For T_{2  Flip flop,}

For T₁ Flip flop,

Step 4: Lastly according to the equation got from K map create the design for 2 bit synchronous up down counter.

Related posts:

Design a 2 bit Synchronous down counter using T Flip flop?
Design a 2 bit Synchronous up counter using T Flip flop? 

Product Of Sum or POS Form

POS stands for Product of Sum and totally opposite to SOP form . When an expression is expressed in a product of binary terms ( A term refers to a set of binary variables, where each binary variable is combined with an operation) called Maxterms than it is said to be Product of Sum.

In other words, An expression consisting only Maxterms is called Product of Sum. For  example, (A+B)(A’+B) is a POS expression.
[other concept Minterms, A.B+A’B’]

POS can be categorized in two forms :

– Canonical or Standard POS form: In this, each and every binary variable must have in each term. For example :- (A+B).(A’+B).

– Minimal POS form: In this, the standard POS expression is reduced up in the minimum possible expression.

A Question can be asked in three ways:-

1) In the form Truth table
2) In the form of non-canonical Expression
3) In the of form of Boolean function

 For the given table, simplify it in POS expression

Or

Find POS from Truth Table

Points to Remember :

• Always consider low output (0)
• In Product of Sum or POS, every term in the expression is refereed to Maxterm
• A Maxterm is represented as M(Capital M)
• Consider A’ =1, A=0

Step 1. Since there are 2 variables , so therefore there would be 2ⁿ combinations which is 2² =4.
We consider a low output as Maxterm . a Maxterm is denoted as M.
Y= M₀+M₁
Y = (A+B).(A+B’)                           :- It is in Canonical POS form

In Product of Sum each term is combined with AND operation and within each term, every variable combined with OR operation.

Step 2. Now narrow the founded expression down to minimal Product of Sume or POS form. In this, you should know rules of Boolean expression or K-map

Y= A+BB’                         :-  x+yz = (x+y)(x+z)
Y= A + 0                            :- x.x’ =0
Y= A

OR

Considering, A= 0, A’=1

Y= A

A is your answer.

A multiplexer is often abbreviated as MUX or many to one circuit or parallel to serial circuit.

It is a data selector that provides the mechanism to select single binary information from many input lines and passes it to output line

Advantages of Multiplexer:–

• It is less costly and reduces transmission circuit complexity
•  It can be used to implement many combinational circuits
• It reduces number of wires

Applications of Multiplexer:

• It is used in communication system i.e Satellite systems, telephone networks
• It is used to read data from memory locations in computer memory

Types of Multiplexer
There are various types of multiplexers and few are given below:

• 2:1 MUX
• 4:1 MUX
• 8:1 MUX
• 16:1 MUX
• 32:1 MUX

In this article, we’ll be discussion 4:1 MUX.

Here are the steps to design or construct 4 to 1 Multiplexer or 4:1 MUX using Logic Gates :

1) Now, make a diagram of multiplexer with 4 input lines, 2 selection lines and 1 output. In below diagram, A₀ , A₁ , A₂ and A₃ are input data lines, S₀ and S₁ are Selection lines and lastly one output line named Y.

 

2) This is how a truth table for 4 to 1 MUX looks like . According to the truth table, the output of the multiplexer fully depends on selection lines (binary data , 00,01,10 & 11) and one input would be selected from all the input data lines as the output.


Truth table

Selection Lines		Output
S0	S1	Output
0	0	A0
0	1	A1
1	0	A2
1	1	A3

Above  table is created as per follow :

When S₀ =0 and S₁=0 , then A₀ would be the output.
Similarly When S₀ =0 and S₁=1 , then A₁ would be the output.

We can represent this by an expression.
Output = S₀‘.S₁‘A₀ + S₀‘.S₁A₁+ S₀.S₁‘A₂ + S₀.S₁ A₃

3) In last step, design 4 to 1 multiplexer by using 4 AND gates and a single OR gate.

Explanation:

In above diagram, there were two selection lines along with their respective complements using Inverters. Each and every AND gate were holding three inputs from S₁, S₀ and a particular input A. lastly, outputs of all AND gates became the input for OR gate and providing a single output.

The main difference between them is, Go-Back-N protocol retransmits all the frames starting from the damaged or corrupted frame, whereas Selective Repeat protocol only retransmits frames that are damaged.

Difference between Selective Repeat and Go-Back- N sliding window protocol:

Selective Repeat sliding window protocol:

Selective repeat is one of the sliding window protocols which is essentially responsible for detecting and correcting the error caused in the data link layer.

The Selective repeat protocol basically only retransmits the damaged or lost frame.

The retransmitted frame in the selective repeat protocol is always received out of sequence.

Go-back-N sliding window protocol:

Go-back-N is also one of the sliding window protocols. This protocol mechanism is essentially used to control and detect the errors occurring in the data link layer.

During the data transmission between the sender and the receiver; if the acknowledgement is lost or the frame has been damaged then the sender has to resend all the frames starting from the damaged or corrupted frame.

1. Synchronous data transmission
2. Asynchronous data transmission

Both are data transmission methods and both have their own significance.

The major difference between them is, synchronous transmission maintains an external clock to make sender and receiver synchronised before transferring data, whereas, the asynchronous transmission uses start and stop bits to identify the correct order of data before transmission starts.

Difference between Synchronous and Asynchronous transmission

Synchronous Data Transmission

Synchronous refers to “appearing at same time”.
Similarly, throughout the transmission both sender and receiver are synchronised.

The type of transmission in which there is a continuous stream of data signals coupled with time-based signals for an efficient data transfer is called Synchronous Data transmission. It provides full duplex type transmission to deliver data frames.

This transmission is done to ensure that the transmitters, as well as the receiver, are in coordination with each other.

In case of synchronous transmission, there is greater need to firstly have synchronized clock with both the sender as well as the receiver before actual data transmission.

It uses an external clock in order to ensure both sender and receiver are synchronised. Both uses that particular common clock. It maintains a fixed time interval to transmit data frames.

It is suitable for delivering a large amount of data. These data bytes are followed by a special character called ‘syn’ which is used to make the connection synchronised.

Asynchronous Data Transmission

The type of transmission in which there is a voluntary start bit is sent to mark the beginning of a data transfer is called Asynchronous data transmission.

In this transmission, the whole process of data transfer is governed by the start and stop bits.

There is no need to have synchronized clocks but there is an addition of the parity bit to the actual data before the transmission happens.

In this type of transmission, data bytes are transmitted bit by bit commonly having 8 bits of characters with the special bits. It provides half-duplex type transmission to deliver data bytes.

To identify the correct order of a sequence of data, these two special bits are used.

The two bits is stop bit represented by 1 and start bit by 0, also known as partial bits. To achieve this type of transmission, stop-bit and start-bit is sent along with data bytes through the transmission medium.

There are two types of modes, User Mode and Kernel Mode. A kernel mode is also known as supervisor mode.

User mode

It has restricted access to the resources. CPU has restrictions, therefore, it can have only access to limited instructions and memory. Utility applications such as text editor, media player are run in this mode.

When an application or program is executed, its initial state and operation mode are loaded on stack. At this point, CPU starts executing the program in this particular mode. Interrupts and traps are used to signal  or flag the CPU to switch back to Kernel mode and do the essential tasks by storing the current state of the user program to the stack again. After completing it, CPU resumes the program from where it left.

Kernel Mode

It has full access to memory, I/O and other resources. In this, CPU can execute any instructions and have full access to underlying hardware. The core functionalities of the operating system always run in Kernel mode.

Having these authorities, processes using this mode have full rights to access resources, allowing them read/write to the storage media, enable and disable hardware and more. Difference between Kernel Mode and User Mode :

Key Differences:

1. The mode in which there is an unconditional, unrestricted and full permission to access the system’s hardware by the current executing piece of code is known as the kernel mode. The mode in which there is no means of accessing the system’s hardware directly by the current piece of code is also known as the user mode.
2. The kernel mode is a very powerful and impactful mode which means that it can refer to any memory block of the system and can also orders to execute an instruction to the CPU. The user mode is standardized and normal viewing mode which means that it cannot reference to any memory block or execute any information on its own as it requires some Application Protocol Interface (API) to do these tasks.

3. The kernel mode is the most unrestricted and candid mode that a system can have which means that only the trustable sources can be allowed to operate in this very mode. The user mode is more like a generic mode that can have, which means that any user can access this mode for a particular system and is allowed to operate in this particular mode.

4. As the kernel mode is very important and candid this means that if the system crashes in this mode then it could be very fatal and increases the complexity. As the user mode is quite general and user-friendly this means that even if the system crashes in this mode then it is not fatal at all and can simply restart the session.

5. The kernel mode is very crucial to the system as well as the system programmer so everything that runs easily runs on your PC might not run here because its purpose is to employ hardware for a particular task. The user mode is user friendly space where all the general code will definitely execute.

Subnetting and Supernetting are the two ways to organise these IP addresses. The main difference between them is, Subnetting is a technique of dividing a network into smaller ones, on other hand, Supernetting is a technique of combining several networks to a large network. Both techniques has their own advantages and disadvantages

Difference Between Subnetting And Supernetting:

SUBNETTING

The technique of dividing the Physical network into various smaller subnetworks which are essentially logical and known as Subnetting. “Subnets” is the nomenclature given to these smaller and downsized subnetworks. There is a combination of the host segment and the network segment to form the IP address of these subnetworks. The major objective of the subnetting is to convert all the host related bits into the network bits.

SUPERNETTING

The technique which is completely opposite to the process of Subnetting; this means that various other networks are merged and joined to form one single network, this is known as Supernetting.

There are various other names of Supernetting like aggregation and Router summarization. The major objective of Supernetting is to convert all the network related bits into the host bits.

Key Differences:

1. The subnetting is the technique to divide the network into smaller subnetworks. The Supernetting is the technique of uniting various other networks to form one single network.

2. In subnetting, the network address’s numbers of bits are dramatically increased whereas, in Supernetting the host address’s numbers of bits are dramatically increased.

3. In subnetting, the movement of the masked bits is towards the right of the default mask. While, in Supernetting the movement of the masked bits is towards the left of the default mask.

4. In subnetting, the technique of masking used is Variable-Length Subnet Masking. In Supernetting, the technique of masking used is Classless Interdomain Masking.

Difference between Hub and Switch:

What is Hub ?

It is a networking device that is used to connect various devices on an internal network. It provides ports for various devices which can be used to connect with the help of Ethernet cables. It is not capable of filtering data packets and transmuting  data to respective destination. When a data packet is received from one of the port, it is copied and broadcast to all the connecting devices, exposing that data to  others.

It results in unnecessary traffic on network and creates security issues. It can only identify when a device is connected to a hub.

What is Switch?

It is similar to hub, the only thing that makes it different from hub is, a switch is intelligent. It can read physical addresses or mac address of a connected devices and stored it in a table. Therefore, when a data packet is received from on of the port, it is only delivered to actual receiver’s port.

Key Differences:

1.LAYER

Hub works in the PHYSICAL LAYER and the hubs are often termed as the Layer 1 devices of the OSI model.

A switch works in the DATA LINK LAYER and the switch is often termed as the Layer 2 device of the OSI model.

2. FUNCTION

The main function of a hub is to connect a network which consists of personal computers together. This can be accomplished by the use of a central hub.

The switch has various functions ranging from connecting devices, managing the VLAN (Virtual LAN) security and also manages ports.

3. DATA TRANSMISSION FORM

In the case of a hub, the data is sent in the form of electrical impulses or bits.

In the case of a switch, frames are used for data transmission in L2 switch and packets are used for data transmission in L3 switch.

4. PORTS

A hub has about 4/12 ports.

A switch is considered as a Multi-port bridge, that is why it has 24/48 ports.

5. TRANSMISSION TYPE

A hub follows broadcast transmission.

A switch  follows unicast, multicast as well as broadcast transmission.

6. DEVICE TYPE

A hub is also known as a Passive device, which is without any software.

A switch is also known as an Active device, which is with software and also networking device.

7. TRANSMISSION MODE

In a hub, the basic transmission mode which is followed is a half duplex.

In a switch, the basic transmission mode which is followed is full/half duplex.

8. SPEED

The hub device can offer you a speed which is about 10Mbps.

The switch device can offer you speeds ranging from 10-100 Mbps and it can even offer a speed of 1 Gbps.