Boolean Expression

4.2.2.1   Peraturan Boolean Algebra.

Ekspresi Boolean boleh di ringkaskan dan boleh di manipulasi.Jadual 2 menunjukkan peraturan asas Boolean Algebra dapat membantu memanipulasi dan menyelesaikan persamaan logik.

                                       Jadual 4 – 2 : Peraturan Asas Boolean Algebra.

	AND Form	OR Form
Identity Law	A.1 = A	A + 0 = A
Zero and One Law	A.0 = 0	A + 1 = 1
Inverse Law	A. = 0	A +  = 1
Idempotent Law	A.A = A	A + A = A
Commutative Law	A.B = B.A	A + B = B + A
Associative Law	A.( B.C ) = ( A.B ).C	A + ( B + C ) = ( A+B ) + C
Distributive Law	A + ( B.C ) = (A + B ).( A + C )	A.( B + C ) = ( A.B ) + ( A.C )
Absorption Law	A( A + B) = A	A + A.B = A A + A’B = A + B
DeMorgan’s Law	( ) = +	( ) = .
Double Complement Law	= X	= X

 

DERIVATION

Absorption Law Derivation

A( A+B ) = A ( 1 + B )                                               à1 + B = 1                          

                = A(1)                                                         à A . 1 = A

                = A

Absorption Law Derivation

A( A + B ) = AA + AB                                              à A = A . A

                  = A + AB                                                 àA ( 1 + B ) = A (1)

                  = A

Absorption Law Derivation

A + A’B = ( A + AB) + A’B                                    à A = A .A

               = ( AA + AB ) + A’B                               à ( AA + BB ) + A’B = AA + ( AB + A’B )

               = AA + AB + A’B

               = ( A + A’ ) + ( A + B)                             à ( A + A’) (A + B) = AA +AB + A’B

              = 1. ( A + B )                                            à A + A’ = 1

           = ( A + B ) 

Distributive Law Reverse Derivation

( A + B ) . ( A + C ) = AA + AC + AB + BC                          à AA = A   

                                = A + AC +AB +BC                               à A ( 1 + C ) = A( 1) = A

                                = A + AB + BC                                      à A (1 + B ) = A ( 1) = A

                               = A ( 1 + B ) + BC

                               = A . 1 + BC

                               = A + BC

4.2.2.1.1   De Morgan’s Law

“ jika garisan di putuskan , maka tandanya akan berubah”

            =  +

              = .