binary number system,

conversion between number systems, Boolean algebra, and Karnaugh maps.

• Design and build a digital logic system including– combinatorial logic, sequential state machines and

basic computer micro-architecture elements using schematic entry and Verilog or VHDL design tools

Objective of Course

ENGR 303

<5>

• Text Book:

– Digital Design and Computer Architecture, Second Edition– August 7, 2012, by David Harris and Sarah Harris ISBN-13: 978-0123944245

• Altera Quartus II version 181 design software will be available for download

– https://www.flc.losrios.edu/about-us/faculty-and-staff-directory/dr-chuck-brown

– Quartus is also available via remote access to FLC lab

Course Material

ENGR 303

<6>

• Prerequisites: – Apply algebra concepts in a problem-solving setting

– Manipulate algebraic expressions and solve simple algebraic equations

– Some previous exposure to a programming language and be able to interpret and modify supplied hardware descriptive language code segments

• Grading:– Problem Sets / Quizes (15%)

– Lab Assignments (45 %)

– Midterm (20 %) and Final Exam (20 %)

Course Policies

ENGR 303

<7>

• Lab handout is available on Canvas

• Lab report

– one lab report per lab is due typically one session

after the completion of each lab

• Save all your work to your H: drive

Lab Policies

ENGR 303

<8>

• Number systems, logic gates, combinatorial logic, Boolean equations, Karnaugh maps

• Digital Building blocks - multiplexers, decoders, adder, multipliers

• Sequential logic - latches, flip-flops, registers, counters, finite state machines

• Hardware Descriptive Language and FPGA implementation

• Computer microarchitecture – data path, ALU, instruction decoder

Class Outline

ENGR 303

<9>

• Breaking the details

into more manageable

parts

focu

s o

f th

is c

ou

rse

programs

device drivers

instructions

registers

datapaths

controllers

adders

memories

AND gates

NOT gates

amplifiers

filters

transistors

diodes

electrons

Abstraction

ENGR 303

<10>

• Most physical variables are continuous

– Voltage on a wire

– Frequency of an oscillation

– Position of a mass

• Digital abstraction considers discrete

subset of values

– Hi or Lo

– On or Off

The Digital Abstraction

ENGR 303

<11>

• Two discrete values:

– 1’s and 0’s

– 1, TRUE, HIGH

– 0, FALSE, LOW

• 1 and 0: voltage levels, rotating gears, fluid levels, etc.

• Digital circuits use voltage levels to represent 1 and 0

• Bit: Binary digit

Digital Discipline: Binary Values

ENGR 303

<12>

• Born to working class parents

• Taught himself mathematics and

joined the faculty of Queen’s

College in Ireland

• Wrote An Investigation of the Laws

of Thought (1854)

• Introduced binary variables

• Introduced the three fundamental

logic operations: AND, OR, and

NOT

George Boole, 1815-1864

ENGR 303

<13>

537410

=

10

's c

olu

mn

10

0's

co

lum

n

10

00

's c

olu

mn

1's

co

lum

n

11012 =

2's

co

lum

n

4's

co

lum

n

8's

co

lum

n

1's

co

lum

n

• Decimal numbers, base = 10

• Binary numbers, base = 2

Number Systems

ENGR 303

<14>

537410

= 5 × 103 + 3 × 102 + 7 × 101 + 4 × 100

five

thousands

10

's c

olu

mn

10

0's

co

lum

n

10

00

's c

olu

mn

three

hundreds

seven

tens

four

ones

1's

co

lum

n

11012 = 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20 = 13

10one

eight

2's

co

lum

n

4's

co

lum

n

8's

co

lum

n

one

four

no

two

one

one1

's c

olu

mn

• Decimal numbers, base = 10

• Binary numbers, base = 2

Number Systems

ENGR 303

<15>

• 20 = 1

• 21 = 2

• 22 = 4

• 23 = 8

• 24 = 16

• 25 = 32

• 26 = 64

• 27 = 128

• 28 = 256

• 29 = 512

• 210 = 1024

• 211 = 2048

• 212 = 4096

• 213 = 8192

• 214 = 16384

• 215 = 32768

ENGR 303

International Electrotechnical Commission Standard… Binary Powers of Two

<16> ENGR 303

GigaByte vs. GibiByteInternational Electrotechnical Commission standard:kibi = 210, Mebi = 220, Gibi 230, etc. are binary based

1 GibiByte = 230 bytes = 1.073741824 x 109 Gib

International System of Quantities:kilo = 103, Mega = 106), Giga = 109), etc. are decimal based

1 GigaByte = 1 x 109 GB

Aside: Storage is marketed in GB, although Windows OS sees GiB

128GB Drive; Windows displays as 119.2 GB (actual GiB)

<17>

• Decimal to binary conversion:– Convert 100112 to decimal

• Decimal to binary conversion:– Convert 4710 to binary

Number Conversion

ENGR 303

<18>

• Decimal to binary conversion:– Convert 100112 to decimal

– 16×1 + 8×0 + 4×0 + 2×1 + 1×1 = 1910

• Decimal to binary conversion:– Convert 4710 to binary

– 32×1 + 16×0 + 8×1 + 4×1 + 2×1 + 1×1 = 1011112

Number Conversion

ENGR 303

<19>

• N-digit decimal number – How many values? – Range? – Example: 3-digit decimal number:

• N-bit binary number– How many values? – Range:– Example: 3-digit binary number:

Binary Values and Range

ENGR 303

<20>

• N-digit decimal number – How many values? 10N

– Range? [0, 10N - 1]– Example: 3-digit decimal number:

• 103 = 1000 possible values• Range: [0, 999]

• N-bit binary number– How many values? 2N

– Range: [0, 2N - 1]– Example: 3-digit binary number:

• 23 = 8 possible values• Range: [0, 7] = [0002 to 1112]

Binary Values and Range

ENGR 303

<21>

Hex Digit Decimal Equivalent Binary Equivalent

0 0 0000

1 1 0001

2 2 0010

3 3 0011

4 4 0100

5 5 0101

6 6 0110

7 7 0111

8 8 1000

9 9 1001

A 10 1010

B 11 1011

C 12 1100

D 13 1101

E 14 1110

F 15 1111

Hexadecimal Numbers – Base 16

ENGR 303

<22>

• Hexadecimal to binary conversion:– Convert 4AF16 (also written 0x4AF) to binary

• Hexadecimal to decimal conversion:– Convert 0x4AF to decimal

Hexadecimal to Binary Conversion

ENGR 303

<23>

• Hexadecimal to binary conversion:– Convert 4AF16 (also written 0x4AF) to binary

– 0100 1010 11112

• Hexadecimal to decimal conversion:– Convert 4AF16 to decimal

– 162×4 + 161×10 + 160×15 = 119910

Hexadecimal to Binary Conversion

ENGR 303

<24>

• Bits

• Bytes & Nibbles

• Bytes in HEX

10010110nibble

byte

CEBF9AD7least

significant

byte

most

significant

byte

10010110least

significant

bit

most

significant

bit

Bits, Bytes, Nibbles…

ENGR 303

<25>

• Logic functions: – 3 basic logic functions:

• NOT (inverter or complement), AND, OR

– Combine NOT with AND, OR to get • NAND, NOR

– Combine to get special operations • XOR, XNOR

• Single-input: – NOT gate, buffer

• Two or more inputs: – AND, OR, NAND, NOR, XOR, XNOR

Logic Gates

ENGR 303

<26> ENGR 303

Truth Table

• A chart that shows the truth value of every

possible combination of all inputs of a logic

expression

• 2n rows for n input variable

• Example: 2-input AND function Y = AB

A B Y

0 0 0

0 1 0

1 0 0

1 1 1

<27>

NOT

Y = A

A Y0

1

A Y

BUF

Y = A

A Y0

1

A Y

Single-Input Logic Gates

ENGR 303

<28>

NOT

Y = A

A Y0 1

1 0

A Y

BUF

Y = A

A Y0 0

1 1

A Y

Single-Input Logic Gates

ENGR 303

Verilog Assign Y = ~A;or

not (y,a);

Assign Y = A;or

buf (y,a);

<29>

AND

Y = AB

A B Y0 0

0 1

1 0

1 1

AB

Y

OR

Y = A + B

A B Y0 0

0 1

1 0

1 1

AB

Y

Two-Input Logic Gates

ENGR 303

<30>

AND

Y = AB

A B Y0 0 0

0 1 0

1 0 0

1 1 1

AB

Y

OR

Y = A + B

A B Y0 0 0

0 1 1

1 0 1

1 1 1

AB

Y

Two-Input Logic Gates

ENGR 303

“Any Ones”“All Ones”

Verilog Assign Y = A & B;or

and (Y, A, B);

Assign Y = A | B;or

or (Y, A, B);

<31>

XNOR

Y = A + B

A B Y0 0

0 1

1 0

1 1

AB

Y

XOR NAND NOR

Y = A + B Y = AB Y = A + B

A B Y0 0

0 1

1 0

1 1

A B Y0 0

0 1

1 0

1 1

A B Y0 0

0 1

1 0

1 1

AB

YAB

YAB

Y

More Two-Input Logic Gates

ENGR 303

<32>

XNOR

Y = A + B

A B Y0 0

0 1

1 0

1 1

AB

Y

XOR NAND NOR

Y = A + B Y = AB Y = A + B

A B Y0 0 0

0 1 1

1 0 1

1 1 0

A B Y0 0 1

0 1 1

1 0 1

1 1 0

A B Y0 0 1

0 1 0

1 0 0

1 1 0

AB

YAB

YAB

Y

1

0

0

1

More Two-Input Logic Gates

ENGR 303

“Even Number Ones”“Odd Number Ones” “Not Zeros”“Not Ones”

Verilog Assign Y = A ^ B;or

xor (Y, A, B);

Assign Y = A ~& B;or

nand (Y, A, B);

Assign Y = A ~| B;or

nor (Y, A, B);

Assign Y = A ~^ B;or

xnor (Y, A, B);

<33>

NOR3

Y = A+B+C

B C Y0 0

0 1

1 0

1 1

AB YC

A0

0

0

0

0 0

0 1

1 0

1 1

1

1

1

1

Multiple-Input Logic Gates

AND3

Y = ABC

AB YC

B C Y0 0

0 1

1 0

1 1

A0

0

0

0

0 0

0 1

1 0

1 1

1

1

1

1

ENGR 303

<34>

NOR3

Y = A+B+C

B C Y0 0

0 1

1 0

1 1

AB YC

A0

0

0

0

0 0

0 1

1 0

1 1

1

1

1

1

1

0

0

0

0

0

0

0

Multi-input XOR: Odd parity generator

Multiple-Input Logic GatesAND3

Y = ABC

AB YC

B C Y0 0

0 1

1 0

1 1

A0

0

0

0

0 0

0 1

1 0

1 1

1

1

1

1

0

0

0

0

0

0

0

1

ENGR 303

Verilog Assign Y = A & B & C;or

and (Y, A, B, C);

Assign Y = ~( A | B | C );or

nor (Y, A, B, C);