**Introduction - Digital Signals and Logic Gates****Basic Logic Gates****Example****Problem***Go to Next Chapter or Home Page*

Engineers know that it is easier to design devices than multi-state devices. In logic systems, variables, circuits, statements, etc., can be treated in one of two distinct states: true or false, yes or no, on or off, present or absent, energized or not energized, conducting or non-conducting, high voltage or low voltage, and so on.

In digital electronics, we distinguish two distinct values of
voltage, V_{H} corresponding to the higher of the two voltages and
V_{L} corresponding to the lower of the two voltages. There are three
ways in which we can assign binary values to these voltages :

1.We shall use positive logic throughout this course. The description of the other two assignments can be found in elsewhere [Ref.1].Positive logic assignment: True [ 1 ] : V_{H}False [ 0 ] : V_{L}2.Negative logic assignment: True [ 1 ] : V_{L}False [ 0 ] : V_{H}3.Mixed logic assignment: Allow the designers to use positive or negative logic at any point in their design, as they desire.

All digital systems can be constructed by only three basic logic gates. These basic gates are called the AND gate, the OR gate, and the NOT gate. Some textbooks also include the NAND gate, the NOR gate and the EOR gate as the members of the family of basic logic gates. The description of the operations of these gates are listed below [Ref.2]:

**AND gate**- The AND gate is a circuit which gives a high output (logic 1)
if all its inputs are high. A dot () is used to indicate the
AND operation. In practice, however, the dot is
*usually omitted*. **OR gate**- The OR gate is a circuit which gives a high output if one or
more of its inputs are high. A plus sign (+) is used to
indicate the OR operation.
**NOT gate**- The NOT gate is a circuit which produces at its output the
negated (inverted) version of its input logic. The circuit is
also known as an
*inverter*. If the input variable is A, the inverted output is written as . **NAND gate**- The NAND gate is a NOT-AND circuit which is equivalent to an
AND circuit followed by a NOT circuit. The output of the NAND
gate is high if any of its inputs is low.
**NOR gate**- The NOR gate is a NOT-OR circuit which is equivalent to an OR
circuit followed by a NOT circuit. The output of the NOR gate
is low if any of its inputs is high.
**EOR gate**- The Exclusive-OR gate is a circuit which gives a high output
if either of its two inputs is high, but not both. A
encircled plus sign () is used to indicate the EOR operation.

__Figure 1.1__ Symbols for logic gates

The functions of these basic building blocks are summarized by
means of a *Truth Table* as shown in Table 1.1. The table
shows *all possible* input/output combinations for two inputs.
A truth table with n inputs (logic variables) has 2^{n} rows.

__Table 1.1__ Truth table representation of logic gates

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