- Boolean Algebra #1
- Boolean algebra #2: Basic problems
- Boolean algebra #3: Basic problems
- Boolean algebra #4: Different terminology and notations
- Boolean algebra #5: Truth tables - introduction
- Boolean algebra #6: Truth tables - variables combinations
- Boolean algebra #7: Truth tables - example problems
- Boolean algebra #8: Truth tables - into expressions/statements
- Boolean algebra #9: truth tables - into expressions (continued)
- Boolean algebra #10: Truth tables - example
- Boolean algebra #11: Truth tables - example (continued)
- Boolean algebra #12: Karnaugh maps
- Boolean algebra #13: Karnaugh maps example (continued)
- Boolean algebra #14: Karnaugh maps - short summary
- Boolean algebra #15: Karnaugh maps - from expressions
- Boolean algebra #16: Karnaugh maps - from expressions (continued)
- Boolean algebra #17: Karnaugh maps - grouping
- Boolean algebra #18: Karnaugh maps - grouping (continued)
- Boolean algebra #19: Karnaugh maps - getting the result
- Boolean algebra #20: Karnaugh maps - getting the result (continued)
- Boolean algebra #21: Karnaugh maps - getting the result (continued)
- Boolean algebra #22: Karnaugh maps - final example
- Boolean algebra #23: DeMorgan's theorem - introduction
- Boolean algebra #24: DeMorgan's theorem - examples
Boolean algebra #25: DeMorgan's theorem - examples (continued)- Boolean algebra #26: Sum of products (SOP) form
- Boolean algebra #27: Standard SOP form
- Boolean algebra #28: Standard SOP form (continued)
- Boolean algebra #29: Product of sums (POS) form
- Boolean algebra #30: Product of sums (POS) form (continued) Web Tutorials
- Karnaugh Maps 1
- Karnaugh Maps 2
- Karnaugh Maps 3
Simplification of Boolean Logic
Boundedness Law
Boundedness Law
X + 1 = 1
X . 0 = 0
Absorption Law
X + (X . Y) = X
X . (X + Y ) = X
Elimination Law
X + (X' . Y) = X + Y
X.(X' + Y) = X.Y
Unique Complement theorem
If X + Y = 1 and X.Y = 0 then X = Y'
Involution theorem
X'' = X
0' = 1
Associative Properties
X + (Y + Z) = (X + Y) + Z
X . ( Y . Z ) = ( X . Y ) . Z
Duality Principle
Interchanging AND and OR operators and replace 0's by 1's and 1's by 0's.
Duality of X.Y+Z' = (X'+Y').Z
Minterms and Maxterms
Any boolean expression may be expressed in terms of either minterms or maxterms.
Literal
A literal is a single variable within a term which may or may not be complemented.
A minterm is the product of N distinct literals where each literal occurs exactly once.
A maxterm is the sum of N distinct literals where each literal occurs exactly once.
The minterms and maxterms for a two-variable expression is
A B Minterm Maxterm
0 0 A'.B' A+B
0 1 A'.B A+B'
1 0 A.B' A'+B
1 1 A.B A'+B'
The minterms and maxterms for a three variable expression is
A B C Minterm Maxterm
0 0 0 A'.B'.C' A+B+C
0 0 1 A'.B'.C A+B+C'
0 1 0 A'.B.C' A+B'+C
0 1 1 A'.B.C A+B'+C'
1 0 0 A.B'.C' A'+B+C
1 0 1 A.B'.C A'+B+C'
1 1 0 A.B.C' A'+B'+C
1 1 1 A.B.C A'+B'+C'
