Boolean Logic George Boole In 1854 George Boole

Boolean Logic

George Boole In 1854, George Boole published “An investigation into the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities. ” Boole outlined a system of logic and a corresponding algebraic language dealing with true and false values. 100 th Anniversary Edition

Boolean Logic Boolean logic is a form of mathematics in which the only values used are true and false. Boolean logic is the basis of all modern computing. There are three basic operations in Boolean logic – AND, OR, and NOT. 100 th Anniversary Edition

The AND Operation The AND operation is a binary operation, meaning that it needs two operands. c = a AND b Both a and b must be true for the result to be true. AND a b T F T T F F

The OR Operation The OR operation is also a binary operation with two operands. c = a OR b If either a OR b is true, then the result is true. OR a b T F T T T F

The NOT Operation The NOT operation is a unary operation with only one operand. NOT c = NOT (a) It simply reverses the true or false value of the operand. a T F F T

Logical Conditions Logical comparisons that are either true or false are most often used as the basis for the true and false values in Boolean logic. They are often used for simple conditions in branching and looping instructions. If (hours > 40) pay overtime If (age < 12) stay in the back seat While (count 10) print count increment count

Logical Comparison Operators Six different comparison operators are used in mathematics and computer programming. Condition In Math In Programming A equals B A=B A = B or A == B A is not equal to B A<> B or A != B A is less than B A<B A is greater than B A>B A is less than or equal to B A <= B A is greater than or equal to B A >= B

Compound Conditions Compound Boolean conditions can be created using the Boolean AND, OR and NOT operations in branching and looping instructions. If ( (hours > 40) AND (type = hourly) ) pay overtime If ( (age < 12) OR (height < 42 in. ) ) stay in the back seat While ( (count <= 10) AND NOT (status = away) ) print name. count increment count

Boolean Functions The Boolean comparison functions can be used to create simple true or false conditions.

Boolean Functions The Boolean logic functions can be used to create compound conditions.

Boolean Functions They can be used anywhere that a Boolean value is needed, such as in this If/Else command.