Binary Addition In Digital Electronics-Digital Electronics

Binary Addition

Rules:

          1.   0+0=0

          2.   0+1=1

          3.   1+0=1

          4.   1+1=0,1in carry

For Example: 

          

1.                 Addition of  0101+1010

Therefore it will be: 0101+1010=1111

2.                Addition of 0101+0110

Therefore it will be: 0101+0110=1011

3.                Addition of     00111001+00101001

Therefore it will be: 00111001+00101001=01100010

4.               Addition of       0011+0011

Therefore it will be: 0011+0011=0110

Thus we find the addition of two binary number.

                             

         

Note: Always remember that carry portion which is 1+1=0, carry 1.

This is so much important while adding two binary numbers

2's Complement-Digital Eletronics

2's Complement

In Digital Electronics we generally find 2's complement of any given number. To find 2's complement in digital electronics is very simple.

Here we are going to understand, how to find 2's complement. So, let's get started.

Rules: 

          1.  First, find 1's complement of that given number.

          2.  Add '+1'

To see how to find 1's complement click here

For an example:

                          Let's take 0010

We have to find 2's complement of this number.

So, first, we will find 1's complement.

Which will be:   1101

Now we will add '+1' with that 1's complement.

Therefore the answer will be:  1101+1=1110

This is the 2's complement of that number.

Thus we can find 2's complement of any given number.

1's Complement-Digital Electronics

1's Complement

In Digital Electronics to find 1's complement is very very easy. It is nothing but changing the binary number. If it is 0 then will write it as 1 and if it is 1 then we will write it as 0.

For An Example:

                             The given number is 10101010

So, therefore, the 1's complement of that number will be 01010101.

As you guys can see that it is nothing but just changing the number between 0 and 1. It is as simple as that.

10's Complement-Digital Electronics

10's Complement

To find 10's complement for a given number is very easy to do.Here we are going to discuss the rules to find 10's complement and then we will talk about an example.So let's get started.

Rules:

           1.   First, find 9's complement.

           2.   Add ' +1' with that 9's complement.

Formula:

                    10ⁿ -1

where n=number of digits

 ^{For Example:}

                         ^{452 is a given number.And we have to find the 9's complement of this.}

^{So, as mentioned above, we will count the number of digits. And here we see that there are 3 digits.}

^{Now we will use the mentioned formula.}

^{So the result will be:}  10ⁿ

where n=3

therefore the answer will be 999

Now we have to subtract 452 from 999.

Therefore 999-452=547

Thus we find 9's complement of a given number.

After finding this 9's complement we have to add ' +1' with that result.

Hence the answer will be: 547+1=548

Thus we find 10's complement of a given number.

9's Complement-Digital Electronics

9's Complement

To find 9's complement for a given number is very easy to do. Here we are going to discuss the rules to find 9's complement and then we will talk about an example. So let's get started.

Rules:

           1.   First, check how many numbers are there in that given number.

           2.   Subtract that number from 9(number of digits=number of 9)

Formula:

                    10ⁿ -1

where n=number of digits

 ^{For Example:}

                         ^{452 is a given number. And we have to find the 9's complement of this.}

^{So, as mentioned above, we will count the number of digits. And here we see that there are 3 digits.}

^{Now we will use the mentioned formula.}

^{So the result will be:}  10ⁿ

where n=3

therefore the answer will be 999

Now we have to subtract 452 from 999.

Therefore 999-452=547

Thus we find 9's complement of a given number.

Number System-Number System

Number System

In Digital Electronics there are 4 Types of number system. These are given below:

Decimal Number:

                            A decimal number is a number with a decimal point in it like 17.587

The number to the left of the decimal is an ordinary number. Here the first number to the right of the decimal is the number of tenths (1/10s). The second is the number of hundredths(1/100s) and like others.

                                               

Decimal Number

Binary Number:

                            In mathematics and digital electronics, a binary number is a number expressed in the base-2 number system or binary numeral system, which uses only two symbols: 0 and 1

                                           

Binary Number

Octal Number:

                             The octal number system is based on 8 number system and uses the digits 0 to 7.

Octal Numbers can be made from binary numbers by grouping consecutive binary digits into groups of three(starting from the right).

                                               

Octal Number

Hexadecimal Number:

                              A hexadecimal number based on the number 16. As well as the familiar digits 0 to 9, there are also the letters "A", "B", "C", "D", "E", "F" in place of the decimal numbers 10 to 15.

                                         

Hexadecimal Number

Levels Of Integration In Digital Electronics-Digital Electronics

Levels Of Integration In Digital Electronics

Digital  ICs are basically categorized according to their complexity of circuit and also their logic gates. According to this, there are 5 standards levels of complexity in digital electronics. These all are given below:

Small Scale Integration(SSI):

                                               In this circuit, less than 12 gate circuit can stay on a single chip. It is to be noted that flip-flop and logic gates are in this category.

Medium Scale Integration(LSI):

                      In this circuit, 12 to 99 logic gate circuit can stay on a single chip.Counter,Register,multiplexers,demultiplexers,decoder,encoder are in this category.

                                                     

Large Scale Integration(LSI):

                                               In this circuit, 100 to 9999 logic gates can stay on a single chip.

Small memories, microprocessors belong in this category.

Very Large Scale Integration(VLSI)

                                                In this kind of circuit 10,000 to 99,999 logic gates stay per chip. Large memories, microprocessors belong to this category.

Ultra Large Scale Integration(ULSI):

                                                 This is a very complex circuit. Above 100,000 logic gates can stay on a single chip. Very large memories, microprocessors belong in this category.

Why Digital System Have A Number Of Advantages Than Analog System

Advantages Of Digital System

There are so many reasons that are why the digital system has a number of advantages than analog. Some of the reasons are given below:

Versatile:

                        It is easy to design a digital system whose operation is controlled by a set of stored instruction, which is called by us as a program. Any time the operation is to be changed,it can easily be done by modifying the program whereas in analog it cannot be possible.

Though analog systems can also be programmed, but the scope of changing is limited here.

Storage Of Information Become Easy:

                There are many types of magnetic memory which can store data for a longer time as required. Not only that there are semiconductors of large capacity which helps to store data for a longer period of time.

Easy To Design:

                The switching circuit in which there are only two levels of voltage, HIGH and LOW, which are easy to design. But in case of an analog system, there are such complex things which are not easy to design in a little bit of time. The exact values of voltages are not always essential, because they have only logic. But in analog, the exact values are very important.

Accuracy:       

                         Digital system is much accurate than analog because a digital system can be easily expanded to handle more digits by adding more switching circuits to make the value correct. In that case, the analog system is very slow to compute.

                   

Digital Circuitry can be fabricated on IC chips:

                  The fabrication of digital ICs is much simpler than the analog system. Because the digital system does not require any high-value capacitors. It does not need any kind of resistors, transformers like an analog system.But in the analog system these all components are very essential


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What Is Digital Electronics

Digital Electronics

                                                   

Digital Electronics is an electronics that use the binary form of a number. Basically, it is a device which can understand only 0 and 1.

Digital System is two kinds of:

                                                  1.   Analog

                                                  2.   Digital

Analog:

             Analog circuits are those in which voltages and currents vary continuously through the given range. They can take infinite values within a specified range.3

Digital:

            A Digital circuit is one in which the voltage levels assume a finite number of distinct values.

It is to be noted that digital circuits are also called switching circuits because the voltage levels in a digital circuit are assumed to be switched from one value to another. And switching circuit are two types of:

             1.  Combinational Switching Circuit

             2.  Sequential Switching Circuit

Combinational Switching Circuit:

                                                          It is a switching circuit which output depends on present inputs only. It has no memory.

                                                   

                                             

                                                  Combinational Switching Circuit   

Sequential Switching Circuit:

                                                     It is a switching circuit which output depends not only on present inputs but also present state as well as past inputs also.

It can say that sequential circuits are nothing but combinational circuits with memory.

                                   

                                           

                                                   Sequential Switching Circuit

Sequential Switching circuits may be two types of:

                                                                                 1. Synchronous

                                                                                 2. Asynchronous

Synchronous Switching Circuit:

                                                      In synchronous switching circuit state transition can take place only when the inputs are applied along with a clock pulse.

                                                 

Synchronous Circuit

Asynchronous Switching Circuit:

                                                        In asynchronous switching circuit state transition can take place any time the inputs are applied.

                                           

                                           

                                                      

It is a very important note that, Digital Circuits are also called logic circuits because each type of digital circuit obeys a set of logic rules.

Digital system is used extensively in computation and all other processing,


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