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.
(a) 0X = 0 and (b) 1+X = 1
(a) 1X = X and (b) 0+X = X
(a) X . X . X . ………X = X and (b) X+X+X +···+X = X
(a) X . X’ = 0 and (b) X+X’ = 1
(a) X+Y = Y +X and (b) XY = YX
(a) X+Y +Z = Y +Z+X = Z+X+Y and (b) XYZ = YZX = ZXY
(a) X(Y +Z) = XY +XZ and (b) X+YZ = (X+Y) . (X+Z)
(a) XY +XY’ = X and (b) (X+Y) (X+Y’) = X
(a) (X+Y’). Y = XY and (b) XY’ +Y = X+Y
(a) X+XY = X and (b) X. (X+Y) = X
(a) ZX+ZX’Y = ZX+ZY and (b) (Z+X). (Z+X’+Y) = (Z+X). (Z+Y)
(a) X.Y +X’.Z+YZ = X.Y +X’. Z and
(b) (X+Y). (X’+Z). (Y +Z) = (X+Y). (X’+Z)
(a) (X+Y+Z)’ = X’. Y’. Z’ and (b) (X.Y.Z)’ = X’+Y’+Z’
(a) XY +X’Z = (X+Z). (X’+Y) and (b) (X+Y). (X’+Z) = XZ+X’Y
Boolean Alegbra Quiz