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# Topic: Karnaugh map

###### In the News (Sat 15 Jun 19)

 Karnaugh maps: representations for configurations Here are the structures of two- three- and four-variable Karnaugh maps (figures 2.2, 2.3 and 2.4 respectively; inside the cells are written the binary combinations of variables). Inside the Karnaugh map the sequence of configurations does not follow the usual progressive order; it is arranged so that any two adjacent configurations differ from each other by the change of only one variable. Inside each cell of the Karnaugh map are put the value of the "dependent" variable, the one for which a function is sought. tecfa.unige.ch /~lemay/thesis/THX-Doctorat/node33.html   (651 words)

 NationMaster - Encyclopedia: Karnaugh map A Karnaugh map is unique in that only one variable changes value between squares, in other words, the rows and columns are ordered according to the principles of Gray code. Karnaugh maps make use of the human brain's excellent 'pattern matching' capability to decide which terms should be combined to get the most simple expression. Karnaugh maps make use of the human brain's excellent pattern-matching capability to decide which terms should be combined to get the simplest expression. www.nationmaster.com /encyclopedia/Karnaugh-map   (317 words)

 Karnaugh map The Karnaugh map (K-map for short) was invented in 1950 by Maurice Karnaugh[?]. Karnaugh maps make use of the human brain's excellent 'pattern matching' capability to decide which terms should be combined to get the most simple expression. A Karnaugh map is an excellent aid for simplification of up to six variables; with more variables it becomes hard even for our brain to discern optimal patterns. www.ebroadcast.com.au /lookup/encyclopedia/ka/Karnaugh_map.html   (471 words)

 Science Fair Projects - Karnaugh map The Karnaugh map was invented in 1950 by Maurice Karnaugh, a telecommunications engineer at Bell Labs. After the Karnaugh map has been constructed our next task is to find the minimal terms to use in the final expression. Karnaugh maps are useful for detecting and eliminating race hazards. www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Karnaugh_map   (1003 words)

 Karnaugh Maps Primer The important factor in the design of the Karnaugh map is the fact that the map is laid out so that, across any "axis" one and only one bit in the binary value of the term(s) represented within, may change. Karnaugh himself described it as being like a torus, such as that shown in figure 14 (in this case, a six-variable map is shown). Figure 13 is of a four-variable map showing the relationships across what appear to be the outside boundary axes (but since the map is 'closed' these axes are not outside boundaries). www.technion.ac.il /~es/DigitalSystems/Karnaugh_Maps/Karnaugh_Maps_Primer.htm   (9453 words)

 Karnaugh Maps The diagram below illustrates the correspondence between the Karnaugh map and the truth table for the general case of a two variable problem. Around the edge of the Karnaugh map are the values of the two input variable. That is the logic values of the variables A and B (with one denoting true form and zero denoting false form) form the head of the rows and columns respectively. www.ee.surrey.ac.uk /Projects/Labview/minimisation/karnaugh.html   (600 words)

 Springer Online Reference Works The combinations of the input map variables (usually called discriminants of the map function) are ordered according to the reflected binary code (known also as the Gray code). The ancestor of the Karnaugh map is the logical diagram proposed by A. The most famous use of the map is for minimization of a switching function, i.e., to obtain a formula for the function in sum-of-products (disjunction of conjunctions) form that has a minimum number of prime implicants as the primary objective and that has a minimum number of literals as the secondary objective. eom.springer.de /K/k110040.htm   (962 words)

 Karnaugh map Information - karnaugh map The Karnaugh map was invented in 1953 by Maurice Karnaugh, a telecommunications engineer at Bell Labs. The encirclings must be rectangular karnaugh map and must have an area that is a positive power of two (i.e. Every processor /node coordinates are their Karnaugh coordinates and the whole set is a hypercube with six dimensions. www.inanot.com /Ina-Electronics_Topics_I_-_K-/Karnaugh_map.html   (1051 words)

 Karnaugh map - Wikipedia, the free encyclopedia A Karnaugh map is unique in that only one variable changes value between squares, in other words, the rows and columns are ordered according to the principles of Gray code. When using a Karnaugh map to derive a minimized function, one "covers" the ones on the map by rectangular "coverings" that contain a number of boxes equal to a power of 2 (for example, 4 boxes in a line, 4 boxes in a square, 8 boxes in a rectangle, etc). Karnaugh maps also allow easy minimizations of functions whose truth tables include "don't care" conditions (that is sets of inputs for which the designer doesn't care what the output is) because "don't care" conditions can be included in a ring to make it larger but do not have to be ringed. en.wikipedia.org /wiki/Karnaugh_map   (1636 words)

 Karnaugh Maps The Karnaugh map, as it was initially envisioned, was considered to be directly capable of minimizing Boolean equations of up to only four variables. Then, about a decade after Karnaugh's paper, an individual named Matthew Mahoney observed a symmetrical reflecting approach behind the process of map construction which showed that maps could be extended in design beyond four variables, and from that approach he came up with a slightly different design which, was termed the 'Mahoney Map'. The important factor in the design of the Karnaugh map is the fact that the map is laid out so that, across any "axis" one and only one bit in the binary value of the term(s) represented within, may change. www.physicsforums.com /showthread.php?t=100628   (6346 words)

 Karnaugh Maps Karnaugh maps are a more formal way to approach minimization than looking for pairs to combine. Karnaugh maps are not particularly fast to use since they use the exponential space like a truth table but are useful when the structure of the function is unknown. Once the Karnaugh map is made (this is just a reordering of the truth table in a way), one looks for rectangular blocks with lengths of one, two, or four. cs-people.bu.edu /jconsidi/teaching/notes/cs210/node11.html   (398 words)

 comKarnaugh Boolean Calculator The Karnaugh map, or K-map is a graphical interpretation of the truth table for a Boolean function. Karnaugh maps are useful as ways to reduce a boolean function to the minimum expression necessary to express a desired truth table. This is done by mapping a truth table to a two dimensional grid and marking the minterms where the function is true. student.johnpdaigle.com /karnaughpaper.html   (1855 words)

 PHY107 Karnaugh Maps Karnaugh maps or K-maps are a useful graphic technique to perform the minimization of a canonical form. A detailed example of using Karnaugh maps for circuit simplification is available in the Solved Problems. For minterm expressions, the correct labelling for a Karnaugh map corresponding to a 4-input circuit (inputs A, B, C and D) is www.shef.ac.uk /physics/teaching/phy107/kmap.html   (604 words)

 Karnaugh Map Logic Minimization Karnaugh maps provide a visual representation of the relationship between minterms in an expression. The Karnaugh map does this as well, but the layout is such that each term is logically adjacent to any orthogonally adjacent term. With the data entered into the Karnaugh map, we make the largest possible groups of adjacent 1's (remembering that the map wraps on its edges). people.uncw.edu /norris/133/logic/digital/KarnaughMaps.htm   (273 words)

 Karnaugh Maps - Free Computer Science Tutorials - Provided by Laynetworks.com A Karnaugh map provides a pictorial method of grouping together expressions with common factors and therefore eliminating unwanted variables. Around the edge of the Karnaugh map are the values of the two input variable. There is a two-dimensional map that can be used for up to four variables, and a three-dimensional map for up to six variables. www.laynetworks.com /Karnaugh%20Maps.htm   (629 words)

 Minimizing Boolean Functions The idea behind a Karnaugh Map (Karnaugh, 1953) is to draw an expression’s truth table as a matrix in such a way that each row and each column of the matrix puts minterms that differ in the value of a single variable adjacent to each other. The top row of the Karnaugh Map is labeled with a' and the lower row with a: Any minterms appearing in the top row have the literal a' in them, and any minterms in the bottom row have the literal a in them. A Karnaugh Map is used to produce a minimal sum of products implementation of an expression by drawing rectangles around groups of adjacent minterms in the map; each rectangle will correspond to one product term, and the full expression will be constructed as the OR (sum) of all the product terms. babbage.cs.qc.edu /courses/Minimize   (3641 words)

 FEEE - Fundamentals of Electrical Engineering and Electronics: Making a Venn diagram look like a Karnaugh map What we have so far resembles a 1-variable Karnaugh map, but is of little utility. Karnaugh maps are labeled like the illustration at right. The above two different forms of a 3-variable Karnaugh map are equivalent, and is the final form that it takes. www.vias.org /feee/karnaugh_05.html   (817 words)

 Karnaugh map handout for cos250 To use a Karnaugh map we draw the following map which has a position (square) corresponding to each of the 8 possible combinations of the 3 Boolean variables. The map is easier than algebraic minimization because we just have to recognize patterns of 1s in the map instead of using the algebraic manipulations. At first it may seem that we have two sets, one on the left of the map and the other on the right. www.cs.usm.maine.edu /~welty/karnaugh.htm   (1027 words)

 Karnaugh Maps The Karnaugh map (K map) provides a systematic method for simplifying a Boolean expression or a truth table function. To simplify a SOP for of a Boolean expression using a K map, first identify all the input combinations that produce an output of logic level 1 and place them in their appropriate K map cell. When simplifying K maps with don’t care states, the contents of the undefined cells (1 or 0) are chosen according to preference. scitec.uwichill.edu.bb /cmp/online/p10f/karnaugh.htm   (709 words)

 Math Forum - Ask Dr. Math A Karnaugh map is a technique used to simplify Boolean expressions (and logic circuits) related to Venn diagrams. On a two-variable map, we look for a pair of 1's that are either in the same row or column. Four-variable Karnaugh maps are similar to three-variable maps, but both vertical and horizontal directions need to be shared by two variables. mathforum.org /library/drmath/view/51855.html   (1207 words)

 Lessons In Electric Circuits -- Volume IV (Digital) - Chapter 8 Karnaugh maps work well for up to six input variables, are usable for up to eight variables. Don't cares in a Karnaugh map, or truth table, may be either 1s or 0s, as long as we don't care what the output is for an input condition we never expect to see. Karnaugh map cells are organized in Gray code order so that we may visualize redundancy in Boolean expressions which results in simplification. www.ibiblio.org /kuphaldt/electricCircuits/Digital/DIGI_8.html   (10154 words)

 Karnaugh map The input variables can be combined in 16 different ways, therefore our Karnaugh map has to have 16 positions. The most convenient way to arrange this is in a 4x4 Karnaugh map. The optimal encirclings in this map is marked by the green, red and blue encirclings. www.shoppingland.us /information/notes/ka/Karnaugh_map.html   (531 words)

 Digital Logic - Karnaugh Maps In the case of the Karnaugh Map the advantage is that the Karnaugh Map is designed to present the information in a way that allows easy grouping of terms that can be combined. The Karnaugh Map is a visual technique that allows you to generate groupings of terms that can be combined with a simple visual inspection. Karnaugh Maps are useful for more than three variables, and we'll look at how to extend ideas to four variables here. www.facstaff.bucknell.edu /mastascu/eLessonsHTML/Logic/Logic3.html   (1546 words)

 [No title] The idea for a theory of transformations on Karnaugh maps was developed by the second author (Ph.D. advisor of the first). Karnaugh Maps of higher order The definition of a 3-dimensional Karnaugh map is straightforward. The sums of the diagonals of the 2-dimensional Karnaugh maps are (54, 198), (70, 182), (78, 174), (110, 142), (120, 132) or (124, 128). www.members.shaw.ca /hdhcubes/Downloads/Karnaugh-to-Cubes.doc   (1794 words)

 [No title] The idea for a theory of transformations on Karnaugh maps was developed by the second author (Ph.D. advisor of the first). Karnaugh Maps of higher order The definition of a 3-dimensional Karnaugh map is straightforward. The sums of the diagonals of the 2-dimensional Karnaugh maps are (54, 198), (70, 182), (78, 174), (110, 142), (120, 132) or (124, 128). members.shaw.ca /hdhcubes/Downloads/Karnaugh-to-Cubes.doc   (1794 words)

 Karnaugh Map The rules of mapping are to map the output terms into the boxes relating to each logic term. In fact if you will look closely at the map to the right the order of change of the columns is different from the order of the rows. Although the map is flat, it should be thought of as a continous cylinder from side to side or top to bottom for association purposes. www.geocities.com /washad0/karnaugh.html   (326 words)

 CMSC 313 Lecture 21, A Karnaugh map, K-map, is a visual representation of a Boolean function. After the map is drawn and labeled, a '1' is placed in each square corresponding to a minterm of the function. The map is a toroid such that the top row is logically adjacent to the bottom row and the right column is logically adjacent to the left column. www.csee.umbc.edu /~squire/s04-313/cs313_l21.html   (964 words)

 Making a Venn diagram look like a Karnaugh map : KARNAUGH MAPPING We expand circle A at (b) and (c), conform to the rectangular A' universe at (d), and change A to a rectangle at (e). Figure (a) above is the same as the previous Venn diagram showing A and A' above except that the labels A and A' are above the diagram instead of inside the respective regions. Mark the cell corresponding to the Boolean expression AB in the Karnaugh map above with a 1 www.allaboutcircuits.com /vol_4/chpt_8/4.html   (797 words)

 Definition of Karnaugh map The Karnaugh map, also known as a Veitch diagram (K-map or KV-map for short), was invented in 1950 by Maurice Karnaugh, a telecommunications engineer at Bell Labs. It is a very useful tool to facilitate Boolean algebraic expressions. Whether this glitch does occur depends on the physical nature of the implementation, and whether we need to worry about it depends on the application. www.wordiq.com /definition/Karnaugh_map   (841 words)

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