Boolean Algebra and Logic Gates CE 40 B 18 June 2003.
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Transcript of Boolean Algebra and Logic Gates CE 40 B 18 June 2003.
Boolean Algebra and Logic Gates
CE 40 B18 June 2003
Basic Definitions Common Postulates
Closure Associative Law Commutative Law Identity Element Inverse Distributive Law
Field set of elements with two binary operators
Axiomatic Definition of Boolean Algebra
George Boole Two binary operators (+ and ·) Huntington Postulates
Closure, Identity, Commutative, Distributive, Complement
Show that Huntington Postulates are valid for B = {0,1}
Basic Theorems and Properties of Boolean Algebra
Duality Expression remains valid even after
operators and identity elements are interchanged
Some theorems x + xy = x (x + y)’ = x’y’
Boolean Functions
Logical relationship between binary variables
Can be represented by a truth table Can be transformed into a logic
diagram Example: f = x + y’z
Example – f = x + y’z
Canonical and Standard Forms
Maxterms and Minterms Canonical Forms
Sum of Minterms Product of Maxterms
Standard Forms Sum of products Product of sums
Other Logic Operations
Formed from combination AND, OR, and NOT.
16 possible functions for 2 binary variables
Digital Logic Gates
Integrated Circuits
IC Silicon chip containing electronic
components for constructing digital gates
Different Levels of Integration Circuit complexity Number of logic gates in one package SSI, MSI, LSI, VLSI
Integrated Circuits Digital Logic Families
Circuit technology – how the logic gates are constructed
TTL, ECL, MOS, CMOS Characteristics
Fan-out Fan-in Power dissipation Propagation delay Noise margin
Integrated Circuits
Computer-Aided Design Complex designs require computers Electronic Design Automation (EDA) Hardware Description Language (HDL)
Verilog, VHDL