1099:— for the information in the truth table. Adjacent 1s in the Karnaugh map represent opportunities to simplify the expression. The minterms ('minimal terms') for the final expression are found by encircling groups of 1s in the map. Minterm groups must be rectangular and must have an area that is a power of two (i.e., 1, 2, 4, 8...). Minterm rectangles should be as large as possible without containing any 0s. Groups may overlap in order to make each one larger. The optimal groupings in the example below are marked by the green, red and blue lines, and the red and green groups overlap. The red group is a 2 × 2 square, the green group is a 4 × 1 rectangle, and the overlap area is indicated in brown.
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3214:) minimum equation. A minterm is defined as an expression that gives the most minimal form of expression of the mapped variables. All possible horizontal and vertical interconnected blocks can be formed. These blocks must be of the size of the powers of 2 (1, 2, 4, 8, 16, 32, ...). These expressions create a minimal logical mapping of the minimal logic variable expressions for the binary expressions to be mapped. Here are all the blocks with one field.
1049:
3225:
1338:
1057:
2952:{\displaystyle {\begin{aligned}f(A,B,C,D)&={\overline {\overline {f(A,B,C,D)}}}\\&={\overline {{\overline {A}}\,{\overline {B}}+{\overline {A}}\,{\overline {C}}+{\overline {A}}\,D}}\\&=\left({\overline {{\overline {A}}\,{\overline {B}}}}\right)\left({\overline {{\overline {A}}\,{\overline {C}}}}\right)\left({\overline {{\overline {A}}\,D}}\right)\\&=\left(A+B\right)\left(A+C\right)\left(A+{\overline {D}}\right)\end{aligned}}}
2260:{\displaystyle {\begin{aligned}f(A,B,C,D)&={\overline {\overline {f(A,B,C,D)}}}\\&={\overline {{\overline {A}}\,{\overline {B}}+{\overline {A}}\,{\overline {C}}+BCD}}\\&=\left({\overline {{\overline {A}}\,{\overline {B}}}}\right)\left({\overline {{\overline {A}}\,{\overline {C}}}}\right)\left({\overline {BCD}}\right)\\&=\left(A+B\right)\left(A+C\right)\left({\overline {B}}+{\overline {C}}+{\overline {D}}\right)\end{aligned}}}
3245:
3297:
3273:
3324:
1066:
1675:{\displaystyle {\begin{aligned}f(A,B,C,D)={}&{\overline {A}}BC{\overline {D}}+A{\overline {B}}\,{\overline {C}}\,{\overline {D}}+A{\overline {B}}\,{\overline {C}}D+A{\overline {B}}C{\overline {D}}+{}\\&A{\overline {B}}CD+AB{\overline {C}}\,{\overline {D}}+AB{\overline {C}}D+ABC{\overline {D}}\\={}&A{\overline {C}}+A{\overline {B}}+BC{\overline {D}}\end{aligned}}}
2342:" conditions. A "don't care" condition is a combination of inputs for which the designer doesn't care what the output is. Therefore, "don't care" conditions can either be included in or excluded from any rectangular group, whichever makes it larger. They are usually indicated on the map with a dash or X.
3218:
cylindrical. The fields at edges on the left and right are adjacent, and the top and bottom are adjacent. K-Maps for four variables must be depicted as a donut or torus shape. The four corners of the square drawn by the k-map are adjacent. Still more complex maps are needed for 5 variables and more.
3044:
Whether glitches will actually occur depends on the physical nature of the implementation, and whether we need to worry about it depends on the application. In clocked logic, it is enough that the logic settles on the desired value in time to meet the timing deadline. In our example, we are not
1142:
connected, which means that rectangular groups can wrap across the edges (see picture). Cells on the extreme right are actually 'adjacent' to those on the far left, in the sense that the corresponding input values only differ by one bit; similarly, so are those at the very top and those at the
3217:
A block can be continued across the bottom, top, left, or right of the chart. That can even wrap beyond the edge of the chart for variable minimization. This is because each logic variable corresponds to each vertical column and horizontal row. A visualization of the k-map can be considered
1171:
Diagram showing two K-maps. The K-map for the function f(A, B, C, D) is shown as colored rectangles which correspond to minterms. The brown region is an overlap of the red 2×2 square and the green 4×1 rectangle. The K-map for the inverse of f is shown as gray rectangles, which correspond to
280:(POS) leads to OR gates feeding an AND gate. The POS expression gives a complement of the function (if F is the function so its complement will be F'). Karnaugh maps can also be used to simplify logic expressions in software design. Boolean conditions, as used for example in
253:, and each cell position represents one combination of input conditions. Cells are also known as minterms, while each cell value represents the corresponding output value of the Boolean function. Optimal groups of 1s or 0s are identified, which represent the terms of a
2565:
3839:
1863:
1086:
rather than binary numerical order. Gray code ensures that only one variable changes between each pair of adjacent cells. Each cell of the completed
Karnaugh map contains a binary digit representing the function's output for that combination of inputs.
3078:
would eliminate the potential race hazard, bridging between the green and blue output states or blue and red output states: this is shown as the yellow region (which wraps around from the bottom to the top of the right half) in the adjacent diagram.
2976:. Race hazards are very easy to spot using a Karnaugh map, because a race condition may exist when moving between any pair of adjacent, but disjoint, regions circumscribed on the map. However, because of the nature of Gray coding,
3004:
changes from 1 to 0 (moving from the blue state to the green state). For this case, the output is defined to remain unchanged at 1, but because this transition is not covered by a specific term in the equation, a potential for a
1060:
K-map construction. Instead of the output values (the rightmost values in the truth table), this diagram shows a decimal representation of the input ABCD (the leftmost values in the truth table), therefore it is not a
Karnaugh
66:, is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Knowledge.
1078:
In the example above, the four input variables can be combined in 16 different ways, so the truth table has 16 rows, and the
Karnaugh map has 16 positions. The Karnaugh map is therefore arranged in a 4 × 4 grid.
284:, can get very complicated, which makes the code difficult to read and to maintain. Once minimised, canonical sum-of-products and product-of-sums expressions can be implemented directly using AND and OR logic operators.
2441:. In this case, the don't care has dropped a term (the green rectangle); simplified another (the red one); and removed the race hazard (removing the yellow term as shown in the following section on race hazards).
851:
1327:
1011:
4038:
3717:, Christopher R. Clare, J. Robert Burgoon, Larry L. Dornhoff, William I. Fletcher, Ali M. Rushdi and others (several successive Karnaugh map extensions based on variable inputs for a larger numbers of inputs)
1176:
Once the
Karnaugh map has been constructed and the adjacent 1s linked by rectangular and square boxes, the algebraic minterms can be found by examining which variables stay the same within each box.
2589:
1887:
1343:
238:
The
Karnaugh map reduces the need for extensive calculations by taking advantage of humans' pattern-recognition capability. It also permits the rapid identification and elimination of potential
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3168:
2425:
52:
4671:
1752:
3121:
3076:
2334:= 1111 is replaced by a "don't care". This removes the green term completely and allows the red term to be larger. It also allows blue inverse term to shift and become larger
2326:
378:
173:
4194:. The first section says that they are labeled with a code that changes only one bit between entries and the second section says that such a code is called Gray code.)
3205:
1038:
878:
3714:
3024:
are both 1, with C changing from 1 to 0 (moving from the blue state to the red state). In this case the glitch wraps around from the top of the map to the bottom.
4242:
3831:
2980:
has a special definition explained above – we're in fact moving on a torus, rather than a rectangle, wrapping around the top, bottom, and the sides.
4209:
69:
Do not translate text that appears unreliable or low-quality. If possible, verify the text with references provided in the foreign-language article.
3123:
must be added to the inverse to eliminate another potential race hazard. Applying De Morgan's laws creates another product of sums expression for
4412:
4555:
KV-Diagramme in der
Schaltalgebra - Verknüpfungen, Beweise, Normalformen, schaltalgebraische Umformungen, Anschauungsmodelle, Paradebeispiele
729:
4678:
1267:
889:
257:
of the logic in the original truth table. These terms can be used to write a minimal
Boolean expression representing the required logic.
2349:(1,1,1,1) replaced by a "don't care". This allows the red term to expand all the way down and, thus, removes the green term completely.
1186:
is the same and is equal to 1 throughout the box, therefore it should be included in the algebraic representation of the red minterm.
4310:
4560:
KV diagrams in
Boolean algebra - relations, proofs, normal forms, algebraic transformations, illustrative models, typical examples
3670:
3178:
The following are all the possible 2-variable, 2 × 2 Karnaugh maps. Listed with each is the minterms as a function of
707:
Following are two different notations describing the same function in unsimplified
Boolean algebra, using the Boolean variables
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1686:
1102:
The cells are often denoted by a shorthand which describes the logical value of the inputs that the cell covers. For example,
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4542:
4246:
4004:
260:
Karnaugh maps are used to simplify real-world logic requirements so that they can be implemented using the minimal number of
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3923:
2560:{\displaystyle {\overline {f(A,B,C,D)}}={\overline {A}}\,{\overline {B}}+{\overline {A}}\,{\overline {C}}+{\overline {A}}D}
4385:
in that circles are replaced by squares and arranged in a form of matrix. The Veitch diagram labels the squares with the
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4275:
3747:
77:
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2358:
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can be a valid term—it includes cells 12 and 8 at the top, and wraps to the bottom to include cells 10 and 14—as is
90:
Content in this edit is translated from the existing German
Knowledge article at ]; see its history for attribution.
4442:
4101:
3897:
1096:
254:
4636:
4011:
3689:, 1963) by Matthew V. Mahoney (a reflection-symmetrical extension of Karnaugh maps for larger numbers of inputs)
4459:
4093:
3752:
3725:(MRM, 1990) by Thomas R. McCalla (a three-dimensional extension of Karnaugh maps for larger numbers of inputs)
1858:{\displaystyle {\overline {f(A,B,C,D)}}={\overline {A}}\,{\overline {B}}+{\overline {A}}\,{\overline {C}}+BCD}
3890:
3768:
1082:
The row and column indices (shown across the top and down the left side of the Karnaugh map) are ordered in
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4205:
3637:
34:
4428:
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4534:
1095:
After the Karnaugh map has been constructed, it is used to find one of the simplest possible forms — a
277:
265:
4400:
3096:
3051:
3840:
Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics
3773:
3502:
281:
4771:
3997:
1700:
The three terms to cover the inverse are all shown with grey boxes with different colored borders:
85:
4393:
assigned 1s and 0s to the squares and their labels and deduced the numbering scheme in common use.
4716:
4137:
3741:
293:
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3558:
3530:
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336:
219:
but now with a focus set on its utility for switching circuits. Veitch charts are also known as
148:
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4129:
3803:
This should not be confused with the negation of the result of the previously found function.
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106:
3012:
There is a second potential glitch in the same example that is more difficult to spot: when
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does not maintain the same state (it shifts from 1 to 0), and should therefore be excluded.
1016:
856:
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8:
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It would also have been possible to derive this simplification by carefully applying the
1114:
are true, i.e. the cells numbered 13, 9, 15, 11 in the diagram above. On the other hand,
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3346:
4504:
4488:
4357:
4062:(NB. Quite many secondary sources erroneously cite this work as "A logical diagram for
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3872:
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3479:
3456:
3036:
2338:
Karnaugh maps also allow easier minimizations of functions whose truth tables include "
129:
An example Karnaugh map. This image actually shows two Karnaugh maps: for the function
125:
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does not change. It is always 0, so its complement, NOT-C, should be included. Thus,
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is 0 and has to be negated before it can be included. The second term is therefore
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4706:
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3744:(BDD), a data structure that is a compressed representation of a Boolean function
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1689:, but the time it takes to do that grows exponentially with the number of terms.
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functions. For example, consider the Boolean function described by the following
192:
4427:
Lind, Larry Frederick; Nelson, John Christopher Cunliffe (1977). "Section 2.3".
2345:
The example on the right is the same as the example above but with the value of
1697:
The inverse of a function is solved in the same way by grouping the 0s instead.
1251:. Note that it is acceptable that the green grouping overlaps with the red one.
4626:
POCKET–PC BOOLEAN FUNCTION SIMPLIFICATION, Ledion Bitincka — George E. Antoniou
4136:(1 ed.). Binghamton, New York, USA: Litton Educational Publishing, Inc. /
4083:
4039:
The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science
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The solutions of each grouping are combined: the normal form of the circuit is
239:
208:
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onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered in
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4175:
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3028:
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4190:(NB. The two page sections taken together say that K-maps are labeled with
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3957:
1052:
K-map drawn on a torus, and in a plane. The dot-marked cells are adjacent.
4731:
4565:
3889:. The Bell Laboratories Series (1 ed.). Princeton, New Jersey, USA:
3677:
297:
261:
246:
4751:
4300:
1065:
88:
to the source of your translation. A model attribution edit summary is
4570:(e-book) (in German) (1 ed.). Berlin, Germany: viademica Verlag.
3946:
Proceedings of the 1952 ACM national meeting (Pittsburgh) on - ACM '52
846:{\displaystyle f(A,B,C,D)=\sum _{}m_{i},i\in \{6,8,9,10,11,12,13,14\}}
4521:
4191:
1083:
1048:
250:
4656:
1214:
Thus the first minterm in the Boolean sum-of-products expression is
4408:
3928:(viii+635 pages) (NB. This book was reprinted by Chin Jih in 1969.)
3086:
in terms of the static logic of the system, but such redundant, or
1322:{\displaystyle A{\overline {C}}+A{\overline {B}}+BC{\overline {D}}}
1056:
1041:
1006:{\displaystyle f(A,B,C,D)=\prod _{}M_{i},i\in \{0,1,2,3,4,5,7,15\}}
881:
269:
4386:
4155:
3944:(1952-05-03) . "A chart method for simplifying truth functions".
273:
138:
134:
4376:
63:
4111:
3040:
Above diagram with consensus terms added to avoid race hazards.
3832:"The Map Method for Synthesis of Combinational Logic Circuits"
1139:
3090:, are often needed to assure race-free dynamic performance.
4468:
1069:
In three dimensions, one can bend a rectangle into a torus.
292:
Karnaugh maps are used to facilitate the simplification of
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to map (i.e., rows that have output 0 in the truth table).
884:
to map (i.e., rows that have output 1 in the truth table).
145:() signifies a sum of minterms, denoted in the article as
4643:
4243:
Erik Jonsson School of Engineering and Computer Science
2972:
Karnaugh maps are useful for detecting and eliminating
3184:
4134:
Introduction to the Methodology of Switching Circuits
3133:
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2587:
2453:
2361:
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1755:
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Thus the Karnaugh map has guided a simplification of
1270:
1019:
892:
859:
732:
339:
151:
245:
The required Boolean results are transferred from a
59:
4617:, Circuit design project to control traffic lights.
4355:Wickes, William E. (1968). "3.5. Veitch Diagrams".
3009:(a momentary transition of the output to 0) exists.
137:(colored rectangles) and for its complement, using
55:
a machine-translated version of the German article.
4356:
3994:Boolean Reasoning - The Logic of Boolean Equations
3887:A new approach to the design of switching circuits
3199:
3162:
3115:
3070:
2951:
2559:
2419:
2320:
2259:
1857:
1674:
1321:
1254:In the same way, the blue grouping gives the term
1106:would mean a cell which covers the 2x2 area where
1032:
1005:
872:
845:
372:
167:
4430:Analysis and Design of Sequential Digital Systems
4334:Switching Theory: Insight Through Predicate Logic
227:-(albeit only rarely)- and even Karnaugh maps as
4763:
4518:Computer Arithmetic and Verilog HDL Fundamentals
4332:Vingron, Shimon Peter (2004) . "Karnaugh Maps".
4132:(May 1972). "Reference Notations to Chapter 2".
3642:Related graphical minimization methods include:
120:Graphical method to simplify Boolean expressions
4232:"Simplifying Logic Circuits with Karnaugh Maps"
4020:
4018:
3822:
3820:
4078:
4076:
3996:(reissue of 2nd ed.). Mineola, New York:
3163:{\displaystyle \left(A+{\overline {D}}\right)}
2420:{\displaystyle f(A,B,C,D)=A+BC{\overline {D}}}
84:accompanying your translation by providing an
46:Click for important translation instructions.
33:expand this article with text translated from
4672:
4615:Using Karnaugh maps in practical applications
3936:
3934:
4086:(1958). "6. Marquand's Machine and Others".
4015:
3987:
3985:
3983:
3981:
3979:
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3817:
3631:
1000:
952:
840:
792:
4163:
4124:
4122:
4073:
3638:Logic optimization § Graphical methods
2444:The inverse case is simplified as follows:
4679:
4665:
4426:
4223:
4197:
4172:Digital Design: Principles & Practices
3931:
3878:
3173:
96:{{Translated|de|Karnaugh-Veitch-Diagramm}}
4621:K-Map Tutorial for 2,3,4 and 5 variables
4528:
4263:
4206:"Karnaugh Maps – Rules of Simplification"
3972:
3797:
3032:Race hazards are present in this diagram.
2988:, a potential race condition exists when
2857:
2819:
2781:
2744:
2720:
2696:
2530:
2506:
2112:
2074:
2018:
1994:
1832:
1808:
1554:
1463:
1436:
1425:
199:introduced it in 1953 as a refinement of
4515:
4453:Holder, Michel Elizabeth (March 2005) .
4398:
4311:The Benjamin/Cummings Publishing Company
4119:
4024:
3826:
3035:
3027:
2274:
1166:
1064:
1055:
1047:
124:
4331:
4169:
4082:
4764:
4644:California State University San Marcos
4452:
4354:
4272:"Using Karnaugh Maps to Simplify Code"
4203:
3940:
3884:
2352:This yields the new minimum equation:
268:(SOP) can always be implemented using
4686:
4660:
4551:
4359:Logic Design with Integrated Circuits
4229:
3991:
3871:(NB. Also contains a short review by
4722:Propositional directed acyclic graph
4531:Switching and Finite Automata Theory
4399:Maxfield, Clive "Max" (2006-11-29).
4299:
4128:
4066:terms" or "On a logical diagram for
3765:(1905), a similar diagram in biology
207:, which itself was a rediscovery of
15:
4529:Kohavi, Zvi; Jha, Niraj K. (2009).
4455:"A modified Karnaugh map technique"
4230:Dodge, Nathan B. (September 2015).
3950:Association for Computing Machinery
3048:In our case, an additional term of
1159:, which includes the four corners.
13:
4637:"Guide To The K-Map (Karnaugh Map"
4293:
3748:Espresso heuristic logic minimizer
3697:(RKM) techniques (from 1969) like
14:
4798:
4602:
4239:The University of Texas at Dallas
4030:"XXXIII: On Logical Diagrams for
3210:
3093:Similarly, an additional term of
2430:Note that the first term is just
141:(gray rectangles). In the image,
4750:
4336:. Berlin, Heidelberg, New York:
4269:
3611:
3584:
3557:
3529:
3501:
3478:
3455:
3424:
3393:
3369:
3345:
3322:
3295:
3271:
3243:
3223:
3116:{\displaystyle {\overline {A}}D}
3071:{\displaystyle A{\overline {D}}}
20:
4587:from the original on 2022-11-12
4415:from the original on 2017-04-19
4278:from the original on 2017-04-18
4252:from the original on 2017-04-18
4212:from the original on 2017-04-18
2962:
1232:maintain the same state, while
1073:
4598:(282 pages with 14 animations)
4460:IEEE Transactions on Education
4094:McGraw-Hill Book Company, Inc.
3992:Brown, Frank Markham (2012) .
3885:Curtis, Herbert Allen (1962).
3855:. Paper 53-217. Archived from
3753:List of Boolean algebra topics
3194:
3191:
2967:
2660:
2636:
2619:
2595:
2484:
2460:
2389:
2365:
2315:
2291:
2270:
1958:
1934:
1917:
1893:
1786:
1762:
1373:
1349:
920:
896:
760:
736:
367:
343:
94:You may also add the template
1:
4609:Detect Overlapping Rectangles
4092:(1 ed.). New York, USA:
3891:D. van Nostrand Company, Inc.
3810:
3711:variable-entered Karnaugh map
2985:
191:) is a method of simplifying
4204:Belton, David (April 1998).
3150:
3105:
3063:
2935:
2862:
2852:
2831:
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2814:
2793:
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2691:
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2230:
2217:
2150:
2124:
2118:
2107:
2086:
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2013:
2000:
1989:
1966:
1962:
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1827:
1814:
1803:
1790:
1663:
1644:
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1579:
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1404:
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1295:
1279:
685:
7:
4742:Method of analytic tableaux
4727:Sentential decision diagram
4568:-capable browser on CD-ROM)
4564:(Windows/Mac executable or
4089:Logic Machines and Diagrams
3729:
3127:, but with a new factor of
3045:considering clocked logic.
1210:changes, so it is excluded.
1162:
1121:would mean the cells where
1090:
10:
4803:
4535:Cambridge University Press
3635:
3207:and the race hazard free (
2321:{\displaystyle f(A,B,C,D)}
1692:
373:{\displaystyle f(A,B,C,D)}
304:Truth table of a function
287:
278:product-of-sums expression
266:sum-of-products expression
168:{\displaystyle \sum m_{i}}
58:Machine translation, like
4787:Logic in computer science
4748:
4692:
4516:Cavanagh, Joseph (2008).
4306:Contemporary Logic Design
4170:Wakerly, John F. (1994).
4052:10.1080/14786448108627104
3769:Quine–McCluskey algorithm
3713:(VEKM) by G. W. Schultz,
3632:Related graphical methods
1746:This yields the inverse:
1687:axioms of Boolean algebra
665:
645:
625:
605:
585:
565:
545:
525:
505:
485:
465:
445:
425:
405:
385:
35:the corresponding article
4782:Electronics optimization
3998:Dover Publications, Inc.
3942:Veitch, Edward Westbrook
3853:10.1109/TCE.1953.6371932
3790:
1224:For the green grouping,
221:Marquand–Veitch diagrams
4717:Binary decision diagram
4178:. pp. 48–49, 222.
4138:D. van Nostrand Company
4114:. ark:/13960/t5cc1sj6b.
3926:. ark:/13960/t56d6st0q.
3742:Binary decision diagram
3174:2-variable map examples
105:For more guidance, see
4552:Grund, Jürgen (2011).
4485:10.1109/TE.2004.832879
3201:
3164:
3117:
3072:
3041:
3033:
2953:
2561:
2421:
2335:
2322:
2261:
1859:
1676:
1323:
1179:For the red grouping:
1173:
1070:
1062:
1053:
1034:
1007:
874:
847:
374:
282:conditional statements
176:
169:
4611:, by Herbert Glarner.
4365:John Wiley & Sons
3958:10.1145/609784.609801
3774:Reed–Muller expansion
3736:Algebraic normal form
3703:map-entered variables
3636:Further information:
3202:
3200:{\textstyle \sum m()}
3165:
3118:
3073:
3039:
3031:
2954:
2562:
2422:
2323:
2278:
2262:
1860:
1677:
1324:
1170:
1068:
1059:
1051:
1035:
1033:{\displaystyle M_{i}}
1008:
875:
873:{\displaystyle m_{i}}
848:
375:
170:
128:
107:Knowledge:Translation
78:copyright attribution
4702:Square of opposition
4381:a refinement of the
3952:. pp. 127–133.
3785:Zhegalkin polynomial
3707:variable-entered map
3699:infrequent variables
3694:Reduced Karnaugh map
3182:
3131:
3097:
3052:
2585:
2451:
2359:
2285:
1883:
1753:
1339:
1268:
1017:
890:
857:
730:
723:and their inverses.
337:
229:Karnaugh–Veitch maps
149:
4477:2005ITEdu..48..206H
4401:"Reed-Muller Logic"
4174:. New Jersey, USA:
3687:designation numbers
2578:can be determined:
2570:Through the use of
1876:can be determined:
1868:Through the use of
1204:should be included.
1143:bottom. Therefore,
1129:is false (that is,
305:
4631:K-Map troubleshoot
4340:. pp. 57–76.
4301:Katz, Randy Howard
4274:. Quantum Rarity.
4096:pp. 104–116.
3873:Samuel H. Caldwell
3830:(November 1953) .
3758:Logic optimization
3197:
3160:
3113:
3068:
3042:
3034:
2949:
2947:
2557:
2417:
2336:
2318:
2257:
2255:
1855:
1672:
1670:
1319:
1174:
1071:
1063:
1054:
1030:
1003:
932:
870:
843:
772:
370:
303:
177:
165:
86:interlanguage link
4759:
4758:
4687:Diagrams in logic
4577:978-3-939290-08-7
4544:978-0-521-85748-2
4363:. New York, USA:
4160:(xvi+573+1 pages)
4130:Klir, George Jiří
4006:978-0-486-42785-0
3948:. New York, USA:
3828:Karnaugh, Maurice
3715:Thomas E. Osborne
3153:
3108:
3066:
2938:
2865:
2855:
2834:
2828:
2817:
2796:
2790:
2779:
2752:
2742:
2729:
2718:
2705:
2694:
2671:
2667:
2552:
2539:
2528:
2515:
2504:
2491:
2415:
2246:
2233:
2220:
2153:
2127:
2121:
2110:
2089:
2083:
2072:
2045:
2027:
2016:
2003:
1992:
1969:
1965:
1841:
1830:
1817:
1806:
1793:
1666:
1647:
1631:
1607:
1582:
1563:
1552:
1527:
1504:
1491:
1472:
1461:
1445:
1434:
1423:
1407:
1391:
1317:
1298:
1282:
926:
766:
705:
704:
118:
117:
47:
43:
4794:
4754:
4737:Sequent calculus
4681:
4674:
4667:
4658:
4657:
4653:
4651:
4650:
4641:
4595:
4593:
4592:
4586:
4569:
4548:
4525:
4512:
4448:
4423:
4421:
4420:
4395:
4362:
4351:
4328:
4309:. Vol. 26.
4287:
4286:
4284:
4283:
4267:
4261:
4260:
4258:
4257:
4251:
4236:
4227:
4221:
4220:
4218:
4217:
4201:
4195:
4189:
4167:
4161:
4159:
4126:
4117:
4115:
4080:
4071:
4061:
4059:
4058:
4022:
4013:
4010:
3989:
3970:
3969:
3938:
3929:
3927:
3924:978-0-44201794-1
3882:
3876:
3870:
3868:
3867:
3861:
3836:
3824:
3804:
3801:
3722:Minterm-ring map
3661:Edward W. Veitch
3647:Marquand diagram
3615:
3588:
3561:
3533:
3505:
3482:
3459:
3428:
3397:
3373:
3349:
3326:
3299:
3275:
3247:
3227:
3211:previous section
3206:
3204:
3203:
3198:
3169:
3167:
3166:
3161:
3159:
3155:
3154:
3146:
3122:
3120:
3119:
3114:
3109:
3101:
3077:
3075:
3074:
3069:
3067:
3059:
2958:
2956:
2955:
2950:
2948:
2944:
2940:
2939:
2931:
2918:
2914:
2899:
2895:
2874:
2870:
2866:
2861:
2856:
2848:
2845:
2839:
2835:
2830:
2829:
2821:
2818:
2810:
2807:
2801:
2797:
2792:
2791:
2783:
2780:
2772:
2769:
2757:
2753:
2748:
2743:
2735:
2730:
2722:
2719:
2711:
2706:
2698:
2695:
2687:
2684:
2676:
2672:
2663:
2631:
2630:
2572:De Morgan's laws
2566:
2564:
2563:
2558:
2553:
2545:
2540:
2532:
2529:
2521:
2516:
2508:
2505:
2497:
2492:
2487:
2455:
2440:
2439:
2433:
2426:
2424:
2423:
2418:
2416:
2408:
2329:
2327:
2325:
2324:
2319:
2266:
2264:
2263:
2258:
2256:
2252:
2248:
2247:
2239:
2234:
2226:
2221:
2213:
2206:
2202:
2187:
2183:
2162:
2158:
2154:
2149:
2138:
2132:
2128:
2123:
2122:
2114:
2111:
2103:
2100:
2094:
2090:
2085:
2084:
2076:
2073:
2065:
2062:
2050:
2046:
2041:
2028:
2020:
2017:
2009:
2004:
1996:
1993:
1985:
1982:
1974:
1970:
1961:
1929:
1928:
1870:De Morgan's laws
1864:
1862:
1861:
1856:
1842:
1834:
1831:
1823:
1818:
1810:
1807:
1799:
1794:
1789:
1757:
1742:
1738:
1733:
1732:
1728:
1727:
1722:
1717:
1716:
1712:
1711:
1706:
1681:
1679:
1678:
1673:
1671:
1667:
1659:
1648:
1640:
1632:
1624:
1617:
1608:
1600:
1583:
1575:
1564:
1556:
1553:
1545:
1528:
1520:
1514:
1510:
1505:
1497:
1492:
1484:
1473:
1465:
1462:
1454:
1446:
1438:
1435:
1427:
1424:
1416:
1408:
1400:
1392:
1384:
1380:
1328:
1326:
1325:
1320:
1318:
1310:
1299:
1291:
1283:
1275:
1260:
1259:
1250:
1249:
1220:
1219:
1203:
1202:
1158:
1157:
1154:
1149:
1148:
1134:
1133:
1128:
1124:
1120:
1119:
1113:
1109:
1105:
1039:
1037:
1036:
1031:
1029:
1028:
1012:
1010:
1009:
1004:
942:
941:
931:
879:
877:
876:
871:
869:
868:
852:
850:
849:
844:
782:
781:
771:
722:
718:
714:
710:
381:
379:
377:
376:
371:
306:
302:
272:feeding into an
217:Marquand diagram
201:Edward W. Veitch
197:Maurice Karnaugh
174:
172:
171:
166:
164:
163:
97:
91:
64:Google Translate
45:
41:
24:
23:
16:
4802:
4801:
4797:
4796:
4795:
4793:
4792:
4791:
4772:Boolean algebra
4762:
4761:
4760:
4755:
4746:
4707:Porphyrian tree
4688:
4685:
4648:
4646:
4639:
4635:
4605:
4590:
4588:
4584:
4578:
4563:
4545:
4445:
4435:Macmillan Press
4418:
4416:
4348:
4338:Springer-Verlag
4325:
4296:
4294:Further reading
4291:
4290:
4281:
4279:
4268:
4264:
4255:
4253:
4249:
4234:
4228:
4224:
4215:
4213:
4202:
4198:
4186:
4168:
4164:
4148:
4127:
4120:
4104:
4084:Gardner, Martin
4081:
4074:
4056:
4054:
4046:(75): 266–270.
4026:Marquand, Allan
4023:
4016:
4007:
3990:
3973:
3939:
3932:
3900:
3883:
3879:
3865:
3863:
3859:
3834:
3825:
3818:
3813:
3808:
3807:
3802:
3798:
3793:
3732:
3671:Antonín Svoboda
3640:
3634:
3627:
3616:
3607:
3589:
3580:
3562:
3553:
3534:
3525:
3506:
3497:
3483:
3474:
3460:
3451:
3429:
3420:
3398:
3389:
3374:
3365:
3350:
3341:
3327:
3318:
3300:
3291:
3276:
3267:
3248:
3239:
3228:
3183:
3180:
3179:
3176:
3145:
3138:
3134:
3132:
3129:
3128:
3100:
3098:
3095:
3094:
3088:consensus terms
3058:
3053:
3050:
3049:
2984:In the example
2974:race conditions
2970:
2965:
2946:
2945:
2930:
2923:
2919:
2904:
2900:
2885:
2881:
2872:
2871:
2847:
2846:
2844:
2840:
2820:
2809:
2808:
2806:
2802:
2782:
2771:
2770:
2768:
2764:
2755:
2754:
2734:
2721:
2710:
2697:
2686:
2685:
2683:
2674:
2673:
2632:
2629:
2622:
2588:
2586:
2583:
2582:
2576:product of sums
2544:
2531:
2520:
2507:
2496:
2456:
2454:
2452:
2449:
2448:
2437:
2435:
2431:
2407:
2360:
2357:
2356:
2286:
2283:
2282:
2280:
2273:
2254:
2253:
2238:
2225:
2212:
2211:
2207:
2192:
2188:
2173:
2169:
2160:
2159:
2139:
2137:
2133:
2113:
2102:
2101:
2099:
2095:
2075:
2064:
2063:
2061:
2057:
2048:
2047:
2019:
2008:
1995:
1984:
1983:
1981:
1972:
1971:
1930:
1927:
1920:
1886:
1884:
1881:
1880:
1874:product of sums
1833:
1822:
1809:
1798:
1758:
1756:
1754:
1751:
1750:
1740:
1736:
1730:
1729:
1725:
1724:
1720:
1714:
1713:
1709:
1708:
1704:
1695:
1669:
1668:
1658:
1639:
1623:
1618:
1616:
1610:
1609:
1599:
1574:
1555:
1544:
1519:
1512:
1511:
1509:
1496:
1483:
1464:
1453:
1437:
1426:
1415:
1399:
1383:
1381:
1379:
1342:
1340:
1337:
1336:
1309:
1290:
1274:
1269:
1266:
1265:
1257:
1255:
1247:
1245:
1217:
1215:
1200:
1199:
1165:
1155:
1152:
1151:
1146:
1144:
1131:
1130:
1126:
1122:
1117:
1115:
1111:
1107:
1103:
1093:
1076:
1024:
1020:
1018:
1015:
1014:
937:
933:
930:
891:
888:
887:
864:
860:
858:
855:
854:
777:
773:
770:
731:
728:
727:
720:
716:
712:
708:
338:
335:
334:
332:
294:Boolean algebra
290:
240:race conditions
213:logical diagram
193:Boolean algebra
159:
155:
150:
147:
146:
121:
114:
113:
112:
95:
89:
48:
42:(February 2018)
25:
21:
12:
11:
5:
4800:
4790:
4789:
4784:
4779:
4774:
4757:
4756:
4749:
4747:
4745:
4744:
4739:
4734:
4729:
4724:
4719:
4714:
4709:
4704:
4699:
4693:
4690:
4689:
4684:
4683:
4676:
4669:
4661:
4655:
4654:
4633:
4628:
4623:
4618:
4612:
4604:
4603:External links
4601:
4600:
4599:
4576:
4549:
4543:
4533:(3 ed.).
4526:
4520:(1 ed.).
4513:
4450:
4443:
4424:
4396:
4379:. p. 36:
4352:
4346:
4329:
4323:
4295:
4292:
4289:
4288:
4262:
4222:
4196:
4184:
4162:
4158:. C4463-000-3.
4146:
4140:. p. 84.
4118:
4102:
4072:
4014:
4005:
3971:
3930:
3898:
3877:
3847:(5): 593–599.
3815:
3814:
3812:
3809:
3806:
3805:
3795:
3794:
3792:
3789:
3788:
3787:
3782:
3776:
3771:
3766:
3763:Punnett square
3760:
3755:
3750:
3745:
3739:
3731:
3728:
3727:
3726:
3718:
3690:
3674:
3664:
3654:
3651:Allan Marquand
3633:
3630:
3629:
3628:
3617:
3610:
3608:
3590:
3583:
3581:
3563:
3556:
3554:
3535:
3528:
3526:
3507:
3500:
3498:
3484:
3477:
3475:
3461:
3454:
3452:
3430:
3423:
3421:
3399:
3392:
3390:
3375:
3368:
3366:
3351:
3344:
3342:
3328:
3321:
3319:
3301:
3294:
3292:
3277:
3270:
3268:
3249:
3242:
3240:
3229:
3222:
3196:
3193:
3190:
3187:
3175:
3172:
3158:
3152:
3149:
3144:
3141:
3137:
3112:
3107:
3104:
3065:
3062:
3057:
3026:
3025:
3010:
2969:
2966:
2964:
2961:
2960:
2959:
2943:
2937:
2934:
2929:
2926:
2922:
2917:
2913:
2910:
2907:
2903:
2898:
2894:
2891:
2888:
2884:
2880:
2877:
2875:
2873:
2869:
2864:
2860:
2854:
2851:
2843:
2838:
2833:
2827:
2824:
2816:
2813:
2805:
2800:
2795:
2789:
2786:
2778:
2775:
2767:
2763:
2760:
2758:
2756:
2751:
2747:
2741:
2738:
2733:
2728:
2725:
2717:
2714:
2709:
2704:
2701:
2693:
2690:
2682:
2679:
2677:
2675:
2670:
2666:
2662:
2659:
2656:
2653:
2650:
2647:
2644:
2641:
2638:
2635:
2628:
2625:
2623:
2621:
2618:
2615:
2612:
2609:
2606:
2603:
2600:
2597:
2594:
2591:
2590:
2568:
2567:
2556:
2551:
2548:
2543:
2538:
2535:
2527:
2524:
2519:
2514:
2511:
2503:
2500:
2495:
2490:
2486:
2483:
2480:
2477:
2474:
2471:
2468:
2465:
2462:
2459:
2428:
2427:
2414:
2411:
2406:
2403:
2400:
2397:
2394:
2391:
2388:
2385:
2382:
2379:
2376:
2373:
2370:
2367:
2364:
2317:
2314:
2311:
2308:
2305:
2302:
2299:
2296:
2293:
2290:
2272:
2269:
2268:
2267:
2251:
2245:
2242:
2237:
2232:
2229:
2224:
2219:
2216:
2210:
2205:
2201:
2198:
2195:
2191:
2186:
2182:
2179:
2176:
2172:
2168:
2165:
2163:
2161:
2157:
2152:
2148:
2145:
2142:
2136:
2131:
2126:
2120:
2117:
2109:
2106:
2098:
2093:
2088:
2082:
2079:
2071:
2068:
2060:
2056:
2053:
2051:
2049:
2044:
2040:
2037:
2034:
2031:
2026:
2023:
2015:
2012:
2007:
2002:
1999:
1991:
1988:
1980:
1977:
1975:
1973:
1968:
1964:
1960:
1957:
1954:
1951:
1948:
1945:
1942:
1939:
1936:
1933:
1926:
1923:
1921:
1919:
1916:
1913:
1910:
1907:
1904:
1901:
1898:
1895:
1892:
1889:
1888:
1866:
1865:
1854:
1851:
1848:
1845:
1840:
1837:
1829:
1826:
1821:
1816:
1813:
1805:
1802:
1797:
1792:
1788:
1785:
1782:
1779:
1776:
1773:
1770:
1767:
1764:
1761:
1744:
1743:
1734:
1718:
1694:
1691:
1683:
1682:
1665:
1662:
1657:
1654:
1651:
1646:
1643:
1638:
1635:
1630:
1627:
1622:
1619:
1615:
1612:
1611:
1606:
1603:
1598:
1595:
1592:
1589:
1586:
1581:
1578:
1573:
1570:
1567:
1562:
1559:
1551:
1548:
1543:
1540:
1537:
1534:
1531:
1526:
1523:
1518:
1515:
1513:
1508:
1503:
1500:
1495:
1490:
1487:
1482:
1479:
1476:
1471:
1468:
1460:
1457:
1452:
1449:
1444:
1441:
1433:
1430:
1422:
1419:
1414:
1411:
1406:
1403:
1398:
1395:
1390:
1387:
1382:
1378:
1375:
1372:
1369:
1366:
1363:
1360:
1357:
1354:
1351:
1348:
1345:
1344:
1316:
1313:
1308:
1305:
1302:
1297:
1294:
1289:
1286:
1281:
1278:
1273:
1212:
1211:
1205:
1193:
1187:
1164:
1161:
1097:canonical form
1092:
1089:
1075:
1072:
1046:
1045:
1027:
1023:
1002:
999:
996:
993:
990:
987:
984:
981:
978:
975:
972:
969:
966:
963:
960:
957:
954:
951:
948:
945:
940:
936:
929:
925:
922:
919:
916:
913:
910:
907:
904:
901:
898:
895:
885:
867:
863:
842:
839:
836:
833:
830:
827:
824:
821:
818:
815:
812:
809:
806:
803:
800:
797:
794:
791:
788:
785:
780:
776:
769:
765:
762:
759:
756:
753:
750:
747:
744:
741:
738:
735:
703:
702:
699:
696:
693:
690:
687:
683:
682:
679:
676:
673:
670:
667:
663:
662:
659:
656:
653:
650:
647:
643:
642:
639:
636:
633:
630:
627:
623:
622:
619:
616:
613:
610:
607:
603:
602:
599:
596:
593:
590:
587:
583:
582:
579:
576:
573:
570:
567:
563:
562:
559:
556:
553:
550:
547:
543:
542:
539:
536:
533:
530:
527:
523:
522:
519:
516:
513:
510:
507:
503:
502:
499:
496:
493:
490:
487:
483:
482:
479:
476:
473:
470:
467:
463:
462:
459:
456:
453:
450:
447:
443:
442:
439:
436:
433:
430:
427:
423:
422:
419:
416:
413:
410:
407:
403:
402:
399:
396:
393:
390:
387:
383:
382:
369:
366:
363:
360:
357:
354:
351:
348:
345:
342:
330:
325:
320:
315:
310:
289:
286:
255:canonical form
225:Svoboda charts
209:Allan Marquand
162:
158:
154:
119:
116:
115:
111:
110:
103:
92:
70:
67:
56:
49:
30:
29:
28:
26:
19:
9:
6:
4:
3:
2:
4799:
4788:
4785:
4783:
4780:
4778:
4775:
4773:
4770:
4769:
4767:
4753:
4743:
4740:
4738:
4735:
4733:
4730:
4728:
4725:
4723:
4720:
4718:
4715:
4713:
4710:
4708:
4705:
4703:
4700:
4698:
4695:
4694:
4691:
4682:
4677:
4675:
4670:
4668:
4663:
4662:
4659:
4645:
4638:
4634:
4632:
4629:
4627:
4624:
4622:
4619:
4616:
4613:
4610:
4607:
4606:
4597:
4583:
4579:
4573:
4567:
4561:
4557:
4556:
4550:
4546:
4540:
4536:
4532:
4527:
4523:
4519:
4514:
4510:
4506:
4502:
4498:
4494:
4490:
4486:
4482:
4478:
4474:
4470:
4466:
4462:
4461:
4456:
4451:
4446:
4440:
4436:
4432:
4431:
4425:
4414:
4410:
4406:
4402:
4397:
4394:
4392:
4388:
4384:
4378:
4374:
4370:
4366:
4361:
4360:
4353:
4349:
4347:3-540-40343-4
4343:
4339:
4335:
4330:
4326:
4324:0-8053-2703-7
4320:
4316:
4312:
4308:
4307:
4302:
4298:
4297:
4277:
4273:
4270:Cook, Aaron.
4266:
4248:
4244:
4240:
4233:
4226:
4211:
4207:
4200:
4193:
4187:
4185:0-13-211459-3
4181:
4177:
4176:Prentice Hall
4173:
4166:
4157:
4153:
4149:
4147:0-442-24463-0
4143:
4139:
4135:
4131:
4125:
4123:
4116:(x+157 pages)
4113:
4109:
4105:
4099:
4095:
4091:
4090:
4085:
4079:
4077:
4069:
4065:
4053:
4049:
4045:
4041:
4040:
4035:
4033:
4027:
4021:
4019:
4012:
4008:
4002:
3999:
3995:
3988:
3986:
3984:
3982:
3980:
3978:
3976:
3967:
3963:
3959:
3955:
3951:
3947:
3943:
3937:
3935:
3925:
3921:
3917:
3913:
3909:
3905:
3901:
3895:
3892:
3888:
3881:
3874:
3862:on 2017-04-16
3858:
3854:
3850:
3846:
3842:
3841:
3833:
3829:
3823:
3821:
3816:
3800:
3796:
3786:
3783:
3780:
3777:
3775:
3772:
3770:
3767:
3764:
3761:
3759:
3756:
3754:
3751:
3749:
3746:
3743:
3740:
3737:
3734:
3733:
3724:
3723:
3719:
3716:
3712:
3708:
3704:
3700:
3696:
3695:
3691:
3688:
3684:
3680:
3679:
3675:
3672:
3668:
3667:Svoboda chart
3665:
3662:
3658:
3655:
3652:
3648:
3645:
3644:
3643:
3639:
3625:
3621:
3614:
3609:
3606:
3602:
3598:
3594:
3587:
3582:
3579:
3575:
3571:
3567:
3560:
3555:
3551:
3547:
3543:
3539:
3532:
3527:
3523:
3519:
3515:
3511:
3504:
3499:
3496:
3492:
3488:
3481:
3476:
3473:
3469:
3465:
3458:
3453:
3450:
3446:
3442:
3438:
3434:
3427:
3422:
3419:
3415:
3411:
3407:
3403:
3396:
3391:
3387:
3383:
3379:
3372:
3367:
3363:
3359:
3355:
3348:
3343:
3340:
3336:
3332:
3325:
3320:
3317:
3313:
3309:
3305:
3298:
3293:
3289:
3285:
3281:
3274:
3269:
3265:
3261:
3257:
3253:
3246:
3241:
3237:
3233:
3226:
3221:
3220:
3219:
3215:
3213:
3212:
3188:
3185:
3171:
3156:
3147:
3142:
3139:
3135:
3126:
3110:
3102:
3091:
3089:
3085:
3080:
3060:
3055:
3046:
3038:
3030:
3023:
3019:
3015:
3011:
3008:
3003:
2999:
2995:
2991:
2987:
2983:
2982:
2981:
2979:
2975:
2941:
2932:
2927:
2924:
2920:
2915:
2911:
2908:
2905:
2901:
2896:
2892:
2889:
2886:
2882:
2878:
2876:
2867:
2858:
2849:
2841:
2836:
2822:
2811:
2803:
2798:
2784:
2773:
2765:
2761:
2759:
2745:
2736:
2731:
2723:
2712:
2707:
2699:
2688:
2680:
2678:
2657:
2654:
2651:
2648:
2645:
2642:
2639:
2633:
2626:
2624:
2616:
2613:
2610:
2607:
2604:
2601:
2598:
2592:
2581:
2580:
2579:
2577:
2573:
2554:
2546:
2541:
2533:
2522:
2517:
2509:
2498:
2493:
2481:
2478:
2475:
2472:
2469:
2466:
2463:
2457:
2447:
2446:
2445:
2442:
2409:
2404:
2401:
2398:
2395:
2392:
2386:
2383:
2380:
2377:
2374:
2371:
2368:
2362:
2355:
2354:
2353:
2350:
2348:
2343:
2341:
2333:
2312:
2309:
2306:
2303:
2300:
2297:
2294:
2288:
2279:The value of
2277:
2249:
2240:
2235:
2227:
2222:
2214:
2208:
2203:
2199:
2196:
2193:
2189:
2184:
2180:
2177:
2174:
2170:
2166:
2164:
2155:
2146:
2143:
2140:
2134:
2129:
2115:
2104:
2096:
2091:
2077:
2066:
2058:
2054:
2052:
2038:
2035:
2032:
2029:
2021:
2010:
2005:
1997:
1986:
1978:
1976:
1955:
1952:
1949:
1946:
1943:
1940:
1937:
1931:
1924:
1922:
1914:
1911:
1908:
1905:
1902:
1899:
1896:
1890:
1879:
1878:
1877:
1875:
1871:
1852:
1849:
1846:
1843:
1835:
1824:
1819:
1811:
1800:
1795:
1783:
1780:
1777:
1774:
1771:
1768:
1765:
1759:
1749:
1748:
1747:
1735:
1719:
1703:
1702:
1701:
1698:
1690:
1688:
1660:
1655:
1652:
1649:
1641:
1636:
1633:
1625:
1620:
1613:
1601:
1596:
1593:
1590:
1587:
1584:
1576:
1571:
1568:
1565:
1557:
1546:
1541:
1538:
1535:
1532:
1529:
1521:
1516:
1506:
1498:
1493:
1485:
1480:
1477:
1474:
1466:
1455:
1450:
1447:
1439:
1428:
1417:
1412:
1409:
1401:
1396:
1393:
1385:
1376:
1370:
1367:
1364:
1361:
1358:
1355:
1352:
1346:
1335:
1334:
1333:
1330:
1311:
1306:
1303:
1300:
1292:
1287:
1284:
1276:
1271:
1262:
1252:
1243:
1239:
1235:
1231:
1227:
1222:
1209:
1206:
1197:
1194:
1191:
1188:
1185:
1182:
1181:
1180:
1177:
1169:
1160:
1141:
1136:
1100:
1098:
1088:
1085:
1080:
1067:
1058:
1050:
1043:
1025:
1021:
997:
994:
991:
988:
985:
982:
979:
976:
973:
970:
967:
964:
961:
958:
955:
949:
946:
943:
938:
934:
927:
923:
917:
914:
911:
908:
905:
902:
899:
893:
886:
883:
865:
861:
837:
834:
831:
828:
825:
822:
819:
816:
813:
810:
807:
804:
801:
798:
795:
789:
786:
783:
778:
774:
767:
763:
757:
754:
751:
748:
745:
742:
739:
733:
726:
725:
724:
700:
697:
694:
691:
688:
684:
680:
677:
674:
671:
668:
664:
660:
657:
654:
651:
648:
644:
640:
637:
634:
631:
628:
624:
620:
617:
614:
611:
608:
604:
600:
597:
594:
591:
588:
584:
580:
577:
574:
571:
568:
564:
560:
557:
554:
551:
548:
544:
540:
537:
534:
531:
528:
524:
520:
517:
514:
511:
508:
504:
500:
497:
494:
491:
488:
484:
480:
477:
474:
471:
468:
464:
460:
457:
454:
451:
448:
444:
440:
437:
434:
431:
428:
424:
420:
417:
414:
411:
408:
404:
400:
397:
394:
391:
388:
384:
364:
361:
358:
355:
352:
349:
346:
340:
331:
329:
326:
324:
321:
319:
316:
314:
311:
308:
307:
301:
299:
295:
285:
283:
279:
275:
271:
267:
263:
258:
256:
252:
248:
243:
241:
236:
234:
230:
226:
222:
218:
214:
210:
206:
202:
198:
195:expressions.
194:
190:
186:
182:
160:
156:
152:
144:
140:
136:
132:
127:
123:
108:
104:
101:
93:
87:
83:
79:
75:
71:
68:
65:
61:
57:
54:
51:
50:
44:
38:
36:
31:You can help
27:
18:
17:
4712:Karnaugh map
4711:
4697:Venn diagram
4647:. Retrieved
4589:. Retrieved
4559:
4554:
4530:
4517:
4464:
4458:
4444:0-33319266-4
4429:
4417:. Retrieved
4404:
4383:Venn diagram
4380:
4358:
4333:
4305:
4280:. Retrieved
4265:
4254:. Retrieved
4225:
4214:. Retrieved
4199:
4171:
4165:
4133:
4103:1-11784984-8
4088:
4067:
4063:
4055:. Retrieved
4043:
4037:
4031:
3993:
3945:
3899:0-44201794-4
3886:
3880:
3864:. Retrieved
3857:the original
3844:
3838:
3799:
3779:Venn diagram
3720:
3710:
3706:
3702:
3698:
3692:
3686:
3682:
3676:
3666:
3657:Veitch chart
3656:
3646:
3641:
3623:
3619:
3604:
3600:
3596:
3592:
3577:
3573:
3569:
3565:
3549:
3545:
3541:
3537:
3521:
3517:
3513:
3509:
3494:
3490:
3486:
3471:
3467:
3463:
3448:
3444:
3440:
3436:
3432:
3417:
3413:
3409:
3405:
3401:
3385:
3381:
3377:
3361:
3357:
3353:
3338:
3334:
3330:
3315:
3311:
3307:
3303:
3287:
3283:
3279:
3263:
3259:
3255:
3251:
3235:
3231:
3216:
3208:
3177:
3124:
3092:
3082:The term is
3081:
3047:
3043:
3021:
3017:
3013:
3006:
3001:
2997:
2993:
2989:
2977:
2971:
2963:Race hazards
2569:
2443:
2429:
2351:
2346:
2344:
2337:
2331:
1867:
1745:
1699:
1696:
1684:
1331:
1263:
1253:
1241:
1237:
1233:
1229:
1225:
1223:
1213:
1207:
1195:
1189:
1183:
1178:
1175:
1138:The grid is
1137:
1125:is true and
1101:
1094:
1081:
1077:
1074:Construction
706:
327:
322:
317:
312:
291:
259:
244:
237:
232:
228:
224:
220:
216:
212:
205:Veitch chart
204:
188:
184:
181:Karnaugh map
180:
178:
142:
130:
122:
82:edit summary
73:
40:
32:
4732:Truth table
4566:Adobe Flash
4471:: 206–207.
4449:(146 pages)
4367:. pp.
4313:. pp.
3678:Mahoney map
3673:(1907–1980)
3663:(1924–2013)
3653:(1853–1924)
3622:(1,2,3,4);
2968:Elimination
2271:Don't cares
298:truth table
262:logic gates
247:truth table
4766:Categories
4649:2023-12-18
4591:2022-11-26
4419:2017-04-19
4411:. Part 3.
4282:2012-10-07
4256:2017-04-18
4216:2009-05-30
4057:2017-05-15
3908:1036797958
3866:2017-04-16
3811:References
3669:(1956) by
3659:(1952) by
3649:(1881) by
3000:is 1, and
2340:don't care
1140:toroidally
1135:is true).
4522:CRC Press
4501:0018-9359
4493:1557-9638
4405:Logic 101
4303:(1998) .
4192:Gray code
4156:72-181095
3709:(VEM) or
3595:(2,3,4);
3568:(1,3,4);
3540:(1,2,4);
3512:(1,2,3);
3186:∑
3151:¯
3106:¯
3084:redundant
3064:¯
3016:is 0 and
2992:is 1 and
2936:¯
2863:¯
2853:¯
2832:¯
2826:¯
2815:¯
2794:¯
2788:¯
2777:¯
2750:¯
2740:¯
2727:¯
2716:¯
2703:¯
2692:¯
2669:¯
2665:¯
2550:¯
2537:¯
2526:¯
2513:¯
2502:¯
2489:¯
2413:¯
2244:¯
2231:¯
2218:¯
2151:¯
2125:¯
2119:¯
2108:¯
2087:¯
2081:¯
2070:¯
2043:¯
2025:¯
2014:¯
2001:¯
1990:¯
1967:¯
1963:¯
1839:¯
1828:¯
1815:¯
1804:¯
1791:¯
1664:¯
1645:¯
1629:¯
1605:¯
1580:¯
1561:¯
1550:¯
1525:¯
1502:¯
1489:¯
1470:¯
1459:¯
1443:¯
1432:¯
1421:¯
1405:¯
1389:¯
1315:¯
1296:¯
1280:¯
1172:maxterms.
1084:Gray code
950:∈
928:∏
790:∈
768:∑
270:AND gates
251:Gray code
153:∑
100:talk page
37:in German
4777:Diagrams
4582:Archived
4509:25576523
4413:Archived
4409:EE Times
4391:Karnaugh
4387:minterms
4377:68-21185
4276:Archived
4247:Archived
4210:Archived
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882:minterms
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276:, and a
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