logic (from london) - Lecture 1 An Introduction to Boolean...

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DOC112: Computer Hardware Lecture 1 Page 1 Lecture 1: An Introduction to Boolean Algebra The operation of almost all modern digital computers is based on two-valued or binary systems. Binary systems were known in the ancient Chinese civilisation and by the classical Greek philosophers who created a well structured binary system, called propositional logic, in which propositions may be TRUE or FALSE, and are stated as functions of other propositions which are connected by the three basic logical connectives: AND, OR, and NOT. Hence the statement IF it is raining OR the weather forecast is bad THEN I will take an umbrella with me connects the proposition I will take an umbrella with me functionally to the two propositions it is raining and the weather forecast is bad . We can see that the 'umbrella' proposition can be considered as output while the other two as inputs and consequently a simple block diagram of this rule can be drawn (Diagram 1.1). The meaning of the OR connective is that the output is TRUE if either one of the input propositions is TRUE. Since there are only two possible values for any proposition, we can easily calculate a truth value for I will take an umbrella for all possible input conditions. This produces the Truth Table of the basic OR function as: Raining Bad Forecast Umbrella FALSE FALSE FALSE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE We can make the propositons as complex as we require. For example, if we want to include the propostion I will take the car , we may make a statement such as:
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