UNDERSTANDING BOOLEAN LOGIC AND ITS APPLICATIONS

In the 1800’s (1815-1864), George Boole, a English mathematician who did extensive work in the subject of logic, invented a system of mathematics in which the abstract concepts of true and false can be used in computations. In an attempt to create a new form of mathematics, Mr. Boole identified certain patterns of logic that were later found to be easily translated into an electronic language—essentially, a "switchon/switchoff" pattern. Today, using tiny electronic switching mechanisms inside the computer, "decisions" are made with lightning speed within the central processing unit (CPU). These decisions are based on whether a tiny switch is on or off at any given time. Computer programmers follow prescribed sets of instructions to "teach" computers how to make decisions to carry out instructions. Programming is made possible by sets of instructions called languages. Many of these languages are made up of the logic building blocks identified by Mr. Boole more than 100 years ago, long before computers. The building blocks that Mr. Boole identified are AND logic, OR logic, NOT logic, NAND logic, and NOR logic. Computer decisions are made from these patterns of logic. All programming languages allow you to create expressions that can be evaluated as either true or false, which are called Boolean expressions. A Boolean condition is a conditional statement containing a Boolean expression, and another name for a conditional statement is a hypothesis. In computer programming languages, a hypothesis is formed by using the word “if” with a Boolean expression. The Boolean expression can be evaluated as True or False. When the Boolean expression within the hypothesis is true, then the conclusion occurs. The conclusion will not happen unless this hypothesis is satisfied as True. So, the “if” statement uses the Boolean expression as a way of deciding whether the conclusion that follows is executed. If the Boolean expression is True, the conclusion is executed. Typically, the Boolean expression that is tested by an If-Then statement is formed with a relational operator, which determines whether a specific relationship exists between two values. Because the expression can be only true or false, it is considered to be a Boolean expression. Examples of Boolean expressions which use relational operators are as follows: x >= y Is x greater than or equal to y? x != y Is x not equal to y?
In the general format, the condition is any Boolean expression. If the expression is true, the statements that appear next are executed up to the line that reads Else; likewise, if the expression is false, the statements that appear between Else and End If are executed. Programming languages provide a set of operators known as logical operators, which you can use to create complex Boolean expressions. The logical AND operator and the logical OR operator allow you to connect multiple Boolean expressions to create a compound expression. The logical NOT operator reverses the truth of a Boolean expression. Examples of compound Boolean expressions that use logical operators are as follows: x > y AND a < b Is x greater than y AND is a less than b? x == y OR x == z Is x equal to y OR is x equal to z? NOR (x > y) Is the expression x > y NOT true?
The AND operator takes two Boolean expressions as operands and creates a compound Boolean expression that is true only when both subexpressions are true. The OR operator takes two Boolean expressions as operands and creates a compound Boolean expression that is true when either of the subexpressions is true. The NOT operator is a unary operator that takes a Boolean expression as its operand and reverses its logical value. A Boolean variable can hold one of two values: true or false. Boolean variables are commonly used as flags, which indicate whether specific conditions exist. When the flag variable is set to False, it indicates the condition does not exist. When the flag variable is set to True, it means the condition does exist. You declare a Boolean variable in the following ways: Declare Boolean flag; Set answer = True; Set x = False flag = 16 > 15 (flag holds true) answer = -12 < 4 (answer holds true) x = 8.5