In this section you will study the four basic logic gates that make up the foundation for digital equipment. You will see the types of logic that are used in equipment to accomplish the desired results. This section includes an introduction to Boolean algebra, the logic mathematics system used with digital equipment. Certain Boolean expressions are used in explanation of the basic logic gates, and their expressions will be used as each logic gate is introduced.
Logic is defined as the science of reasoning. In other words, it is the development of a reasonable or logical conclusion based on known information. 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).
In studying each gate, we will introduce various mathematical symbols known as Boolean algebra expressions. These expressions are nothing more than descriptions of the input requirements necessary to activate the circuit and the resultant circuit output.
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 as NOT P.
In some cases, more than one variable is used in a single expression. For example, the expression ABCD is spoken "A AND B AND NOT C AND D."
So far in this section, we have discussed the two conditions of logical statements, the logic states representing these two conditions and logic levels and associated electrical signals. We are now ready to proceed with individual logic device operations. These make up the majority of computer circuitry.
As each of the logic devices are presented, a chart called a truth table will be used to illustrate all possible input and corresponding output combinations. Truth tables are particularly helpful in understanding a logic device and for showing the differences between devices.
The logic operations you will study in the next sections are the AND, OR, NOT, NAND, and NOR. The devices that accomplish these operations are called logic gates, or more informally, gates. These gates are the foundation for all digital equipment. They are the "decision-making" circuits of computers and other types of digital equipment. By making decisions, we mean that certain conditions must exist to produce the desired output.