LOGIC GATES
- A logic gate is a device that produces signals of 1 or 0 when the input logic requirements
are met and are used in manipulating binary information.
- Logic gates are the building blocks of digital technology. A logic gate is a device (or
electrical circuit) that performs one or more logical operations on one or more input
signals. Its output represent Boolean(T or F) or binary values (1 or 0) as voltages.
- They can be used in applications like:
Building computer chips, Programming traffic signals, Chips for automatic
alarm systems, Chips for automated control systems, etc -Electronic circuits operate
using binary logic gates.
- Logic gates process signals which represent TRUE or FALSE,ON or OFF, 1 or 0
Main Logic Gates
The main logic gates are:
(a) OR gate
(b) AND gate
(c) NOT gate
(d) NOR gate
(e) NAND gate
Logic gates are used with truth tables.
• A truth table is a table which shows how a logic circuit's output responds to various
combinations of the inputs, using logic 1 for true and logic 0 for false.
• A truth table is a table that describes the behaviour of a logic gate.
• It lists the value of the output for every possible combination of the inputs Truth tables
contains 1s and 0s and are an integral part of logic gates functionality.
• Truth table and logic gates use the following:
- 1 (True, ON, Not False)
- 0 (False, OFF, Not True)
The number of rows in a truth table shows the number of combinations of the inputs
of a particular circuit. The number of rows for each gate is found using the
following formulae: rows = 2n , n being the number of inputs in the gate or circuit.
For example, a gate or circuit has the following rows corresponding to the number
of input (excluding column headings): -1 input = 21 = 2 rows
- 2 inputs = 22 = 4 rows
- 3 inputs = 23 = 8 rows - …..
Graphical Representation of Gates and their Truth Tables
Each logic gate has its own unique graphical representation, which can be in general form
or in standard form.
(1) General form
Each logic gate has a circle and the name of the gate to differentiate it from the
rest as given below:
The name inside the gate gives us the type of the gate
(2) Standard Representation
In standard form, each logic gate has its own unique diagram. Even if the name
of the gate is not written, one knows what it stands for because of the shape. The
following are the logic gates and their shapes in standard form.
(a)OR gate
This represents two inputs entering the gate and one output from the gate. The
inputs can be represented by any alphabetic characters, e.g. A and B, while the
output can be X, given as follows:
Logic Gate Diagram Truth table
Standard Form General Form
- X= A OR B
- The output (X) is true if the INPUT A OR INPUT B are true.
- Thus if any one of the inputs is 1, the output is automatically 1 - Output only becomes
0 if all inputs are 0
(b) AND gate
This is represented as follows:
Logic Gate Diagram Truth table
Standard Form General Form
The output (X) is only true if the INPUT A AND INPUT B are both true. If any one of
the inputs is 0, then the output becomes 0 also. Thus X = A AND B.
(c) NOT gate
Logic Gate Diagram Truth table
Standard Form General Form
The NOT gate has only one input and one output. The input is negated. Thus if input is 1,
output is 0, and vice versa.
The output (X) is true when the INPUT A is NOT TRUE.
The output (X) is False when the INPUT A is TRUE.
(d) NOR gate
Logic Gate Diagram Truth table
Standard Form General Form
- This is an OR gate with the output X inverted.
- The output (X) is true if NOT (INPUT A OR INPUT B) are true.
- Thus X = NOT (A or B)
(e) NAND gate
Logic Gate Diagram Truth table
