Electrical and Computer Engineering 2277A/B Lecture Notes - Lecture 5: Real Number, Algebraic Expression, Distributive Property

• School: Western University
• Department: Electrical and Computer Engineering
• Course: Electrical and Computer Engineering 2277A/B
• Professor: Duane Jacques

Document Summary

Binary logic versus binary arithmetic binary logic binary arithmetic. Truth table for and operation and multiplication are identical. Consider the set {0, 1} and the operators and and or. The set is closed with respect to both operators. Applying either operator to any pair of elements of the set yields a member of the set. The set includes identity elements for both and and or. Definition: identity element for operation yields for all x in the set. Given any valid boolean algebraic expression, the dual of the expression is also valid. In binary logic, a dual expression is obtained by: Changing all to + and vice versa. Also changing all 0 to 1 and vice versa. Distributive property of + over is not valid in real number algebra. Boolean algebra has no analogs for subtraction or division. Real number algebra has no analog for the complement (not) operator.