MatKul Sistem Digital Bab 2 - Aljabar & Fungsi Boolean

Aljabar Boolean ialah aljabar logika; sifat biner dari proposisi/dalil logis (TRUE or FALSE). Sesuai dng nmnya, aljabar ini digagas oleh George Boole.

Berikut ini disajikan tabel teori aljabar Boolean.

Elementer	1. x + 0 = x	1d. x . 1 = x
	2. x + x' = 1	2d. x . x' = 0
	3. x + x = x	3d. x . x = x
	4. x + 1 = 1	4d. x . 0 = 0
	5, (x')' = x
Commutative	6. x + y = y + x	6d. x . y = y . x
Assocoative	7. x + (y + z) = (x + y) + z	7d. x (yz) = (xy) z
Distributive	8. x(y + z) = xy + xz	8d. x + (yz) = (x + y)(x + z)
Teori DeMorgan	9. (x + y)' = x'y'	9d. (xy)' = x' + y'
Absorption	10. x + xy = x	10d. x (x + y) = x

Bukti Teori DeMorgan

Dengan Truth Table:

x	y	x + y	(x+y)’	x’	y’	x’y’
0	0	0	1	1	1	1
0	1	1	0	1	0	0
1	0	1	0	0	1	0
1	1	1	0	0	0	0

Contoh Soal Penyederhanaan Aljabar Boolean:

F(A, B, C) = ABC + A'B + ABC'

                  = B(AC + A' + AC')

                  = B(A' + A(C + C'))

                  = B(A' + A)

                  = B

Sumber:

File Presentasi Sistem Digital

(To be Continued)