Fall 2002

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Fall 2002 ECE 221 Introduction to
Digital System Design http//tennis.ecs.umass.edu
/ece221 Prof. F. S. Hill, hill_at_ecs.umass.edu,
KEB 309B 5-0767 Prof. W. Gong, gong_at_ecs.umass.edu,
KEB 211E 5-0384

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Course Description Covers the theory of digital
circuits and computer systems stressing general
techniques for the analysis and synthesis of
combinational and sequential logic systems.
Limited to EE and CSE majors. Course Meetings
Lectures M,W,F 800 850 MARCUS AUDITORIUM
(McLaughlin) Discussion W 500 550 PM GSMN 64
(Gong) Textbook Ronald J. Tocci and Neal S.
Widmer, Digital Systems - Principles and
Applications, 8th edition, Prentice Hall, 2001
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Exams There will be 2 midterm quizzes given
during the semester in addition to a
comprehensive final exam at the end of the term.
Each quiz will constitute 20 of the course
grade, and the final exam will constitute 30 of
the grade. Dates and formats for these tests will
be provided once the term is underway.
Homework Homework will be assigned weekly.
Problem sets will be due in class one week after
they are assigned. Late homework will be
accepted, with penalty, until the time the
solutions are posted to this website. No
homeworks will be accepted once the solutions are
posted. Homeworks will constitute 10 of the
course grade. Project A design project will be
assigned that will constitute 20 of the course
grade. Details will be provided once the term is
underway.
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Text Coverage

• Ch1 Introductory Concept
• Ch2 Number Systems and Codes
• Ch3 Logic Gates and Boolean Algebra
• Ch4 Combinatorial Logic
• Ch5 Sequential Logic
• Ch6 Digital Arithmetic
• Ch7 Counters and Registers
• Ch9 MSI Logic Circuits
• Ch10 Interfacing with the Analog World (Time
  Permitting)
• Ch11 Memory Devices

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Announcements

• Check the web site.
• No discussion session tonight (9/5/01).
• Read chapters 1 2.
• Homework 1 is posted. Due Friday 9/13/01.

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Ch2 Number systems and codes
Octal(base 8)
Decimal(base 10)
Binary(base 2)
Hexadecimal (base16)
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Examples

• Decimal numbers(base 10)
• 36.210 9810
• Hexadecimal number(base 16)
• 3F216
• Binary number(base 2)
• 10112

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Positional system

• Each digit carries a certain weight based on its
  position.
• 346.17?463.71 Position matters
• Weight vs Position

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Decimal Positional System(Base 10 or radix 10)
decimal point
tenths position
ones position
tens position
hundredth position
hundreds position
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Binary Positional System (Base 2 or radix 2)
binary point
halves position
ones position
twos position
quarters position
fours position
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Example
Decimal Example
Binary Example
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Binary to Decimal Conversion

• What is 1101012 in decimal?

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(No Transcript)
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Decimal-To-Binary Conversions(method 1)

• The decimal number is simply expressed as a sum
  of powers of 2, and then 1s and 0s are written in
  the appropriate bit positions.

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(Method 2)Flowchart for Repeated Division
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Example for Repeated Division
quotient remainder 50/2
25 0 LSB 25/2 12 1 12/2 6 0 6/2
3 0 3/2 1 1 1/2 0
1 MSB 50101100102
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Example for Repeated Division
quotient remainder 346/2 173 0 173/2 86 1 8
6/2 43 0 43/2 21 1 21/2 10 1 10/2 5 0 5/2
2 1 2/2 1 0 1/2 0 1 346101010110102
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• How many different values can we represent with
  N binary digits? Decimal digits? Octal digits?
  Radix Z digits?
• Decimal 1 digit 0-9 10
  different values
• 2 digits 10X10100 different
  values
• .. 6 digits 1061,000,000 different
  values
• Binary 1 digit 0,1 2 different
  values21
• 2 digits 00,01,10,11 4 different
  values22
• n digits 2n different values
• Radix Z digits n digits Zn different values(0
  thru. Zn-1)

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Octal-to-Decimal Conversion

• Octal-to-Decimal Conversion

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Decimal-to-Octal Conversion

• Convert 26610 to Octal
• quotient remainder
• 266/8 33 2 LSB
• 33/8 4 1
• 4/8 0 4 MSB
• 266104128

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Octal-to-Binary Conversion

• Convert 4728 to binary
• 4 7 2
• ? ? ?
• 100 111 010
• Convert 54318 to binary
• 5 4 3 1
• ? ? ? ?
• 101 100 011 001

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Binary-to-Octal Conversion

• Convert 1001110102 to octal
• Convert 110101102 to octal

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Octal-to-hex Conversion

• Convert B2F16 to octal
• B2F161011 0010 1111 convert to binary
• 101 100 101 111 group into three-bit
  groupings
• 5 4 5 78 Convert to octal

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2-5 BCD Code

• If each digit of a decimal number is represented
  by its binary equivalent, the result is a code
  called binary-code-decimal(BCD).
• 8 7 4 (decimal)
• ? ? ?
• 1000 0111 0100 (BCD)
• 9 4 3 (decimal)
• ? ? ?
• 1001 0100 0011 (BCD)

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Example

• Convert 0110100000111001(BCD) to its decimal
  equivalent.
• Convert the BCD number 011111000001 to its
  decimal equivalent.

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Comparison of BCD and Binary

• A straight binary code takes the complete decimal
  number and represents it in binary.
• A BCD code converts each decimal digit to binary
  individually.
• 13710100010012 (binary)
• 137100001 0011 0111 (BCD)
• BCD uses more bits, easier to convert to and from
  decimal.

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Review Questions

• Represent the decimal value 178 by its straight
  binary equivalent. Then encode the same decimal
  number using BCD.
• How many bits are required to represent an
  eight-digit decimal number in BCD?
• What is an advantage of encoding a decimal number
  in BCD as compared with straight binary? What is
  a disadvantage?

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2-6 Putting it ALL together(TBA)
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2-7 The byte

• A string of 8 bits is called a byte.
• How many bytes are in a 32-bit string?
• What is the largest decimal value that can be
  represented in binary using two bytes?
• How many bytes are needed to represent the
  decimal value 846,569 in BCD?

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Review Questions

• How many bytes are needed to represent 23510 in
  binary?
• What is the largest decimal value that can be
  represented in BCD using two bytes?

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2-8 Alphanumeric Codes

• Codes representing letters of the alphabet,
  punctuation marks, and other special characters
  as well as numbers are called alphanumeric codes.
• The most widely used alphanumeric code is the
  American Standard Code for Information
  Interchange(ASCII). The ASCII(pronounced askee)
  code is a seven-bit code.

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Partial listing of ASCII code
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Example

• The following is a message encoded in ASCII code.
  What is the message?
• 1001000 1000101 1001100 1010000
• An operator is typing in a JAVA program at the
  keyboard of a certain microcomputer. The computer
  converts each keystroke into its ASCII code and
  stores the code as a byte in memory. Determine
  the binary strings that will be entered into
  memory when the operator types in the following
  JAVA statement.
• import java.applet.

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Review Questions

• Encode the following message in ASCII code using
  the hex representation COST72.
• The following padded ASCII-coded message is
  stored in successive memory location in a
  computer
• 01010011 01010100 01001111 01010000
• What is the message?

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2-9 Parity method for error detection
Whenever information is transmitted from one
device to another device, there is a possibility
that errors can occur such that the receiver does
not receive the identical information that was
sent by the transmitter.
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Parity Bit

• A parity bit is an extra bit that is attached to
  a code group that is being transferred from one
  location to another.
• Even-parity
• The value of the parity bit is chosen so that the
  total number of 1s in the code group(including
  the parity bit) is an even number.
• 1 1 0 0 0 0 1 1
• ?
• Added parity bit
• Odd-parity
• The parity bit is chosen so that the total number
  of 1s(including the parity bit) is an odd number.
• The parity bit is issued to detect any single-bit
  errors during the transmission of a code from one
  location to another.

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Example

• Computers often communicate with other remote
  computers over the telephone lines. For example,
  this is how some communication over the internet
  takes place. When one computer is transmitting a
  message to another, the information is usually
  encoded in ASCII.What actual bit strings would a
  computer transmit to send the message HELLO,
  using ASCII with even parity?

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Review Questions

• Attach an odd-parity bit to the ASCII code for
  the symbol, and express the result in
  hexadecimal.
• Attach an even-parity bit to the BCD code for
  decimal 69.
• Why cant the parity method detect a double error
  in transmitted data?

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2-10 Applications

• A typical CD-ROM can store 650 megabytes of
  digital data. Since mega220, how many bits of
  data can a CD-ROM hold?
• An automotive parts shop uses a computer to store
  all of its parts numbers in 7-bit ASCII code with
  an odd parity bit. The codes for each part are
  stored in successive memory locations. List the
  binary contents of memory that stores the part
  number JR2-5.
• A small process-control computer uses octal codes
  to represent its 12-bit memory addresses.
• How many octal digits are required?
• What is the range of addresses in octal?
• How many memory locations are there?

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Applications(cont.)

• A typical PC uses a 20-bit address code for its
  memory locations.
• How many hex digits are needed to represent a
  memory address?
• What is the range of addresses?
• What is the total number of memory locations?
• Most calculators use BCD to store the decimal
  values as they are entered into the keyboard and
  to drive the digit displays.
• If a calculator is designed to handle 8-digit
  decimal numbers, how many bits does this require?
• What bits are stored when the number 375 is
  entered into the calculator?

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Summary

• The octal and hexadecimal number systems are used
  in digital systems and computers as efficient
  ways of representing binary quantities.
• In conversion between octal and binary, one octal
  digit corresponds to three bits. In conversions
  between hex and binary, each hex digit
  corresponds to four bits.
• The repeated-division method is used to convert
  decimal numbers to binary, octal or hexadecimal.
• Using an N-bit binary number, we can represent
  decimal values from 0 to 2N-1.
• The BCD code for a decimal number is formed by
  converting each digit of the decimal number to
  its four-bit binary equivalent.

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Summary(cont.)

• A byte is a string of eight bits.
• An alphanumeric code is one that uses groups of
  bits to represent all of the various characters
  and functions that are part of a typical
  computers keyboard. The ASCII code is the most
  widely used alphanumeric code.
• The parity method for error detection attaches a
  special parity bit to each transmitted group of
  bits.