CSC 4100 Syllabus

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CSC 4100 Syllabus

• 1st Week Basic Data Representation(CH.1)
• 2nd Week Logic Design(Ch2)
• 3rd Week Logic Design Basic Components.
• 4th Week Basic Component
• 5th Week Simple Calculations.
• 6th Week Addressing and Data Organization.
• 7th Subroutine Calling Mechanisms.
• 8th Representing Integers.
• 9th Floating Point Numbers
• 10th Instruction Representation.
• 11th Instruction Interpretation and Translation
  process.
• Device Communication and Interrupts.

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Contact information

• Instructor Dr. T.G.Towfic
• Room 454 State Hall
• E-Mail gtowfic_at_cs.wayne.edu
• Tel[phone].
• Grader Yu Zhang
• Room 468 State Hall
• E-mail Zhangyu_at_cs.wayne.edu.

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Important Dates

• 1st quiz Thursday May 27 1999..630-730
• First Exam Th. June 03 1999.. 530-735.
• 2nd quiz Tuesday June 29 1999..630-730.
• 2nd ExamTuesday July 13 1999.. 530-735
• 3rd quizTuesday July 27 1999, 630-730.
• Final ExamThursday August 3rd ,530-735

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• Grading Policy
• 25 each exam.(total 2 2550).
• 5 each quiz( 5315)
• 35 Assignments( 5 assignments each term,
  including programming assignments).
• Office hours
• Instructor T/Th 400-530
• Grader M/Wed. 430-530

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5/11/99

• Data Representation
• Number Encoding.
• Character encoding.

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Definitions

• Abstraction Capturing the general properties of
  things, while leaving out the details.
• Encoding a binary representation of alphabet.
• Unit symbol and Grouping symbols Each grouping
  of symbol represent a collection of units.
• Digits are grouping symbols used in positional
  numbering systems.
• Most Significant and least significant bitsMSB
  represent the highest power of two in a binary
  representation. LSB represent 20.

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• Sign bit holds the sign information in a sign
  magnitude representation.
• Code is a set of encoding.

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Positional Numbering Systems

• Must Contain
• (1) Radix(Base). We will call it r
• (2) alphabet We will call it d
• Then a sequence of di(i0,1,n-1) for a given
  alphabet with n digits, is represented as
• dn-1 d1 d0
• In Radix form this is given as
• dn-1 . rn-1 ..d0 . r0

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• Radix(Base)

Decimal r10 Maximum digit 9
Octal r8 Max. Digit 7
Hexadecimal r16 Max. Digit 15(F)
Binary r2 Max. digit1
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Examples

• 964 (1704)8
• (11010100001)2 (3241)8
• (4BF)16 (010010111111)2

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Radix Conversion

• I. Binary to others
• (1) Divide by number of digits(start from
• Least Significant Digit, LSD)
• (A) Octal 3,(B) Hexa. 4,(C) Dec.4
• E.g. (1101000101)2
• (a) Decimal 0011 0100 0101
  (345)10345
• (b) Octal 001 101 000 101
  (1505)8
• (C) Hexa ?

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• II. Others to binary
• (1) Choose number of bits according to Base
• Hexa Octal 4bits, Octal 3
• (2) use number of bits in (1) to convert each
  digit to binary.
• Ex (ABC)16 (101010111100)2
• (7762)8(111111110010)2
• 9899 (1001100010011001)2

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• III Others to decimals
• Use positional notation
• n-1
• ? di . ri
• i o

4 Dec.
r
r 8 octal
n total number of digits to be converted
r16 Hexa.
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• Ex (AB23)16 10(16)311(16)22(16)1
• 
  3(16)0 43811..(n4)
• (774)8 7(8)2 7(8)1 4(8)0 508 ..(n3)
• (101111)2 ?

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• IV Decimal to others
• (1) divide number by Base.
• (2) separate quotient from reminder.
• (3) Continue until quotient less than Base.
• (4) arrange reminders as LSD( which has a less
  power than others) to the left.

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• Example
• 995 TO Hexa.
• Decimal quotient
  Reminder
• 995/16 62 3
  (160) LSD
• 62/16 3
  14(161)
• 14/16 0
  14(162)
• Result (EE3)16

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• V. Fraction of Any Base to Decimal
• Use positional number equation for decimal
• n
• ? di . r -i
• i 1

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• Ex.
• 0.AAC16 1016-1 1016-21216-3
• 0.6669921
• 0.76728 78-1 68-278-328-4
• ?

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• VI. Decimal fraction to any base
• (1) multiply by Base.
• (2) separate whole number from fraction.
• (3) multiply fraction by base until fraction
  Continue until fraction gt 0.
• (4) arrange whole numbers as LSD( this time
  last obtained (why)!) to left .

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• Example
• 0.9878 into Hexa.
• Decimal Whole number Fraction
• 0.987816 15
  0.8048
• 0.804816 12
  0.8768
• 0.876816 14
  0.0288
• Result rounded to three digits (FCE)16

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Number Encoding
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• Examples
• (I) sign bit representation
• 28 is 0 11100
• -28 is 111100
• Notice that we followed the positional number
  system.
• (II) BCD
• 28 is 101000101000
• -28 is 101100101000
• notice that,here, we represent each digit by
  iots binary representation( we dont follow
  positional number system).

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• (III) 5-bit 2s Complement
• (1) 28 as a position number system
• 11100
• (2) we take complement
• 00011
• (3) we add 1 to complement
• 00011 1 00100

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• General notes on 2s complement
• (1) we dont need extra bits to be added to the
  number. Remember that we added one digit in sign
  number representation and 4 digits in BCD.
• (2) in genera 2s complement of n bit of a number
  X is
• representation 2n - X
• thus 2s complement of 28 given 5 bits 25 - 28
  4(00100)
• Q How do we recognize compliments from numbers?
  For example how do we know that 00100 is not the
  number 4 but it is -28?
• Hint in 2s compliment numbers with n bit
  representation, encoded values can only be in the
  range -2n-1 and 2n-1 - 1.

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Character Encoding

• Character

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ASCII CHARACTER SET

• Seven digit for all characters(printable and
• non-printable)
• Advantages (1)Capital letters and small letters
  can be recognized easily since they only differ
  in the 2th bit.
• (2) As we normally have 8 bit computers, the
  extra 8th bit can be used to store extra symbols
  (which are not represented by ASCII code) like
  Greek alphabet and graphical symbols.
• (3) control characters are easily recognized as
  it always starts by 001.
• (4) easily encoded by simply dividing strings to
  7 bit subsequent and matching each subsequent
  with its corresponding ASCII representation.

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• Disadvantage of fixed character representation
• does not take into consideration number of
  occurrence of each digit(frequency) in
  a word. In fact it is reasonable to assume that
  digits with more frequency should be represented
  with smaller number of digits so that we can save
  space.

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Assignment

• Write a computer program (Use any convenient
  language) to perform conversion from decimal to
  all other bases. Test your program with Binary,
  Octal and Hexadecimal.
• Deadline Thursday 27th May 1999
• A Floppy of source program with sample test data
  is required.