Don’t Care (X) Conditions in K-Maps

The “Don’t Care” conditions allow us to replace the empty cell of a K-Map to form a grouping of the variables. While forming groups of cells, we can consider a “Don’t Care” cell as either 1 or 0 or we can simply ignore that cell. Therefore, “Don’t Care” condition can help us to form a larger group of cells.

A Don’t Care cell can be represented by a cross(X) in K-Maps representing a invalid combination. For example, in Excess-3 code system, the states 0000, 0001, 0010, 1101, 1110 and 1111 are invalid or unspecified. These are called don’t cares. Also, in design of 4-bit BCD-to-XS-3 code converter, the input combinations 1010, 1011, 1100, 1101, 1110, and 1111 are don’t cares.

A standard SOP function having don’t cares can be converted into a POS expression by keeping don’t cares as they are, and writing the missing minterms of the SOP form as the maxterm of POS form. Similarly, a POS function having don’t cares can be converted to SOP form keeping the don’t cares as they are and write the missing maxterms of the POS expression as the minterms of SOP expression.

Example-1:
Minimise the following function in SOP minimal form using K-Maps:

f = m(1, 5, 6, 12, 13, 14) + d(4) 

Explanation:
The SOP K-map for the given expression is:

Therefore, SOP minimal is,

f = BC' + BD' + A'C'D 

Example-2:
Minimise the following function in SOP minimal form using K-Maps:

F(A, B, C, D) = m(0, 1, 2, 3, 4, 5) + d(10, 11, 12, 13, 14, 15) 

Explanation:
Writing the given expression in POS form:

F(A, B, C, D) = M(6, 7, 8, 9) + d(10, 11, 12, 13, 14, 15) 

The POS K-map for the given expression is:

Therefore, POS minimal is,

F = A'(B' + C') 

Example-3:
Minimise the following function in SOP minimal form using K-Maps: F(A, B, C, D) = m(1, 2, 6, 7, 8, 13, 14, 15) + d(3, 5, 12)

Explanation:
The SOP K-map for the given expression is:

Therefore,

f = AC'D' + A'D + A'C + AB 

Significance of “Don’t Care” Conditions:
Don’t Care conditions has the following significance with respect to the digital circuit design:

1. Simplification:
   These conditions denotes the set of inputs which never occurs for a given digital circuits. Thus, they are being used to further simplify the boolean output expression.
2. Lesser number of gates:
   Simplification reduces the number of gates to be used for implementing the given expression. Therefore, don’t cares make the digital circuit design more economical.
3. Reduced Power Consumption:
   While grouping the terms long with don’t cares reduces switching of the states. This decreases the required memory space which in turn results in less power consumption.
4. States in Code Converters:
   These are used in code converters. For example- In design of 4-bit BCD-to-XS-3 code converter, the input combinations 1010, 1011, 1100, 1101, 1110, and 1111 are don’t cares.
5. Prevention of Hazards:
   Don’t cares also prevents hazards in digital systems.

K-Map (Karnaugh Map)

In many digital circuits and practical problems we need to find expression with minimum variables. We can minimize Boolean expressions of 3, 4 variables very easily using K-map without using any Boolean algebra theorems. K-map can take two forms Sum of Product (SOP) and Product of Sum (POS) according to the need of problem. K-map is table like representation but it gives more information than TRUTH TABLE. We fill grid of K-map with 0’s and 1’s then solve it by making groups.

Steps to solve expression using K-map-

1. Select K-map according to the number of variables.
2. Identify minterms or maxterms as given in problem.
3. For SOP put 1’s in blocks of K-map respective to the minterms (0’s elsewhere).
4. For POS put 0’s in blocks of K-map respective to the maxterms(1’s elsewhere).
5. Make rectangular groups containing total terms in power of two like 2,4,8 ..(except 1) and try to cover as many elements as you can in one group.
6. From the groups made in step 5 find the product terms and sum them up for SOP form.

SOP FORM

1. K-map of 3 variables-

Z= ∑A,B,C(1,3,6,7)

From red group we get product term—

A’C

From green group we get product term—

AB

Summing these product terms  we get- Final expression (A’C+AB)

2. K-map for 4 variables

F(P,Q,R,S)=∑(0,2,5,7,8,10,13,15)

From red group we get product term—

QS

From green group we get product term—

Q’S’

Summing  these product terms  we get- Final expression (QS+Q’S’)

Digital logic | Shift Registers

Flip flops can be used to store a single bit of binary data (1or 0). However, in order to store multiple bits of data, we need multiple flip flops. N flip flops are to be connected in an order to store n bits of data. A Register is a device which is used to store such information. It is a group of flip flops connected in series used to store multiple bits of data.

The information stored within these registers can be transferred with the help of shift registers. Shift Register is a group of flip flops used to store multiple bits of data. The bits stored in such registers can be made to move within the registers and in/out of the registers by applying clock pulses. An n-bit shift register can be formed by connecting n flip-flops where each flip flop stores a single bit of data.
The registers which will shift the bits to left are called “Shift left registers”.
The registers which will shift the bits to right are called “Shift right registers”.

Shift registers are basically of 4 types. These are:

1.Serial In Serial Out shift register

Serial In parallel Out shift register

Parallel In Serial Out shift register

Parallel In parallel Out shift register

Serial-In Serial-Out Shift Register (SISO) –

The shift register, which allows serial input (one bit after the other through a single data line) and produces a serial output is known as Serial-In Serial-Out shift register. Since there is only one output, the data leaves the shift register one bit at a time in a serial pattern, thus the name Serial-In Serial-Out Shift Register.

The logic circuit given below shows a serial-in serial-out shift register. The circuit consists of four D flip-flops which are connected in a serial manner. All these flip-flops are synchronous with each other since the same clock signal is applied to each flip flop.

The above circuit is an example of shift right register, taking the serial data input from the left side of the flip flop. The main use of a SISO is to act as a delay element.

Serial-In Parallel-Out shift Register (SIPO) –

The shift register, which allows serial input (one bit after the other through a single data line) and produces a parallel output is known as Serial-In Parallel-Out shift register.

The logic circuit given below shows a serial-in-parallel-out shift register. The circuit consists of four D flip-flops which are connected. The clear (CLR) signal is connected in addition to the clock signal to all the 4 flip flops in order to RESET them. The output of the first flip flop is connected to the input of the next flip flop and so on. All these flip-flops are synchronous with each other since the same clock signal is applied to each flip flop.

The above circuit is an example of shift right register, taking the serial data input from the left side of the flip flop and producing a parallel output. They are used in communication lines where demultiplexing of a data line into several parallel lines is required because the main use of the SIPO register is to convert serial data into parallel data.

Parallel-In Serial-Out Shift Register (PISO) –

The shift register, which allows parallel input (data is given separately to each flip flop and in a simultaneous manner) and produces a serial output is known as Parallel-In Serial-Out shift register.

The logic circuit given below shows a parallel-in-serial-out shift register. The circuit consists of four D flip-flops which are connected. The clock input is directly connected to all the flip flops but the input data is connected individually to each flip flop through a multiplexer at the input of every flip flop. The output of the previous flip flop and parallel data input are connected to the input of the MUX and the output of MUX is connected to the next flip flop. All these flip-flops are synchronous with each other since the same clock signal is applied to each flip flop.

A Parallel in Serial out (PISO) shift register us used to convert parallel data to serial data.

Parallel-In Parallel-Out Shift Register (PIPO) –

The shift register, which allows parallel input (data is given separately to each flip flop and in a simultaneous manner) and also produces a parallel output is known as Parallel-In parallel-Out shift register.

The logic circuit given below shows a parallel-in-parallel-out shift register. The circuit consists of four D flip-flops which are connected. The clear (CLR) signal and clock signals are connected to all the 4 flip flops. In this type of register, there are no interconnections between the individual flip-flops since no serial shifting of the data is required. Data is given as input separately for each flip flop and in the same way, output also collected individually from each flip flop.

A Parallel in Parallel out (PIPO) shift register is used as a temporary storage device and like SISO Shift register it acts as a delay element.

1. Differences between Synchronous and Asynchronous Counter

Counters are of two types depending upon clock pulse applied. These counters are: Asynchronous counter, and Synchronous counter.
In Asynchronous Counter is also known as Ripple Counter, different flip flops are triggered with different clock, not simultaneously. While in Synchronous Counter, all flip flops are triggered with same clock simultaneously and Synchronous Counter is faster than asynchronous counter in operation.

Let’s see the difference between these two counters:

S.NO	Synchronous Counter	Asynchronous Counter
1.	In synchronous counter, all flip flops are triggered with same clock simultaneously.	In asynchronous counter, different flip flops are triggered with different clock, not simultaneously.
2.	Synchronous Counter is faster than asynchronous counter in operation.	Asynchronous Counter is slower than synchronous counter in operation.
3.	Synchronous Counter does not  produce any decoding errors.	Asynchronous Counter produces decoding error.
4.	Synchronous Counter is also called Serial Counter.	Asynchronous Counter is also called Parallel Counter.
5.	Synchronous Counter designing as well implementation are complex due to increasing the number of states.	Asynchronous Counter designing as well as implementation is very easy.
6.	Synchronous Counter will operate in any desired count sequence.	Asynchronous Counter will operate only in fixed count sequence (UP/DOWN).
7.	Synchronous Counter examples are: Ring counter, Johnson counter.	Asynchronous Counter examples are: Ripple UP counter, Ripple DOWN counter

Best Programming Quotes of all Time:

         

best quote all the time in the history 

• Career Advice
• Job Search
• Management
• WorkPlace
• Inspiratiobest quote all the time in the history 

1. “when you don’t create things, you become defined by your tastes rather than ability. your tastes only narrow & exclude people. so create.”― Why The Lucky Stiff

2. “Java is to JavaScript what Car is to Carpet.”- Chris Heilmann

3. “Lisp isn’t a language, it’s a building material.” – Alan Kay

4. “Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it.” – Brian W. Kernighan

5. The best thing about a boolean is even if you are wrong, you are only off by a bit. – Anonymous

6. The most important thing in the programming language is the name. A language will not succeed without a good name. I have recently invented a very good name and now I am looking for a suitable language. – Donald Knuth

7. “Programmers are in a race with the Universe to create bigger and better idiot-proof programs, while the Universe is trying to create bigger and better idiots.  So far the Universe is winning.” – Rich Cook

8. “There are two ways of constructing a software design: One way is to make it so simple that there are obviously no deficiencies, and the other way is to make it so complicated that there are no obvious deficiencies. The first method is far more difficult.”– C.A.R. Hoare

9. “Programs must be written for people to read, and only incidentally for machines to execute.” ― Harold Abelson

10. “If debugging is the process of removing software bugs, then programming must be the process of putting them in.” – Edsger Dijkstra 

11. “Walking on water and developing software from a specification are easy if both are frozen.”- Edward V Berard

12. Without requirements or design, programming is the art of adding bugs to an empty text file. – Louis Srygley

13. “It is practically impossible to teach good programming to students that have had a prior exposure to BASIC: as potential programmers, they are mentally mutilated beyond hope of regeneration.” – Edsger Dijkstra

14. “Most of you are familiar with the virtues of a programmer.  There are three, of course: laziness, impatience, and hubris.” – Larry Wall

15. “Measuring programming progress by lines of code is like measuring aircraft building progress by weight.”– Bill Gates

16. “Programming today is a race between software engineers striving to build bigger and better idiot-proof programs, and the Universe trying to produce bigger and better idiots. So far, the Universe is winning.” ― Rick Cook

17. “ Rules of Optimization:Rule 1: Don’t do it.Rule 2 (for experts only): Don’t do it yet. ” – Michael A. Jackson

18. “They don’t make bugs like Bunny anymore.”- Olav Mjelde

19. Ready, fire, aim: the fast approach to software development. Ready, aim, aim, aim, aim: the slow approach to software development. – Anonymous

20. “Everyday life is like programming, I guess. If you love something you can put beauty into it.”  – Donald Knuth 

21. “The trouble with programmers is that you can never tell what a programmer is doing until it’s too late.” – Seymour Cray

22. . “Debugging is twice as hard as writing the code in the first place. Therefore, if you write the code as cleverly as possible, you are, by definition, not smart enough to debug it.”– Brian W. Kernighan

23. “Always code as if the guy who ends up maintaining your code will be a violent psychopath who knows where you live” ― John Woods

24. “ Walking on water and developing software from a specification are easy if both are frozen. ” – Edward V Berard

25.  “A programming language is low level when its programs require attention to the irrelevant.”- Alan J. Perlis

26. “It’s not a bug – it’s an undocumented feature.” – Anonymous

27. “You might not think that programmers are artists, but programming is an extremely creative profession. It’s logic-based creativity.” – John Romero

28. “Computer science education cannot make anybody an expert programmer any more than studying brushes and pigment can make somebody an expert painter.” – Eric Raymond

29. “C makes it easy to shoot yourself in the foot; C++ makes it harder, but when you do, it blows away your whole leg.”– Bjarne Stroustrup

30. “The best programs are written so that computing machines can perform them quickly and so that human beings can understand them clearly. A programmer is ideally an essayist who works with traditional aesthetic and literary forms as well as mathematical concepts, to communicate the way that an algorithm works and to convince a reader that the results will be correct.”  ― Donald Ervin Knuth 
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Friendship day

Friendship day

True friendship is a way of being mutually lovable to each other! In fact every flourishing relationship has a whiff friendship into it. It's that transparent and lucid bond between two people where both of the participants are able to share every subtle thing cooking inside the mind even if it is not worth it. And in that way it's indeed important to maintain true friendship in any relationship

International Friendship day is therefore celebrated around the world in order to create awareness and encourage them to instil the sense of friendship in every relationship. People take up variant forms of greeting their best friends some of which include friendship day essays, wishes, messages, parties, friendship day gifts and many more. Here, we are providing to you with few of the essays for friendship day, to help you out for celebrating it with zeal enough to ignite the sense of friendship in people's heart. It's very true that, the abode of love is the heart where it grows and thrives.

Find here a few of the interesting essays on friendship day in English which will be a great help to you. These short essays on friendship day will be very helpful to school and college going students as, in most of the cases this day is heartily celebrated by children and college going students.

Essay on Friendship day in 200 words

Having a true friend is one of the most precious gifts one can ever have in their life. A person should consider himself/herself one of the luckiest persons on the earth if he/she has a true and sweet friend in their life. Real friends give us any sweet and pleasurable memories to rejoice for. None of us will ever want to lose a true friends as that's where we find our self most comfortable. A friend is somebody who will without exaggerating will keep appreciating you to help you keep going with a positive frame of mind. The will keep on thriving forever for all those years you will be there on the earth. Keeping sane balance between two people in friendship is in fact not an easy task and you need to be transparently honest to be able to maintain the balance.

A friend is always devoted to you in helping you out on various issues of life and that develops a sense of feeling protected with a friend. Friendship day is observed around the World in order to give people an opportunity to express their feeling of love. One can express their feeling with International friendship day essays, speeches, wishes, messages and various other means

#python

https://www.python.org Web results Welcome to Python.org

Update version of python 3.7

Python GUI – tkinter

Python offers multiple options for developing GUI (Graphical User Interface). Out of all the GUI methods, tkinter is most commonly used method. It is a standard Python interface to the Tk GUI toolkit shipped with Python. Python with tkinter outputs the fastest and easiest way to create the GUI applications. Creating a GUI using tkinter is an easy task.