Aljabar Boolean

Huku-hukum Aljabar Boolean

1.Hukum identitas (i). a+0= a(ii). a.1 = a

2. Hukum idempotent(i). a+a= a(ii). a.a = a

3.Hukum 4.Hukum

Komplemen(i). a+a,= 1(ii). aa , =0

Dominasi(i). a + ab= a(ii). a(a +b) = a

5.Hukum Involusi(i). ( a ,),= a

6.Hukum penyerapan(i). a+ab= a(ii). a (a +b ) = a

7.Hukum 8.Hukum

Komutatif(i). a+b= b +a(ii). a.b =b. a

Asosiatif(i). a+(b+c)=( a+b)+c(ii). a.(b.c) = (a.b).c

9.Hukum distributivei). a+(bc)=( a+b)

10 hukum DeMorgani). (a+b), = a,b,

(a+c)(ii). a.(b+c) = (a.b)+(ac)

(ii).( a.b), = a,

+b,

11. 0/1(i). 0, =1(ii). 1,=0

Symbol : U(union) diganti +And diganti .

Dua Nilai

a b a+b0 0 00 1 11 0 11 1 1

a b a.b0 0 00 1 01 0 01 1 1

DeMorgan:

(a+b)’ =a’b’

a b a+b (a+b)’

a’ b’ A’b’

0 0 00 1 11 0 11 1 1

(a.b)’= a’ +b’

a b a.b (a.b)’ a’ b’ (a’+b’)0 0 00 1 11 0 11 1 1

Hukum Distributive : (a+b).(a+c) = a +bc

a b c a+b a+c bc (a+b).(a+c) a +bc0 0 0 0 0 0 0 00 0 1 0 1 0 0 00 1 0 1 0 0 0 01 0 0 1 1 0 1 10 1 1 1 1 1 1 11 0 1 1 1 0 1 11 1 0 1 1 1 1 11 1 1 1 1 1 1 1

Hukum Distributive: a.(b+c) = (a.b) +(ac)

a b c a.b a.c b +c (a.b)+(a.c) a .(b +c)0 0 0 0 0 0 0 00 0 1 0 0 1 0 00 1 0 0 0 1 0 01 0 0 0 0 0 0 00 1 1 0 0 1 0 01 0 1 0 1 1 1 11 1 0 1 0 1 1 11 1 1 1 1 1 1 1

Metode peta Karnaugh

x/y Y,=0 Y=1X,=0 X,y, X,yX=1 xY, xy

x/y 0 10 X,y

,X,y

1 xY, xy

Gambarkan peta Karnaugh: f(x,y)= xy+x,y

x/y 0 10 0 11 0 1

Gambarkan peta Karnaugh f(xy)=xy,+xy

x/y 0 10 0 01 1 1

SEDERHANAKAN FUNGSI BOOLEAN BERIKUT INI

1. F(x,y) = x + x’y(x+X’)(x+y)………distributif1.(x+Y)…………….komplemenX+y………………….identitas

2. F(x,y)=x(x’+y)Xx,+xy……………distributif0+xy………………komplemen

Xy …………….identitas

3. F(x,y,z) = x’y’z +x’yz +xy’X’z(y’+y)+xy’……distributifX’z.1+xy’……….. komplemenX’z+xy’…….. identitas

4. 4.F(x,y,z) = xz’+y’z+xyz’Xz’.1 +y’z +xyz’…identitasXz’(1+y) +y’z……distributiveXz’ .1 + y’z………dominasiXz’ +y’z………….identitas

5. F(x,y,z)= (x+z’)(y’+z)(x+y+z’)

Silakan dicoba sendiri…….

Symbol electronic digital Circuits

1.Gerbang NOT

2. Gerbang A ND

3. Gerbang OR

4. Gerbang NOR X

X

X

X Y

X+y

Y

X’X

5. Gerbang X OR

6. Gerbang NAND X

7. Gerbang X NOR X

N0T OR AND NOR NAND XOR XNORx y X, XVY XY (X+Y)’ (XY)’ X * Y (X * Y)’1 1 0 1 1 0 0 0 11 0 0 1 0 0 1 1 00 1 1 1 0 0 1 1 00 0 1 0 0 1 1 0 1

Rangkaian Digital

Gambar 1

1.Gambarkan rangkaian sederhananya

a dcb

2.Gambarkan rangkaian sederhananya

b c da

3.Gambarkan rangkaian sederhananya

b c da