Boolean Algebra

Boolean algebra is mathematics of logic circuits. Other useful techniques based on Boolean theorems include the use of Karnaugh maps known as the mapping method and Quine–McCluskey method known as tabular method.

Difference between Boolean Algebra and ordinary algebra
1. In ordinary algebra, the letter symbols take any number of values. In Boolean algebra, they take two values, i.e. 0 and 1.
2. The values assigned to a variable have a numerical significance in ordinary algebra, whereas in Boolean algebra they have a logical significance.
3. ” . ” and ” + ” are the signs of multiplication and addition in ordinary algebra. In Boolean algebra ” . ” means an AND operation and ” + ” means OR operation.

Boolean Theorems
Theorem 1:
(a) 0X = 0 and (b) 1+X = 1
Theorem 2:
(a) 1X = X and (b) 0+X = X
Theorem 3:
(a) X . X . X . ………X = X and (b) X+X+X +***+X = X
Theorem 4:
(a) X . X’ = 0 and (b) X+X’ = 1
Theorem 5:
(a) X+Y = Y +X and (b) XY = YX
Theorem 6:
(a) X+Y +Z = Y +Z+X = Z+X+Y and (b) XYZ = YZX = ZXY
Theorem 7:
(a) X(Y +Z) = XY +XZ and (b) X+YZ = (X+Y) . (X+Z)
Theorem 8:
(a) XY +XY’ = X and (b) (X+Y) (X+Y’) = X
Theorem 9:
(a) (X+Y’). Y = XY and (b)  XY’ +Y = X+Y
Theorem 10:
(a) X+XY = X and (b) X. (X+Y) = X
Theorem 11:
(a) ZX+ZX’Y = ZX+ZY and (b) (Z+X). (Z+X’+Y) = (Z+X). (Z+Y)
Theorem 12:
(a) X.Y +X’.Z+YZ = X.Y +X’. Z and
(b) (X+Y). (X’+Z). (Y +Z) = (X+Y). (X’+Z)
Theorem 13:
(a) (X+Y+Z)’ = X’. Y’. Z’ and (b) (X.Y.Z)’ = X’+Y’+Z’
Theorem 14:
(a) XY +X’Z = (X+Z). (X’+Y) and (b) (X+Y). (X’+Z) = XZ+X’Y

 

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Boolean Alegbra Quiz