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Boolean theorems
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Provide understanding on Boolean theorems and additional elements revolving around it.
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Class notes EL125 (125) Digital Logic & Computer Design
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Class notes EL125 (125) Digital Logic & Computer Design
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Basic Processing Unit
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Penned By: FAISAL HAROONCOURSE: 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
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