Boolean Algebra
The two-valued system of algebra was invented by George
Boole in 1854. Also called switching algebra
Based on 5 axioms
X = 0 if X ≠ 1
If X = 0, then X’ = 1
0.0=0
1.1=1
0.1=0
Or their duals
X = 1 if X ≠ 0
If X = 1, then X’ = 0
1+1=1
0+0=0
1+0=0+1=1
University of KwaZulu-Natal 1
6-1
ENEL2EBH2 2010
, One Variable Theorems
These can be proved using the axioms
University of KwaZulu-Natal 2
6-2
ENEL2EBH2 2010
The two-valued system of algebra was invented by George
Boole in 1854. Also called switching algebra
Based on 5 axioms
X = 0 if X ≠ 1
If X = 0, then X’ = 1
0.0=0
1.1=1
0.1=0
Or their duals
X = 1 if X ≠ 0
If X = 1, then X’ = 0
1+1=1
0+0=0
1+0=0+1=1
University of KwaZulu-Natal 1
6-1
ENEL2EBH2 2010
, One Variable Theorems
These can be proved using the axioms
University of KwaZulu-Natal 2
6-2
ENEL2EBH2 2010
