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Boolean Algebra Theorems

 

Theorems of Boolean Algebra derived from Huntington postulates - Discussion

T1. Theorem:- x + x = x

x + x = (x + x)*1= (x + x)(x + x’)

From P8, x + xx’ = x

From duality of T1

T2. Theorem:- x*x = x

T3. Theorem:- x + 1 = 1

x + 1= (x + 1).1= (x +1)*(x + x’)

From P8, (x + 1*x’)= (x + x’)= 1

 

From duality of T3

T4. Theorem:- x.0 = 0

T5. x + (y + z) = (x + y) + z

From duality of T5

T6. Theorem:- x(yz) = (xy)z

T7. Theorem:- (x’)’ = x

From duality of T10

T11. Theorem:- x(x+y) = x

T8. Theorem:- (x + y)’ = x’y’

T9. Theorem:- (xy)’ = x’ + y’

T10. Theorem:- x + xy = x

Binary Numbers.
1s_complement.
2s_complement.
Binary Subtraction.
Binary Sub. Ex's.
Sign_magnitude.
SignM EX.
Gray Coding.
BCD coding.
Digital gates.
NAND NOR & XNOR.
Theorems.
Boolean Functions.
BFunc Examples.
Minterm Maxterm.
Sum of Minterms.
Prdt of Maxterms.
2 var K-map.
3 var K-map.
4 var K-map.
5 var K-map.
Prime Implicant.
PI example.
K-map Ex's.
KMap minimization.
2 var EX.