Data Manipulation

1. Data Manipulation CSCI130 Instructor: Dr. Imad Rahal

2. Layered Architecture

3. 0 clock • 16-3000 MHz (~3.0 GHz)

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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)

13. Practice • Try A + (A.B’+B.C)’ • How many gates? • Design circuit • Parenthesis, NOT, AND, and then OR • Find truth table • How many rows?

14. Data Manipulation • given a circuit diagram expression  truth table • Mark every output wire by its label

15. 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)

16. 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)

17. 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

18. 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

19. 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

20. Simplification of Expressions • AB’+B+B’+AB • AB’+1 + AB • 1 Identities Identities

21. Simplification of Expressions Distributive law IdempotencyLaw Idempotency Law Distributive Law

22. 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

23. Circuit for Equivalence

24. Circuit for Addition