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LOGIC DESIGN

LOGIC DESIGN. APPLICATIONS OF BOOLEAN ALGEBRA. EE410. Ertuğrul Eriş. 1. EE33201 COURSE ASSESMENT MATRIX. BINARY BOOLEAN ALGEBRA APPLICATIONS. BINARY BOOLEAN ALGEBRA S={0,1} Alll the functions are Boolean then represented as formulas. PROPOSITIONS ALGEBRA (Önermeler Cebri)

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LOGIC DESIGN

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  1. LOGIC DESIGN APPLICATIONS OF BOOLEAN ALGEBRA EE410 Ertuğrul Eriş Ertuğrul Eriş 1

  2. EE33201 COURSE ASSESMENT MATRIX

  3. BINARY BOOLEAN ALGEBRA APPLICATIONS • BINARY BOOLEAN ALGEBRA S={0,1} • Alll the functions are Boolean then represented as formulas. • PROPOSITIONS ALGEBRA (Önermeler Cebri) • BINARY LOGIC CIRCUITS • Tearnary logic being studied in theory not available in practice • Practice/Theory • Tearnary could be practical • Ternary: there is no boolean algebra for it. EE410 Ertuğrul Eriş Ertuğrul Eriş 3

  4. PREPOSITIONS ALGEBRA(ÖNERMELER CEBRİ ) • S={D(True, doğru),Y(False,Yanlış)} • Preposition • Could be true or false • Formal logic • Operations • Propositions could be considered as variables, «AND»,»OR»»NOT» are operations . ‘An Investigation of the Laws of Thought, 1854’ George Boole(1815-1864) Ertuğrul Eriş

  5. PROPOSITIONAL ALGEBRAOPERATIONS • Boolean Algebra • SUM, PRODUCT, COMPLEMENT • Propositional Algebra • OR, AND, NEGATION • SUM, OR corresponds «AND/OR» in Spoken languge Ertuğrul Eriş

  6. TRUTH FUNCTIONAL PROPOSITIONAL LOGIC • A propositional function is to be found for a unreliable-run of an elavator system • System is unreliable if • Elavator runnig, it is empty and not called and/or • Elavator runnig, its door is open • Variables: U: running elavator; V: empty; Y:called; Y': not called; z:open door • F = UVY'+UZ =U(VY'+Z) Ertuğrul Eriş

  7. BOOLEAN ALGEBRA/LOGIC CIRCUITS • BOOLEAN ALGEBRA2-ary operations: • pruduct, sum • 1-ary operation: • complement • LOGIC CIRCUITS • AND, OR, • NOT GATES (KAPILARI) Interpretation of gates? Ertuğrul Eriş

  8. BASIC LOGIC GATES: AND, OR, NOT AND OR NOT Comparison of Spoken languge OR and Logic OR. Ertuğrul Eriş

  9. GATES Ertuğrul Eriş

  10. INPUT/OUTPUT BIT STREAMS • In bit streams: • inputs could be repeated • inputs could be any order (indeğendent variables) Input variables:2 x,y Different inputs: 4 Input stream lenght: 5 Ertuğrul Eriş

  11. COMMONLY USED OTHER GATES (TÜVE) (TÜVEYA) (AYRICALI VEYA) Gate interpretation (AYRICALI TÜVEYA) Ertuğrul Eriş

  12. MULTIPLE INPUT GATES Ertuğrul Eriş

  13. LOGIC TYPES • Current Logic: • no current→ logic 0, current → logic 1 • Voltage Logic: • no current→ logic 0, current → logic 1 • Positive Logic: 1 in simgelediği gerilim (akım) voltage (current) representing «logic 1>voltage (current) representing «logic 0» • Negative Logic: voltage (current) representing «logic 1<voltage (current) representing «logic 0» Ertuğrul Eriş

  14. LOGIC TYPES Ertuğrul Eriş

  15. FAN-IN/FAN-OUT(GİRİŞ/ÇIKIŞ YELPAZELERİ) • FAN IN (Giriş yelpazesi ) • Number of inputs (variables, wires) to a gate. • FAN OUT (Çıkış yelpazesi ) • Maximum number of outputs that could feed different gate inputs. Ertuğrul Eriş

  16. COMMERCIAL PACKAGES-1 • Have active elements (transistors) • All have one Vcc and one ground terminal • Two-inputs four gates within a package, total 14 terminals SSI • Genellikle 14 bacaklı • 3-4-input, 2-3 gates • SSI Circuits • ÇOK Bacaklı, LSI, VLSI Ertuğrul Eriş

  17. COMMERCIAL PACKAGES-2 • SSI (Sıngle Scale Integrated Circuits) COMPONENTS • Each package includes less than 10 gates • MSI (Medium Scale Integrated Circuits) COMPONENTS • Each package includes less than 100 gates • LSI (Large Scale Integrated Circuits) COMPONENTS • Each package includes less than 1000 gates • VLSI (Very Large Scale Integrated Circuits) COMPONENTS • Each package includes more than 1000 gates Ertuğrul Eriş

  18. COMMERCIAL PACKAGES-3 Ertuğrul Eriş

  19. LOGIC CIRCUITS(MANTIK DEVRELERİ) • LOGIC CIRCUIT: • Definite number of elements • Two different outputs cannot be connected to the same input (opposite could be true) • complete • TECHNOLOGY • TTL (Transistor-transistor logic) • MOS/CMOS(Complementary metal–oxide–semiconductor) Ertuğrul Eriş

  20. CLASSIFICATION OF LOGIC CIRCUITS • COMBINATIONAL • Outputs are determined uniquely once the ,inputs are known. • Gate only, no memory elements • No feedback • SEQUENTIAL • Memory and gates elements included • Could be feedback Ertuğrul Eriş

  21. COMBINATIONAL CIRCUIT ANALYSIS-1 • Given: • Combinational Circuit, • Input variables, Independent variables • Different inputs • If the number of independent variables is n, • Number of different input is 2n • Input bit stream • A sequence of repeatable different inputs • To be found: • Output, dependent variable • Truth Table, Function • Output bit stream Ertuğrul Eriş

  22. COMBINATIONAL CIRCUIT ANALYSIS-2 Ertuğrul Eriş

  23. COMBINATIONAL CIRCUIT ANALYSIS-3 Same function in different forms, equivalent functions) means different but equivalent circuits. Comparison: number of elements, number of diferent type of elements, Levels (delay time), Fan-in’s Sigle type elements Ertuğrul Eriş

  24. COMBINATIONAL CIRCUIT ANALYSIS-3 Two level circuits SOP (sum of products), POS (Product of sums) two level circuits. Minimal SOP and POS circuits. Ertuğrul Eriş

  25. COMBINETIONAL CIRCUIT SYNTHESIS • Given: • Truth Table, function • Word description (Sözle tanım ) • To be found • Cominational logic circuit which does the given • Determination number of input/output variables, • Selection of the gate types, • Find the topology • Solution (could be more than one!) • Circuit corresponding to first type canonical form • Circuit corresponding to second type canonical form Ertuğrul Eriş

  26. COMBINETIONAL CIRCUIT SYNTHESIS: AN EXAMPLE Ertuğrul Eriş

  27. COMBINETIONAL CIRCUIT SYNTHESIS • CANONICAL SOP/POS CIRCUITS • TWO LEVEL • Delay/Response time, • frequency/hız • FAN-IN • Number of input veriables • TYPE OF GATES • NOT, AND, OR • NAND, NOR Ertuğrul Eriş

  28. COMBINETIONAL CIRCUIT SYNTHESIS Level1 Level2 Level1 Level2 Ertuğrul Eriş

  29. EXAMPLE f(x1x2x3) = Σ 5,6,7= x1x'2x3+x1x2x'3+x1x2x3 = Π 0,1,2,3,4 = (x1+x2+x3) (x1+x2+x'3ı (x1+x'2+x3) (x1+x'2+x'3 )(x1+x2+x3 Ertuğrul Eriş

  30. SINGLE TYPE ELEMENT • Is there a sıngle type of element by which NOT, AND and OR gates realized? • Two Solutions • NAND • NOR • Benefit? Ertuğrul Eriş

  31. TWO LEVEL NAND REALISATION Level1 Level2 Level1 Level2 Level1 Level2 Ertuğrul Eriş

  32. PROGRAM DESIGN DEPT, PROGRAM G R A D U A T E S T U D E N T STUDENT P R OG R A M O U T C O M E S PROGRAM OUTCOMES P R OG R A M O U T C O M E S STATE, ENTREPRENEUR FIELD QALIFICATIONS EU/NATIONAL QUALIFICATIONS KNOWLEDGE SKILLS COMPETENCES NEWCOMERSTUDENT ORIENTIATION GOVERNANCE Std. questionnaire ALUMNI, PARENTS ORIENTIATION STUDENT PROFILE Std. questionnaire FACULTY NGO STUDENT, ??? CIRCICULUM ??? INTRERNAL CONSTITUENT Std. questionnaire EXTRERNAL CONSTITUENT EXTRERNAL CONSTITUENT REQUIREMENTS EU/NATIONAL FIELD QUALIFICATIONS PROGRAM OUTCOMES QUESTIONNAIRES QUALITY IMP. TOOLS GOAL: NATIONAL/INTERNATIONAL ACCREDITION

  33. BLOOM’S TAXONOMYANDERSON AND KRATHWOHL (2001) !!Listening !! Doesn’t exits in the original!!! http://www.learningandteaching.info/learning/bloomtax.htm Ertuğrul Eriş

  34. ULUSAL LİSANS YETERLİLİKLER ÇERÇEVESİ BLOOMS TAXONOMY Ertuğrul Eriş

  35. COURSE ASSESMENT MATRIX LEARNING OUTCOMES Ertuğrul Eriş

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