Selasa, 03 Desember 2013

Aljabar Boole - Rangkaian Digital

ALJABAR BOOLE
(Dualitas Persamaan Boole)




A + B = B + A
Gerbang Logika
 
Tabel Kebenaran
A
B
A + B
B + A
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1


A + ( B + C ) = (A + B) +C
Gerbang Logika

Tabel Kebenaran
A
B
C
A + B
B + C
A + ( B+C )
(A+B) + C
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1

A ( B + C ) = AB +AC
Gerbang Logika

Tabel Kebenaran
A
B
C
B + C
AB
AC
A(B + C)
AB + AC
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1


A + 0 = A
Tabel Kebenaran
A
0
A + 0
0
0
0
0
0
0
1
0
1
1
0
1


A + 1 = 1
Tabel Kebenaran
A
1
A + 1
0
1
1
0
1
1
1
1
1
1
1
1


A + A = A
Tabel Kebenaran
A
A
A + A
0
0
0
0
0
0
1
1
1
1
1
1


A + A’ = 1
Gerbang Logika

Tabel Kebenaran
A
A’
1
A + A’
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1

  
A’ + B’ = A’ . B’
Gerbang Logika

Tabel Kebenaran
A
B
A + B
A’+ B’
A . B
A’.B’
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1


A + AB = A
Gerbang Logika


 Tabel Kebenaran
A
A’
1
A + A’
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1


A + A’ B = A + B
Gerbang Logika

Tabel Kebenaran
A
A’
B
A’ B
A + A’ B
A + B
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1




A . B = B . A

Gerbang Logika
Tabel Kebenaran
A
B
A . B
B . A
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1


A (BC) = (AB) C
Gerbang Logika
Tabel Kebenaran
A
B
C
AB
BC
A(BC)
(AB)C
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1

A + (BC) = (A+B).(A+ C)
Gerbang Logika

Tabel Kebenaran
A
B
C
BC
A+B
A+C
A + (BC)
(A+B).(A+ C)
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1


A . 1 = A
Tabel Kebenaran
A
1
A . 1
0
1
0
0
1
0
1
1
1
1
1
1


  A . 0 = 0
Tabel Kebenaran
A
0
A . 0
0
0
0
0
0
0
1
0
0
1
0
0

A . A = A
Tabel Kebenaran
A
A
A . A
0
0
0
0
0
0
1
1
1
1
1
1


A . Ā = 0
Gerbang Logika

Tabel Kebenaran
A
A’
1
A . A’
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0


A’ . B’ = A’ + B’
Gerbang Logika

Tabel Kebenaran
A
B
A . B
A + B
A’ . B’
A’ + B’
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0



A . (A + B) = A
Gerbang Logika

Tabel Kebenaran
A
B
A + B
A . (A + B)
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1



A.(A’ + B) = AB
Gerbang Logika

Tabel Kebenaran
A
A’
B
A’ + B
A.(A’ + B)
A . B
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0






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Image Enhancement

Image Enhancement Diketahui : r 1 = 0,3   ; r 2 =   0,5    ; r 3 = 0,8   s 1 = 0,1   ; s 2 =   0,4   ; s 3 =   0,6 ...