## Introductory Digital Electronics - Logic Gates

### Digital Signals and Logic Gates

Engineers know that it is easier to design two-state 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, VH corresponding to the higher of the two voltages and VL corresponding to the lower of the two voltages. There are three ways in which we can assign binary values to these voltages :

```1. Positive logic assignment : 	True [ 1 ] : VH
False [ 0 ] : VL

2. Negative logic assignment : 	True [ 1 ] : VL
False [ 0 ] : VH

3. Mixed logic assignment : 	Allow the designers to use positive
or negative logic at any point in
their design, as they desire.
```
We shall use positive logic throughout this course. The description of the other two assignments can be found in elsewhere [Ref.1].

### Basic Logic Gates

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.

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 2n rows.

#### Example 1.1

A NAND gate can be used as a NOT gate by the following wiring:

#### Problem 1.1

Draw the logic circuit diagrams similar to those of Example 1.1 to show how a NOR gate can be wired to become a NOT gate.