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Electronics
Electronics Catlog
DIC Catlog

Number System
Conversions Between Number System
Arithematic Operations
1's & 2's Complement
Gray Codes
Arithmetic Circuits
Logical Gates and Truth Table Funtions
Boolean Expressions
Boolean Algebra
Karnaugh Map
Multiplexer
DeMultiplexer
Encoder & Decoder
TTL Circuits
Multivibrators
555 Timer
Flip Flops
RS Flip - Flop
JK Flip - Flop
D Flip - Flop
Shift Register
Schmitt Trigger
Asynchronous Counters
Synchronous Counters
Digital - Analog Conversion
Data Flow
ROM
Memory Drives
Electronics Equation
Resistor Color Codes

Basic Gates and Functions


    Boolean functions may be practically implemented by using electronic gates. The following points are important to understand.

1) Electronic gates require a power supply.

2) Gate INPUTS are driven by voltages having two nominal values, e.g. 0V and 5V representing logic 0 and logic 1 respectively.

3) The OUTPUT of a gate provides two nominal values of voltage only, e.g. 0V and 5V representing logic 0 and logic 1 respectively.

4) There is always a time delay between an input being applied and the output responding.


    Digital systems are said to be constructed by using three basic logic gates. These gates are the AND gate, OR gate and NOT gate. There also exists other logical gates, like the NAND, and the EOR gates. We will only be looking at the first three gates. The basic operations are described below.

AND gate


    The AND gate is an electronic circuit that gives a high output (1) only if all its inputs are high. A dot (.) is used to show the AND operation. Bear in mind that this dot is usually omitted, as shown at the output above.

AND Gates

OR gate


    The OR gate is an electronic circuit that gives a high output if one or more of its inputs are high. A plus (+) is used to show the OR operation.

OR Gates

NOT gate


    The NOT gate is an electronic circuit that produces an inverted version of the input's logic at its output. It is also known as an inverter. If the input variable is A, the inverted output is known as NOT A. This is also shown as A', or A with a bar over the top, as shown at the outputs above.

NOT Gates

NAND gate


    This is a NOT-AND circuit which is equal to an AND circuit followed by a NOT circuit. The outputs of all NAND gates are high if any of the inputs are low.

NAND Gates

NOR gate


    This is a NOT-OR circuit which is equal to an OR circuit followed by a NOT circuit. The outputs of all NOR gates are low if any of the inputs are high.

NOR Gates

EOR gate


    The 'Exclusive-OR' gate is a circuit which will give a high output if either, but not both, of its two inputs are high. An encircled plus sign (EOR Plus) is used to show the EOR operation.

EOR Gates

    The NAND and NOR are called universal functions since with either one the AND and OR functions and NOT can be generated.

    A function in sum of products form can be implemented using NAND gates by replacing all AND and OR gates by NAND gates.

    A function in product of sums form can be implemented using NOR gates by replacing all AND and OR gates by NOR gates.


Logic gate symbols


Logical Gates Symbol Table

    Table shows the input/output combinations for the NOT gate together with all possible input/output combinations for the other gate functions. Also note that a truth table with 'n' inputs has 2n rows.

    A NAND gate can be used as a NOT gate using the following wiring.

NOT Gate

Logic gates representation using the Truth table


Logic Gates


Logical Gates Model

Logical Gates

And Truth Table


Logical AND Truth Table

Or Truth Table


Logical OR Truth Table

Exclusive Or Truth Table


Logical EOR Truth Table

Truth Table