[ Back ] [ Home ] [ Up ] [ Next ]

SUMMARY

This chapter has presented information on logic, fundamental logic gates, and Boolean laws and theorems. The information that follows summarizes the important points of this chapter.

LOGIC is the development of a logical conclusion based on known information.

Computers operate on the assumption that statements have two conditions - TRUE and FALSE.

POSITIVE LOGIC is defined as follows: If the signal that activates the circuit (the 1 state) has a voltage level that is more POSITIVE than the 0 state, then the logic polarity is considered to be POSITIVE.

NEGATIVE LOGIC is defined as follows: If the signal that activates the circuit (the 1 state) has a voltage level that is more NEGATIVE than the 0 state, then the logic polarity is considered to be NEGATIVE.

In DIGITAL LOGIC (positive or negative), the TRUE condition of a statement is represented by the logic 1 state and the FALSE condition is represented by the logic 0 state.

LOGIC LEVELS High and LOW represent the voltage levels of the two logic states. Logic level HIGH represents the more positive voltage while logic level LOW represents the less positive (more negative) voltage. In positive logic, the HIGH level corresponds to the TRUE or 1 state and the LOW level corresponds to the FALSE or 0 state. In negative logic, the HIGH level corresponds to the FALSE or 0 state and the LOW level corresponds to the TRUE or 1 state.

A BOOLEAN EXPRESSION is a statement that represents the inputs and outputs of logic gates.

The AND GATE requires all inputs to be HIGH at the same time in order to produce a HIGH output.

The OR GATE requires one or both inputs to be HIGH in order to produce a HIGH output.

INVERTER (NOT function or negator) is a logic gate used to complement the state of the input variable; that is, a 1 becomes a 0 or a 0 becomes a 1. It may be used on any input or output of any gate to obtain the desired result.

The NAND GATE functions as an AND gate with an inverted output.

The NOR GATE functions as an OR gate with an inverted output.

When deriving the output Boolean expression of a combination of gates, solve one gate at a time.

Boolean algebra is used primarily for the design and simplification of circuits.