# Logic

Logic can be two digits of the binary number system that are represented by the state or condition of electrical or electronic devices. A binary 1 can be represented by a switch that is closed, a lamp that is lit, or a transistor that is conducting.

Conversely, a binary 0 would be represented by the same devices in the opposite state: the switch open, the lamp off, or the transistor in cut-off.

In this tutorial and subsequent tutorials we will present the four basic logic gates that make up the foundation for digital equipment. You will see the different types that are used in equipment to accomplish the desired results.

These tutorials include an introduction to Boolean algebra, the mathematics system used with digital equipment. Certain Boolean expressions are used in explanation of the basic gates, and their expressions will be used as each gate is introduced.

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COMPUTERS

Logic is defined as the science of reasoning. In other words, it is the development of a reasonable or inferred conclusion based on known information.

GENERAL

Consider the following example: If it is true that all navy ships are gray and the U.S. Navy's ships' are grey, then you would reach the conclusion that all U.S. Navy ships are gray.

To reach this conclusion, you must assume the qualifying statement is a condition of truth. For each statement there is also a corresponding false condition. The statement "a U.S. Navy ship is grey" is true; therefore, the statement "a grey U.S. Navy ship 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 conditions of a 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 STATES. These 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 LEVELS called HIGH and LOW. The 1 state might be represented by the presence of anelectrical 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, P ). This variable is spoken asNOT P. In some cases, more than one variable is used in a single expression. For example, the expressionABC D is spoken "A AND B AND NOT C AND D."