LOGIC DESIGN

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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

APPLICATIONS OF BOOLEAN ALGEBRA

EE410

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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

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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)

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

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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)

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BOOLEAN ALGEBRA/LOGIC CIRCUITS
• BOOLEAN ALGEBRA2-ary operations:
• pruduct, sum
• 1-ary operation:
• complement
• LOGIC CIRCUITS
• AND, OR,
• NOT

GATES (KAPILARI)

Interpretation of gates?

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BASIC LOGIC GATES: AND, OR, NOT

AND

OR

NOT

Comparison of Spoken languge OR and Logic OR.

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GATES

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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

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COMMONLY USED OTHER GATES

(TÜVE)

(TÜVEYA)

(AYRICALI VEYA)

Gate interpretation

(AYRICALI TÜVEYA)

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MULTIPLE INPUT GATES

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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»

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LOGIC TYPES

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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.

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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

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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

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COMMERCIAL PACKAGES-3

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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)

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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

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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

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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

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COMBINATIONAL CIRCUIT ANALYSIS-3

Two level circuits

SOP (sum of products), POS (Product of sums) two level circuits.

Minimal SOP and POS circuits.

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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

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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

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COMBINETIONAL CIRCUIT SYNTHESIS

Level1 Level2

Level1 Level2

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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

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

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TWO LEVEL NAND REALISATION

Level1 Level2

Level1 Level2

Level1 Level2

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PROGRAM DESIGN

DEPT, PROGRAM

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PROGRAM OUTCOMES

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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,

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CIRCICULUM

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INTRERNAL CONSTITUENT

Std.

questionnaire

EXTRERNAL CONSTITUENT

EXTRERNAL CONSTITUENT

REQUIREMENTS

EU/NATIONAL

FIELD QUALIFICATIONS

PROGRAM OUTCOMES

QUESTIONNAIRES

QUALITY IMP. TOOLS

GOAL: NATIONAL/INTERNATIONAL ACCREDITION

BLOOM’S TAXONOMYANDERSON AND KRATHWOHL (2001)

!!Listening !!

Doesn’t exits in the original!!!

http://www.learningandteaching.info/learning/bloomtax.htm

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ULUSAL LİSANS YETERLİLİKLER ÇERÇEVESİ

BLOOMS TAXONOMY

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COURSE ASSESMENT MATRIX

LEARNING OUTCOMES

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