Table of Contents
Combinational Logic
Switching Algebra
Switching Algebra (cont’d)
Basic Theorems
Proofs in Switching Algebra
Other Theorems
de Morgan’s Law
Duality - A Meta-Theorem
Formal Definition of Boolean Algebra B
Applying Boolean Algebra
Applying Boolean Algebra (cont’d)
Applying Boolean Algebra (cont’d)
Specification of Switching Functions
Specification of Switching Functions (cont’d)
All Possible Functions of One Variable
All Possible Functions of Two Variables
All Possible Functions of N Variables
Canonical forms: SOP
Canonical Forms: SOP (cont’d)
Canonical Forms: POS
Sum-of-Products and Product-of-Sums
Implementation with Logic Gates
Logic Gates for Canonical Forms
From Boolean Functions to Gates
From Canonical Forms to Gates
Implementing Boolean Functions
Combinational Logic
Analysis
Using De Morgan’s Law
Analysis Examples
Analysis Examples (cont’d)
Analysis Examples (cont’d)
Two-level Realizations
Optimization of Combinational Logic
Two-level Optimization
Uniting Theorem
Boolean Cubes
Boolean Cubes (cont’d)
Cube Example
Larger Cubes
Cubes and Literals
Two-Level Simplification
Two-level Simplification (cont’d)
Two-Level Simplification (cont’d)
Two-Level Simplification (cont’d)
Two-Level Simplification (cont’d)
Minimization Example
Minimization Example (cont’d)
Example of Don’t Cares
Incompletely Specified Functions
Two-Level Simplification
Two-Level Simplification (cont’d)
Definitions for Two-Level Simplification
Examples to Illustrate Terms
Algorithm for Two-Level Minimization
Example of Two-Level Minimization
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