data manipulation n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Data Manipulation PowerPoint Presentation
Download Presentation
Data Manipulation

Loading in 2 Seconds...

play fullscreen
1 / 24

Data Manipulation - PowerPoint PPT Presentation


  • 86 Views
  • Uploaded on

Data Manipulation. CSCI130 Instructor: Dr. Imad Rahal. Layered Architecture. 0. clock. 16-3000 MHz (~3.0 GHz). Overview of Computer Hardware. “necessary” components of a computer CPU , Main memory components needed for convenience computer won’t be very practical to use otherwise

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Data Manipulation' - devona


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
data manipulation

Data Manipulation

CSCI130

Instructor: Dr. Imad Rahal

slide3

0

clock

  • 16-3000 MHz (~3.0 GHz)
overview of computer hardware
Overview of Computer Hardware
  • “necessary” components of a computer
    • CPU, Main memory
  • components needed for convenience
    • computer won’t be very practical to use otherwise
    • Secondary/Auxiliary storage, I/O devices
  • Main memory
    • Connects to the motherboard
    • Divided into two major parts
overview of computer hardware1
Overview of Computer Hardware
      • RAM --- Random Access Memory
        • memory registers which store data before/after CPU processing
        • Available for users and programs so store data in and read data from
        • Volatile --- does not persist when no electric power is supplied to its circuits
      • ROM --- Read Only Memory
        • Permanent
        • Holds programs that are vital for the operation of the computer
        • As the name indicates, can be read but never altered
  • CPU
    • Central Processing Unit
    • Single silicon chip with circuits attached to it
    • Known as microprocessor
    • Sits on a circuit board known as the motherboard
data manipulation1
Data Manipulation
  • Computing an answer to an equation:
    • 5*3 + 62 – 7
    • Assume our computer can’t directly multiply, subtract, or raise to power
  • Multiplication task:
    • 1: Get 1st number, Number_1
    • 2: Get 2nd number, Number_2
    • 3: Answer = 0
    • 4: Add Number_1 to Answer
    • 5: Subtract 1 from Number_2
    • 6: if Number_2>0, go to step 4
    • 7: Stop
data manipulation2
Data Manipulation
  • All tasks done by a general-purpose computer can be accomplished through the following set of operations
    • Input/output
      • Not mentioned in book but important
    • Store data
      • numbers (positive, negative or fractions), text, pictures, etc …
    • Compare data (numbers, pictures, sounds, letters)
    • Add
    • Move data from one storage (memory) location to another
      • Editing a text document
data manipulation3
Data Manipulation
  • Adding and comparing bit patterns is sufficient to achieve an “operational” machines
    • Hard-wired vs. programmed
  • This is done by circuits for adding and comparing bit patterns in registers
  • Circuits are made up of logical gates
  • Gates and Truth Tables
    • Gates needed are NOT, AND, and OR
    • NOT Gate:
      • Single input and single output
      • Reverses input
        • 1  0 and 0  1
        • If there is a strong electric current
          •  shut it off
        • If there is no/weak electric current
          •  turns it on
        • Like a power switch
data manipulation4
Data Manipulation
  • AND Gate
    • Accepts two inputs (or more) and yields one output
    • Output is 0 when any input is 0
    • Requires power coming from both lines in order to give out power
data manipulation5
Data Manipulation
  • OR Gate
    • Accepts two inputs and yields one output
    • Output is 1 when any input is 1
    • Requires power coming from at least one of the input lines in order to give out power
data manipulation6
Data Manipulation
  • These three simple gates are combined to create circuits that perform more complicated operations
    • Circuits, in turn, might then be used (thru programs) to perform even more complicated tasks
  • Gate combinations can be expressed in three ways
    • (1) Through Expressions
      • A AND B  AB
      • A OR B  A+B
      • NOT A  A’
        • A’B’ + AB
slide12

NOT

AND

OR

  • Enough rows to hold all input combinations
    • 1 letter  21 rows
    • 2 letters  22 rows
    • 3 letters 23 rows
    • n letters 2n rows
  • (2) Through Circuit diagrams
    • Given an expression
    • Draw a gate after its inputs have been drawn
    • Try A’B’ + AB
  • (3) Through Truth Tables
    • Each of the representations can be derived from the other
    • Derivetruth tablegiven expression
      • One column for each letter
      • Make 1 additional column for every sub-expression (order: parentheses, NOTs, ANDs, ORs)
practice
Practice
  • Try A + (A.B’+B.C)’
    • How many gates?
    • Design circuit
      • Parenthesis, NOT, AND, and then OR
    • Find truth table
      • How many rows?
data manipulation7
Data Manipulation
  • given a circuit diagram expression  truth table
    • Mark every output wire by its label
sum of products method
Sum of Products Method
  • Given a truth table, how to find expression?
  • Sum-of-product method
    • For each row with a 1 in the final column
      • AND letters with a 1 in their column and negation of the letters with a 0 in their column
      • Connectthe resulting AND groups with ORs
  • A’B’
  • A’B
  • Ignore
  • AB

 A’B’+A’B+AB

 Complicated and UGLY  !!! (requires space, and is costly and slow)

simplification
Simplification
  • Why simplify?
    • UGLY
    • Circuits supposed to be as simple as possible
      • Save on speed (operation execution---fewest gates as possible because every gates slows the operation a bit)
        • (in general) more gates  more time
      • Save space (on motherboard)
        • Notebooks!
      • Save money(not as critical)
simplification of expressions
Laws of Boolean Algebra

Commutative Law

A+B = B+A, A.B=B.A

E.g. addition and multiplication

Distributive Law

A.(B+C) = A.B + A.C, E.g. multiplication over addition

A+(B.C) = (A+B).(A+C)

Idempotency Law

A+A = A, A.A=A

Double Negation

(A’)’ = A

E.g. -(-5) = +5

DeMorgan’s Law

(A+B)’ = A’.B’,

(A.B)’ = A’+B’

Identities

A.0 = 0, A+0=A

A.1 = A, A+1=1

A.A’ = 0, A+A’ = 1

Simplification of Expressions
simplification of expressions1
Simplification of Expressions
  • To simplify (reduce the number of gates)
    • (1) look at two or more terms sharing one or more letters
      • use distributive Law
      • AB + AC = A(B+C)
  • A’B’+A’B+AB // distributive law (#1)
    • A’(B’+B) + AB // identities
    • A’(1) + AB // identities
    • A’ + AB // distributive law (#2)
    • (A’+A)(A’+B) // identities
    • (1)(A’+B) // identities
    • A’+B
simplification of expressions2
Simplification of Expressions
  • A.B’+A’.B’+A’.B
  • B’. (A + A’) + A’.B
  • B’ + A’.B
  • (B’ + A’).(B’ + B)
  • B’ + A’
  • (B.A)’

Distributive law

Distributive

Identities

IdempotencyLaw

Distributive

DeMorgans

Idempotency Law

Distributive Law

simplification of expressions3
Simplification of Expressions
  • AB’+B+B’+AB
  • AB’+1 + AB
  • 1

Identities

Identities

simplification of expressions4
Simplification of Expressions

Distributive law

IdempotencyLaw

Idempotency Law

Distributive Law

circuit for equivalence
Circuit for Equivalence
  • We need to compare the data contents of two registers
  • Data is in binary
    • compare them bit by bit
    • Start right to left
    • Take two inputs
      • If both 0s or 1s, output 1
      • Otherwise, output a zero
    • A’B’+AB
      • (Sum of products method)
        • Ask yourself: when am I getting a 1?
        •  (A+B)’ +AB (simpler)
      • Draw circuit