Boolean theorems

Penned By: FAISAL HAROON
COURSE: COMPUTER ORGANIZATION AND LOGIC DESIGN
ASSIGNMENT: LAB WORK
LOGIC GATES
BOOLEAN ALGEBRA
BOOLEAN THEOREM:

Idem potency X+X=X X•X=X
Redundancy Law X+X`.Y
Double negation X́ = X

Commutative Law X + Y = Y+X

Associative laws X + (Y + Z) = (X + Y) + Z

Distributive laws X (Y + Z) = XY + XZ

Absorption X + XY = X
(X1 + X2 + X3.....) = X1 • X2 • X3.......
De Morgan's theorem
(X1 • X2 • X3.....) = X1 + X2 + X3.......

RULES OF BOOLEAN ALGEBRA
1. X+0=X 7. X.X=X
2. X+1=1 8. X.X= 0
3. X.0=0 9. X.X=X
4. X.1=A 10. X+XB=A
5. X+X=X 11. X+XB=X+B
6. X+X= 1 12. (X+B)(X+C)=X+BC
Verify circuit by using IC’s on breadboard

X+X `= X.X= X.X`=
X X+0 X+1=1 X.0=0 X.1=A X+X=X
1 X 0
0 0 1 0 0 0 1 0 0

1 1 1 0 1 1 1 1 0

Table 4.1

x y Z X + (Y + Z) X + XY X+X.Y x (x + y)
0 0 0 0 0 0 0
0 1 0 1 0 0 0
1 0 1 1 1 1 1
1 1 1 1 1 1 1