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? 

These are the following steps to design a 2 bit synchronous down counter using T Flip flop:

Step 1: To design synchronous down counter, we just require to change the order of present state and next state, just put 0 where is 1 in synchronous up counter. In other words, start from 11 (3) to 00 (0)

Step 2: After that, we need to construct a state table with excitation table.
Note: To construct excitation table from state table you should know the excitation table of respective flip flop, in this case, it is T flip flop. So check the excitation table forT flip flop Which is:

T Flip Flop Excitation Table

Present state	Next State	T
0	0	0
0	1	1
1	0	1
1	1	0

So, the above table is the excitation table for T Flip Flop.

State Table with  excitation  table

Present State		Next State		Flip Flop
Q2	Q1	Q'2	Q'1	T2	T1
0	0	1	1	1	1
0	1	0	0	0	1
1	0	0	1	1	1
1	1	1	0	0	1

Above the table is created as per follow :

When Q₂ =1 which is present state and Q₂‘=1 which is next state then T₂ become 0 [As per excitation table, have a look ]
Similarly, if Q₂ is 1and Q₂‘ is 0 then T_{2 becomes} 1.
In a similar way, it goes on.

Step 3: After making the excitation table the next thing to do is dig out the equation from the boolean algebra or K map for the design of the counter. So For T₁ and T₂ we got 1 and Q₁‘ .

K-Map

 

For T_{2  Flip flop,}

 

 

 

 

T₂= Q₁‘

For T₁ Flip flop,

 

T₁=1

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

In above design T₁ is getting high input  and T₂ is getting input from the output of the T₁ which is complement of the output.  A clock is attached to it which is always high in blue color.

Popular Posts:

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

These are the following step to design a 2 bit Synchronous up counter using T Flip flop

Step 1: To design a synchronous up counter, first we need to know what number of flip flops are required. we can find out by considering a number of bits mentioned in the question. So, in this, we required to make 2 bit counter so the number of flip flops required is 2 [2ⁿ where n is a number of bits].

Step 2: After that, we need to construct a state table with an excitation table.

Note: To construct an excitation table from the state table you should know the excitation table of the respective flip flop, in this case, it is T flip flop. So check the excitation table forT flip flop Which is:

T Flip Flop Excitation Table

So, the above table is the excitation table for T Flip Flop.

State Table with  excitation  table

Above the table is created as per follow :

When Q₂ =0 which is the present state and Q₂‘=0 which is the next state then T₂ becomes 0 [As per excitation table, have a look ]
Similarly, if Q₂ is 0 and Q₂‘ is 1 then T_{2 becomes} 1.
In a similar way, it goes on.

Step 3: After making the excitation table the next thing to do is dig out the equation from the boolean algebra or K map for the design of the counter. So For T₁ and T₂ we got 1 and Q₁ .

K-Map

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 counter.

In the above design, T₁ is getting high input and T₂ is getting input from the output of the T₁ flip flop.  A clock is attached to it which is in blue colour.

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, OSI reference model provides clear distinction between services,interface and protocols, whereas, TCP/IP doesn’t able to differentiate between them.

Difference between TCP/IP And OSI Reference Model in Tabular form

TCP/IP Model

TCP/IP model is older than OSI model and consists 4 layer initially ,later on one more layer were added.

It defines standardised rules that enables network communication between computer as the internet.

These are the layers :-

• Application Layer

It corresponds to Application, Presentation and Session Layer of OSI Model. It contains all the high-level protocols. It provides various services to perform user activities ranging from file transfer to internet surfing.

It consists of HTTP, SMTP, FTP protocols and more.

• Transport Layer

It ensures reliable transmission of data that is sent between hosts in the form of datagrams. It supports flow control and error control to make sure data is received at destination host reliably and correctly.

TCP(Transmission Control Protocol) and UDP(User Datagram Protocol) are protocols used in this layer.

• Internet Layer

It is responsible for transmitting data packets between hosts on a network. It routes independent data packets to correct host. It uses IP(Internet Protocol), ICMP (Internet Control Message Protocol) and ARP ( Address Resolution) protocol to achieve its function.

• Link Layer

It is a combination of the Data Link layer and Physical layer of OSI Model. It acts as an interface between transmission links and hosts. It uses a physical address to find hosts and send data.

OSI Reference Model

OSI Model stands for Open System Interconnection reference model which was developed by ISO. It facilitates open communication systems to communicate using Standard Protocols.

It is not a network architecture as it only states what a layer should do, but not describes the exact services and protocol to be used in each layer.

It follows certain principles on the basis of which it came to the decision of having 7 layers. Each and every layer has its own separate functionality.

These are the following 7 layers in OSI model :-

• Application Layer

It is the only layer that communicates with users for data directly. Network applications such as Skype, Chrome and other applications work in this layer.

They use application layer protocols such as HTTP, SMTP, FTP, POP3 to function. Application layer provides various services to perform user activities ranging from file transfer to internet surfing.

• Presentation Layer

It accepts data from the application layer in the form of a sequence of numbers or characters and transforms it into a machine-understandable form which is binary data (10101010).

After that, data compression is used to reduce the size of the data before handing it over to the next layer. It accelerates the data transmission speed and therefore, it helps in case of video calls.

Lastly, data encryption is used to encrypt data in order to maximise the integrity and security. It secures the transmitting data from intruders.

SSL protocol is one of the protocols used in this layer

Objective Highlights

• • Data Translation
  • Data Compression
  • Data Encryption

• Session layers

It establishes, maintains, manages, and terminates connection or sessions between hosts. It uses various APIs (Application Programming Interface) to connect computers.

When a client requests for connection setup, the server uses authentication and authorisation before allowing the client to use its resources. Authentication can be defined as a process of identifying a user.

The authorisation is a process of identifying the access rights of a user, deciding what resources are allowed to access. Session layer also keeps track of which data packets belong to which file.

Objective Highlights

• • Session Establishment
  • Session Management
  • Session Termination

• Transport Layer

It ensures communication reliability by performing segmentation, error control and flow control.

It accepts data from the session layer and divides it into various segments and each segment consists of the information of the source, destination port number and sequence number. This is known as segmentation.

Port number is used to deliver the data to correct application, whereas the sequence number is used to put the data into the correct sequence.

Further, flow control handles the amount or size of data to be transmitted. Error control comes handy when a data packets are dropped in between transmission & not reached to the destination, then using various techniques, it retransmits data again. It also uses a checksum to identify the received corrupted segment.

TCP (Transmission Control Protocol) and UDP (User Datagram Protocol) are the protocols used in this layer.

Objective Highlights

• • Data Segmentation
  • Error Control
  • Flow Control

• Network Layer

This layer is responsible for transmitting received data segments from source host to destination host over a network.

It performs functions like logical addressing, routing and path determination. In this, each data unit is referred as data packets.

IP addressing done in this layer is called logical addressing. Each computer has an IP address to get uniquely identified on a network.

It assigns sender’s and receiver’s address to each segment, so, that they can reach at correct destination. Furthermore,
routing is also used to find an efficient and effective path from source to destination.

Lastly, path determination can be defined as a technique to select the best path for data delivery. OSPF, BGP, IS-IS are some protocols used in this layer.

Objective Highlights

• • Logical Addressing
  • Routing
  • Path Determination
• Data Link Layer

It accepts data from the network layer. It performs physical addressing that is used to assign MAC address of sender and receiver host to received data packets to form a frame.

It also ensures the data transmission from one node to other must be error-free. It also takes care of the problem of controlling access to the shared channel using a sublayer called medium access control.

• Physical Layer

It converts data received from the data link layer to bitstream and is responsible for actual connectivity between the devices.

It involves physical equipment ranging from cables to switches for data transfer.

Simplify the following expressions using Boolean Algebra :-

•  A + AB

= A.1+AB
= A(1+B)                            :-  OR (A+1 = 1)
= A.1
= A

• AB+AB’

= A(B+B’)                            :- AB+AC = A(B+C)
= A(B+B’)                           :-  A + A’ =1
= A(1)
= A

• A’BC + AC

= C(A’B+A)                         :- A+BC =  (A+B).(A+C)
= C((A’+A).(A+B))             :- A’+A=1
= C(1.(A+B))
= C(A+B)

• A’B+ABC’+ABC

= A’B+AB(C’+C)                       :- A’+A=1
= A’B+AB
= B(A’+A)                                   :- A’+A=1
= B

• A’ B’ C + A’ B C’ + A B’ C’ + A B C