Anyway i will answer thismay be in quora style in kmaps you fill kmaps data with output for different combinations of input. Online karnaugh map solver that makes a kmap, shows you how to group the terms, shows the simplified boolean equation, and draws the circuit for up to 6 variables. Karnaugh maps, truth tables, and boolean expressions. Therefore dont care conditions can either be included in or excluded from any circled group, whichever makes it larger. The karnaugh map is organized so that we may see that commonality. Powtoon gives you everything you need to easily make professional videos and presentations that your clients, colleagues, and friends will love. Knowing how to generate gray code should allow us to build larger maps. Karnaugh map k map can be used to minimize functions of up to 6 variables. X, d, 2 x is probably the most often used can also be used to denote inputs. The dont care conditions are used to replace the empty cell to form a possible grouping of variables. In the f kmap, the designers dont care if the output is a 1 or a 0 for minterms 2 and 7, and so cells 2 and 7 in the kmap can be looped as either a 1 or a 0. Dont care condition definition of dont care condition by.
Digital electronics deals with the discretevalued digital signals. Feb 25, 2019 dont care condition often comes for undefined output. Basically whenever these dont care terms are represented in the k map then these are utilized in the realization of boolean expression if required. Suppose you have a karnaugh map with some 0s, 1s, and a few dont cares. This happens, for example, when we dont input certain minterms to the boolean function. Dont care conditions are represented by x in the k map variable. Groups must contain 1, 2, 4, 8, or in general 2 n cells. The goal, when using a karnaugh map to find a sum of products, is to circle all of the 1s, while leaving all of the 0s not circled.
Bcd uses only 10 of possible 16 input combinations since we dont care what the output, we can use these dont care conditions for logic minimization the output for a dont care condition can be either 0 or 1. In this video lecture we will see the dont care condition in karnaugh maps with the help of example. Both outputs have two rows where the output is a dont care. The map also includes the three dont care conditions. Kmap is directly applied to twolevel networks composed of and and or gates. We simply dont care whether the value of 0 or 1 is assigned to f for a particular minterm. For example, if we use wxyz to represent a number from 0 to 9, we need not worry about the function. If m i is a maxterm of f, then place a 0 in cell i. No design or tech skills are necessary its free, easy, and awesome. Namely, if you group a dont care condition with 1s minterms, it becomes a 1. The output f is true if the month represented by the input 0,0,0,0 january, 1011. Jun 24, 2016 this article provides insight into the karnaugh map k map boolean algebraic simplification technique via a few examples.
Also, give the realization using only two input nand gates. Digital systems examples and solutions 20,276 views. Introduce the concept of don t care entries and show how to extend karnaugh map techniques to include maps with don t care entries. They can be used as either 0 or 1, based on the adjacent variables in the group. This lesson covers the idea behind dont cares and their properties with examples.
What is the significance of the dont care condition in. I know that don t cares mean that it doesn t matter whether it is a 0 or a 1 and when don t cares are just outputs i can kind of understand how they work. The karnaugh map uses the following rules for the simplification of expressions by grouping together adjacent cells containing ones. Karnaugh maps kmaps if m i is a minterm of f, then place a 1 in cell i of the kmap. Online karnaugh map solver with circuit for up to 6 variables. Aug 17, 2017 karnaugh maps also allow easy minimizations of functions whose truth tables include dont care conditions. Dont care condition synonyms, dont care condition pronunciation, dont care condition translation, english dictionary definition of dont care condition.
Optimized implementation of logic functions sections 4. Actually, all we need to do is look at the left to right sequence across the top of the 3variable map, and copy it down the left side of the 4variable map. At the time of grouping of bits inside the kmap, the highest priority is provided to a group of 16, further the priority decreases with 8, 4 and 2 bits pair. I have read that when an input is a don t care the whole input doesn t count. What is the meaning of dont care conditions in karnaugh map.
I have read that when an input is a dont care the whole input doesnt count. A dont care cell can be represented by a cross x in kmaps representing a invalid combination. The dont care conditions allow us to replace the empty cell of a kmap to form a grouping of the variables. Dont care conditions in certain cases some of the minterms may never occur or it may not matter what happens if they do in such cases we fill in the karnaugh map with and x meaning dont care when minimizing an x is like a joker x can be 0 or 1 whatever helps best with the minimization eg. When forming groups of cells, treat the dont care cell as either a 1 or a 0, or ignore the dont cares. While forming groups of cells, we can consider a dont care cell as either 1 or 0 or we can simply ignore that cell. Jul 28, 20 dont cares are usually indicated on the map with a dash or x. Digital logic circuits kmap for product of sums and don. We can minimize boolean expressions of 3, 4 variables very easily using kmap without using any boolean algebra theorems.
These don tcare conditions can be used to provide further simplification of the algebraic expression. K maps for productofsum design productofsums design uses the same principles, but applied to the zeros of the function. Introduction of kmap karnaugh map in many digital circuits and practical problems we need to find expression with minimum variables. K map with dont care conditions when constructing a k map for a logic function with dont care conditions, we enter x into the squares where the function is undefined when a k map contains dont care conditions, we can treat the dont cares as either 1 or 0 we make use of x1for grouping them with adjacent 1s to. Populate the kmap enter the value of one for each productterm into the kmap cell, while filling others with zeros.
A quinemccluskey option is also available for up to 6 variables. A kmap is a truth table graph, which aids in visually simplifying logic. K map is directly applied to twolevel networks composed of and and or gates. Designing with don t care values in some situations, we don t care about the value of a logic function. The algebraic approach we have used previously is also used to analyze complex. Also, it doesnt matter if dont care terms are circled or not, because we dont care about the output for those combinations of inputs. This property of gray code is often useful for digital electronics in general. How to know if a certain number is a dont care in kmap. If the boolean function is given as the sum of minterms, then place a one at the respective cells in the kmap. It is useful for up to 5 or 6 variables, and is a good tool to help understand the process of logic simplification.
The karnaugh map boolean algebraic simplification technique. Using the k map minimize the function in the sum of products form. In digital logic, a dont care term for a function is an inputsequence a series of bits for which the function output does not matter. Minterm solution of k map the following are the steps to obtain simplified minterm solution using k map. Dont care conditions in certain cases some input combinations may never occur, or the output doesnt matter when they do in this case we fill in the truth table k map with an x. Important problem based on karnaughs map in hindi 9. If dont care terms also present, then place dont cares x in the respective cells of k map. Logic simplification with karnaugh maps karnaugh mapping. It also includes a brief note on the advantages and the disadvantages of kmaps. While assigning the dont care conditions to the cells of the kmap, x or d is placed at the respective cell. The cells that contain dont care conditions are represented by an asterisk symbol among the normal. Dont care conditionis input combination that will never occur.
For example, when dealing with bcd binary coded decimal numbers. For example, in excess3 code system, the states 0000, 0001. If you learn how to use the dont cares, you will be able to build even. Dont care conditions are represented by x in the kmap variable. Once you realize the design by way of, for example, logic gates, they will of course produce a definite output, but by not specifying which, you are allowing them to be treated as wild cards, so that the specific values that optimize your final. A dont care condition is a combination of inputs for which the designer doesnt care what the output is. We can minimize boolean expressions of 3, 4 variables very easily using k map without using. Minterm solution of k map the following are the steps to obtain simplified minterm solution using kmap. The example on the right is the same as the example above. Dont care conditions sometimes input combinations are of no concern because they may not exist example. Introduce the concept of dont care entries and show how to extend karnaugh map techniques to include maps with dont care entries. The output f is true if the month represented by the input 0,0,0,0 january, 1011 december is a vacation month for me. Dont care cells in the karnaugh map karnaugh mapping. Simplifying boolean expression using k map electrical4u.
This of course is also true for dont care conditions and grouping with 0s max terms. If d i is a dont care of f, then place a d or x in cell i. Example of the use of a karnaugh map with dont care conditions. Both these types of conditions are treated the same way in logic design and may be referred to collectively as dont care conditions for brevity. Let us now take an example of a function with 4 variables with don. Therefore, dont care conditions can either be included in or excluded from any rectangular group, whichever makes it larger. Reading assignment please use chapter titles since chapter numbers vary by edition chapter 4. If dont care terms also present, then place dont cares x in the respective cells of kmap. When you map the resulting truth table and perform appropriate grouping either 1s or 0s, you effectively establish what the dont care outputs will be. Let us move on to some examples of simplification with 3variable karnaugh maps. Designing with dont care values in some situations, we dont care about the value of a logic function. Design a circuit with four inputs d, c, b, a that are natural 8421binary encoded with d the mostsignificant bit.
A dont care cell can be represented by a crossx in kmaps representing a invalid combination. But i am having a really hard time understanding how they work when they are inputs. Groups may be horizontal or vertical, but not diagonal. The example on the right is the same as the example above but with the value of f 1,1,1,1 replaced by a don t care. However, 5 and 6 variable k map is a little bit complex. What is the significance of the dont care condition in a. What is the use of using dont care conditions in karnaugh. Dont cares in a karnaugh map, or truth table, may be either 1s or 0s, as long as we.
We now look for the cells in which the f s are entered, and see whether they can be used to eliminate any variable or not. The university of texas at dallas computer science. Dont care x should also be included while grouping to make a larger possible group. I know that dont cares mean that it doesnt matter whether it is a 0 or a 1 and when dont cares are just outputs i can kind of understand how they work. Karnaugh maps also allow easy minimizations of functions whose truth tables include dont care conditions. Dont cares in a karnaugh map, or truth table, may be either 1s or 0s, as long as we dont care what the output is for an input condition we never expect to see.
In the f k map, the designers dont care if the output is a 1 or a 0 for minterms 2 and 7, and so cells 2 and 7 in the k map can be looped as either a 1 or a 0. For example, in excess3 code system, the states 0000, 0001, 0010, 1101, 1110 and 1111 are invalid or unspecified. Consider only the dont cares x that are helpful for grouping maximum number of adjacent ones. Karnaugh maps k maps if m i is a minterm of f, then place a 1 in cell i of the k map. The following four variable karnaugh maps illustrate the reduction of. Sep 05, 2014 this feature is not available right now. An input that is known never to occur is a canthappen term. Populate the k map enter the value of one for each productterm into the k map. For example, in 8421 code, input states 1001, 1010, 1011, 1100, 1101, 1110 and 1111 are invalid and the corresponding output is the dont care. Mar 25, 2016 kmap simplification using dont care conditions functions that have unspecified output for some input combinations are called incompletely specified functions. We show how to map the product terms of the unsimplified logic to the k map. Initiate express the given expression in its canonical form step 2. Here, we represent dont care terms by greek letter f, since f may be thought of as a combination of 0 and 1. Don t care values in a karnaugh map relate to output that is generally not reachable under normal circumstances and allow you to simplify the logic more than you would normally be able to.
Previous gate questions on kmap, sop and pos expressions. Examples of don t care terms are the binary values 1010 through 1111 10 through 15 in decimal for a function that takes a binarycoded decimal bcd value, because a bcd value never takes on such values so called pseudotetrades. This same information is also shown in the associated k maps. Dont care values in a karnaugh map relate to output that is generally not reachable under normal circumstances and allow you to simplify the logic more than you would normally be able to. For the love of physics walter lewin may 16, 2011 duration. This very simple k map demonstrates that an nvariable k map contains all the combination of the n variables in the k map space. We plot these cells with an asterisk, among the normal 1s and 0s. Karnaugh map kmap can be used to minimize functions of up to 6 variables. They are usually indicated on the map with a dash or x. Since we dont care what the output, we can use these dont care conditions for logic minimization the output for a dont care condition can be either 0 or 1 we dont care dont care conditions denoted by. Therefore, dont care condition can help us to form a larger group of cells. For the collective input symbols that are not relevant in terms of what output they produce, you should treat their outputs as dont care.
452 1196 547 1561 793 977 1156 1281 337 56 1464 1214 527 316 11 713 1623 1599 1648 1391 1123 749 1107 285 1576 1507 151 1592 1432 84 1161 1049 422 1075 600 11 910 606 234 433