cs2100-3-Boolean-Algebra

# cs2100-3-Boolean-Algebra - CS2100Computer Organisation...

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CS2100 Computer  Organisation http://www.comp.nus.edu.sg/~cs2100/ Boolean Algebra (AY2009/2010) Semester 2

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CS2100 Boolean Algebra 2 WHERE ARE WE NOW? Number systems and codes Boolean algebra Logic gates and circuits Simplification Combinational circuits Sequential circuits Performance Assembly language The processor: Datapath and control Pipelining Memory hierarchy: Cache Input/output Preparation: 2 weeks Logic Design: 3 weeks Computer organisation
CS2100 Boolean Algebra 3 CHECK LIST Have you done the Quick Review Questions for Chapter 2 Number Systems and Code? Have you attempted the Self-Assessment Exercise #1 on IVLE Assessment? Have you clarified your doubts on IVLE forum ? Ready to do a pop quiz ?

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CS2100 Boolean Algebra 4 BOOLEAN ALGEBRA Boolean Algebra Precedence of Operators Truth Table Duality Basic Theorems Complement of Functions Standard Forms Minterms and Maxterms Canonical Forms
CS2100 Boolean Algebra 5 DIGITAL CIRCUITS (1/2) Two voltage levels High, true, 1, asserted Low, false, 0, deasserted Signals in digital circuit High Low Signals in analog circuit A digital watch

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CS2100 Boolean Algebra 6 DIGITAL CIRCUITS (2/2) Advantages of digital circuits over analog circuits More reliable (simpler circuits, less noise-prone) Specified accuracy (determinable) Abstraction can be applied using simple mathematical model – Boolean Algebra Ease design, analysis and simplification of digital circuit – Digital Logic Design
CS2100 Boolean Algebra 7 TYPES OF LOGIC BLOCKS Combinational: no memory, output depends solely on the input Gates Decoders, multiplexers Adders, multipliers Sequential: with memory, output depends on both input and current state Counters, registers Memories

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CS2100 Boolean Algebra 8 BOOLEAN ALGEBRA Boolean values: True (1) False (0) Connectives Conjunction (AND) A B; A B Disjunction (OR) A + B; A B Negation (NOT) ; ¬ A; A' A Truth tables A B A B 0 0 0 0 1 0 1 0 0 1 1 1 A B A + B 0 0 0 0 1 1 1 0 1 1 1 1 A A ' 0 1 1 0 Logic gates A B A B A B A+B A A'
CS2100 Boolean Algebra 9 AND (∙)  Do write the AND operator ∙ instead of omitting it.

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cs2100-3-Boolean-Algebra - CS2100Computer Organisation...

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