The NOR Operation

The NOT-OR operation is known as the NOR operation. The following figure shows 2-input OR gate followed by a NOT gate. The standard symbol of the NOR gate is shown in following diagram. A bubble on the output side of the NOR gate represents the NOT operation.

The operation of this circuit can be described in the following way:

The output of the OR gate Y' can be written as

Y' = A + B + ... + N

and the output of the NOT gate (Y) can be written as
       _      ____________
Y = Y' = A + B + ... + N

The logic operation represented by above equation is known as NOR operation.

The three basic logic operations, AND, OR and NOT can be performed by using only the NOR gates. These are shown in following diagram.

The NAND Operation

The NOT-AND operation is known as the NAND operation. Following figure shows two input NAND gate.
The standard symbol of NAND gate is shown in following diagram. Here, a bubble on the output side of the NAND gate represents NOT operation, inversion.

Figure shows 2-input AND gate followed by a NOT gate. The operation of this circuit can be described in the following way:

The output of the AND gate (Y') can be written as
        
Y' = AB .. N

Now, the output of the NOT gate (Y) can be written as
       _     ________
Y = Y' = (AB ... N)            
The logical operation represented by above equation is known as the NAND operation. 

The three basic logic operations AND, OR and NOT can be performed by using only NAND gates. These are given in following figure.

Basic Digital Circuits

In a digital system there are only a few basic operations performed, irrespective of the complexities of the system. The basic operations are
1) AND
2) OR
3) NOT

The AND, OR and NOT operations are discussed here

1) The AND Operation


A circuit which performs an AND operation is shown in following figure. It has 2 inputs and one output.

Digital signals are applied at the input terminals marked A and B, the output is obtained at output terminal marked 'Output' and it is also a digital signal. The AND operation is defined as : the output of AND gate is 1 if and only if all the inputs are 1. Mathematically, it is written as

Y = A AND B AND C......AND N
    = A * B *  C * ..... * N                                                                                                  (1)

where A,B,C,.....N are the input variables and Y is the output variable. The variables are binary, i.e. each variable can assume only one of the two possible values, 0 or 1. The binary variables are also known as logical variables.
Equation (1) is known as the Boolean equation or the logical equation of AND gate. The term gate is used because of the similarity between the operation of a digital circuit and a gate. For example, for an AND operation the gate opens (Y=1) only when all the inputs are present, i.e. at logic 1 level.

2) The OR Operation


Following figure shows an OR gate with 2 inputs and one output.

The OR operation is defined as : the output of an OR gate is 1 if and only if one or more inputs are 1. Its logical equation is given by

Y = A or B or C......OR N
    = A + B + C + ...+ N                                                                                          

3) The NOT Operation


Following figure shows a NOT gate, which is also known as inverter. It has one input and one output.

Its logical equation is given by

Y = NOT A
    = A'

Digital Signals

A digital signal has two discrete levels or values. These levels can be represented using the terms ON(HIGH) and OFF(LOW). The two discrete signal levels ON and OFF can also be represented by the binary digits 1 and 0 respectively. A binary digit (0 or 1) is referred to as a bit. Since a digital signal can have only one of the two possible values 1 or 0, the binary number system can be used for the analysis and design of digital systems.

Digital signal

The two levels also be designated as TRUE and FALSE. George Boole introduced the concept of binary number system in the studies of mathematical theory of LOGIC in the work entitled. An 'Investigation of the Laws of Thought' in 1854 and developed its algebra known as Boolean algebra.

These logic concepts have been adapted for the design of digital hardware since 1938 when Claude Shannon-organised and systematized Boole's work in Symbolic Analysis of Relay and Switching Circuits.

Fundamental concepts of Digital Electronics

All of us are familiar with the impact of modern digital computers, communication systems, digital display systems, internet, email, etc. on society. One of the main causes of this revolution is the advent of integrated circuits (ICs), which became possible because of the tremendous progress in semiconductor technology in recent years. The operation of computers, communication systems, internet, email, etc., and many other systems, is based on the principles of digital techniques and these systems are referred to as digital systems.

Some of us are familiar with electronic amplifiers. These are used to amplify electrical signals. This type of signals are continuous signals and can have any value in a limited range and are known as analog signals. The electronic circuits used to process these signals are known as analog circuits and the systems built around this kind of operation are known as analog systems.

On the other hand, in an electronic calculator, the input is given with the help of switches. This is converted into electrical signals having two discrete values or levels. One of these known as LOW level and the other as HIGH level. This type of signal is known as digital signal and the circuits inside the calculator used to process these signals are known as digital circuits. A calculator is an example of a digital system.

What is Information Technology?

Information Technology is a field that deals with use of computers to store, retrieve, process and transmit information. In simple words, we can say that information is nothing but processed data. Information is a sequence of symbols that can be interpreted as message. Information can be recorded as signs, or transmitted as signals. Technology deals with a wide variety of areas that include computer software, computer hardware, information systems, programming languages. In short we can say that "Information Technology " uses technology to handle information.