Computer Science 210 Computer Organization

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Computer Science 210Computer Organization

• Course Introduction
• Binary Integers

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A Definition of Computer Science

• Computer Science the study of algorithms,
  including
• Their formal and mathematical properties
• Their hardware realizations
• Their linguistic realizations
• Their applications
• Gibbs and Tucker, A Model Curriculum for a
  Liberal Arts Degree in Computer Science, Comm.
  Of the ACM 29, no. 3(March,1986)

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Our Core Requirements
CS210 Computer Organization(Their hardware
realizations)
CS211Data Structures andAlgorithms(Their
mathematical properties)
Algorithms
CS313 Theory of Computation(Their formal
properties)
CS312Programming LanguageDesign(Their
linguistic realizations)
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Their Applications

• Interactive Computer Graphics
• Image Processing
• Database Management
• Artificial Intelligence
• Genetic Algorithms
• etc.

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Topics for Course

• Internal representation of data and instructions
• Major components of computer - overview
• Low level programming of computer assembly and
  machine language
• High level programs as seen by computer
• Logic gates and computer circuitry
• Detailed look at major components

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Why?

• General education as a computer science
  professional
• Better understanding of high level programming
• More efficient use of computer
• Better understanding of compilers, operating
  system issues
• May have need to operate at low levels from time
  to time

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Review of Binary SystemsHumans use

• Decimal Numbers (base 10)
• Decimal Fractions (23.27)
• Letters for text

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Computers

• Binary Numbers (base 2)
• Binary fractions and floating point
• ASCII (or Unicode) codes for characters (A?65)

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Why binary?

• Information is stored in computer via voltage
  levels.
• Using decimal would require 10 distinct and
  reliable levels for each digit.
• This is not feasible with reasonable reliability
  and financial constraints.
• Everything in computer is stored using binary
  numbers, text, programs, pictures, sounds,
  videos, ...

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Decimal Non-negatives

• Base 10
• Uses decimal digits 0,1,2,3,4,5,6,7,8,9
• Positional System - position gives power
• Example 3845 3x103 8x102 4x101 5x100
• Positions 543210

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Binary Non-negatives

• Base 2
• Uses binary digits (bits) 0,1
• Positional system
• Example 1101 1x23 1x22 0x21 1x20

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Conversions

• External Internal(Human)
  (Computer) 25 11001
  A 01000001
• Humans want to see and enter numbers in decimal.
• Computers must store and compute with bits.

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Binary to Decimal Conversion

• Algorithm
• Expand binary number using positional scheme.
• Perform computation using decimal arithmetic.
• Example110012 ? 1x24 1x23 0x22 0x21
  1x20 24 23 20 16 8
  1 2510

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Decimal to Binary

• Algorithm 1 Set A to 0 (all bits 0) While N ?
  0 do Find largest P with 2P ? N Set bit in
  position P of A to 1 Set N to N - 2P

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Decimal to binary - Example

• Example Convert 32410 to binary N
  Power P A .
  324 256 8 100000000 68
  64 6 101000000 4 4 2
  101000100 0
• 32410 1010001002

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Decimal to Binary

• Algorithm 2 While N ? 0 do Set N to N/2
  (whole part) Record the remainder (1 or 0) Set
  A to remainders in reverse order

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Decimal to binary - Example

• Example Convert 32410 to binary N
  Rem N Rem 324 162 0 5 0
  81 0 2 1 40 1 1 0 20 0 0 1 10 0
• 32410 1010001002

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Binary Addition

• One bit numbers 0 1 0 0
  1 1 1 10
• Example 1111 1 110101 (53)
  101101 (45) 1100010 (98)

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Overflow

• In a given type of computer, the size of integers
  is a fixed number of bits.
• 16 or 32 bits are popular choices
• It is possible that addition of two n bit numbers
  yields a result requiring n1 bits.
• Overflow is the term for an operation whose
  results exceeds the size allowed for a number.

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Negatives Twos complement

• With N bit numbers, to compute negative
• Invert all the bits
• Add 1
• Example -25 in 8-bit twos complement
• 25 ? 00011001
• Invert bits 11100110
• Add 1 1 11100111

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2s Complement Examples

• Compute negative of -25 (8-bits)
• We found -25 to be 11100111
• Invert bits 00011000
• Add 1 00011001
• Recognize this as 25 in binary
• Add -25 and 37 (8-bits)
• 11100111 (-25) 00100101 (
  37) (1)00001100
• Recognize as 12

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Facts about 2s Complement

• Leftmost bit tells whether number is positive or
  negative
• 2s complement is same as before for positives

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2s complement to decimal (examples)

• Assume 8-bit 2s complement
• X 11011001 -X 00100110 1 00100111
  32421 39 (decimal) So, X -39
• X 01011001Since X is positive, we have X
  641681 89

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Ranges for N-bit numbers

• Unsigned (positive)
• 000000 or 0
• 111111 which is 2N-1
• For N8, 0 - 255
• 2s Complement
• 100000 which is -2N-1
• 011111 which is 2N-1 - 1
• For N8, -128 to 127

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Octal Numbers

• Base 8 Digits 0,1,2,3,4,5,6,7
• Not so many digits as binary
• Easy to convert to and from binary
• Often used by people who need to see the internal
  representation of data, programs, etc.

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Octal Conversions

• Octal to Binary
• Simply convert each octal digit to a three bit
  binary number.
• Example 5368 101 011 1102
• Binary to Octal
• Starting at right, group into 3 bit groups
• Convert each group to an octal digit
• Example 110111111010102 011 011 111 101
  010 337528

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Hexadecimal

• Base 16 Digits 0,,9,A,B,C,D,E,F
• Hexadecimal ? Binary
• Just like Octal, only use 4 bits per digit.
• Example 98C316 1001 1000 1100 00112
• Example110100111010112 0011 0100 1110 1011
  34EB