Κανόνες άλγεβρας Boole

Home » Θεωρία » Digital » Κανόνες άλγεβρας Boole
Digital
x*x=x x*x’=0 x+1=1 x+0=x (α+β)’= α’*β’     DeMorgan x+(x*y)=x 
x+x=x x+x’=1 x*1=x x*0=0 (α*β)’= α’+β’     DeMorgan x*(x+y)=x


 

Παραδείγματα:

 

1. Y = (A+1)*A’ + B*0*(B+0) =

=      1*A’    +    0 * B =

=        A’     +     0 =

=        A’

 

2. Y = (A’+0)*A + (B*1)*(B’+0) =

=     A’*A    +    B   *  B’ =

=        0      +        0 =

= 0

 

3. Y = (A+B)*0 + (A’+B’)*1 =

=             0       +  A’ + B’ =

= A’ +B’

 

4. Y = (A + B’) * ( B * B’) + (A + 1)*A’ =

=        (A + B’) * 0            +       1*A’=

=                0                   +       A’ =

=  A’

 

5. Y = A’ * B’ * C’ + A’ * B * C’ + A * B’ *C’ + A  * B * C’ =

= (A’ * B’ * C’ +  A * B’ *C’) +  ( A’ * B * C’ + A  * B * C’) =

= B’ * C’* (A’ + A)                +  B * C’ * ( A’ + A ) =

= B’ * C’ * 1                        +    B * C’ * 1 =

= B’ * C’ + B * C’ =

= C’ * (B’ + B) =

= C’ * 1 =

= C’