Boolean Logic

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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…...

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