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2-2 GENERAL LOGIC Consider the following example: If it is true that all Navy ships are gray and the USS Lincoln is a Navy ship, then you would reach the logical conclusion that the USS Lincoln is gray. To reach a logical conclusion, you must assume the qualifying statement is a condition of truth. For each statement there is also a corresponding false condition. The statement "USS Lincoln is a Navy ship" is true; therefore, the statement "USS Lincoln is not a Navy ship" is false. There are no in-between conditions. Computers operate on the principle of logic and use the TRUE and FALSE logic conditions of a logical statement to make a programmed decision. The conditions of a statement can be represented by symbols (variables); for instance, the statement "Today is payday" might be represented by the symbol P. If today actually is payday, then P is TRUE. If today is not payday, then P is FALSE. As you can see, a statement has two conditions. In computers, these two conditions are represented by electronic circuits operating in two LOGIC STATES. These logic states are 0 (zero) and 1 (one). Respectively, 0 and 1 represent the FALSE and TRUE conditions of a statement. When the TRUE and FALSE conditions are converted to electrical signals, they are referred to as LOGIC LEVELS called HIGH and LOW. The 1 state might be represented by the presence of an electrical signal (HIGH), while the 0 state might be represented by the absence of an electrical signal (LOW). If the statement "Today is payday" is FALSE, then the statement "Today is NOT payday" must be TRUE. This is called the COMPLEMENT of the original statement. In the case of computer math, complement is defined as the opposite or negative form of the original statement or variable. If today were payday, then the statement "Today is not payday" would be FALSE. The complement is shown by placing a bar, or VINCULUM, over the statement symbol (in this case,  ). This variable is spoken as NOT P. Table 2-1 shows this concept and the relationship with logic states and logic levels. Table 2-1. Relationship of Digital Logic Concepts and Terms Example 1: Assume today is payday STATEMENT SYMBOL CONDITION LOGIC STATE LOGIC LEVEL Original: TODAY IS PAYDAY P TRUE 1 HIGH Complement: TODAY IS NOT PAYDAY P FALSE 0 LOW Example 2: Assume today is not payday Original: TODAY IS NOT PAYDAY P FALSE 0 LOW Complement: TODAY IS NOT PAYDAY P TRUE 1 HIGH