1110:— 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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3225:) 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.
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2963:{\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}}}
2271:{\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}}}
3256:
3308:
3284:
3335:
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1686:{\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}}}
2353:" 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.
3229:
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.
3055:
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
1153:
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
3228:
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
1182:
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
291:(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
264:, 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
2576:
3850:
1874:
1097:
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.
3089:
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.
2987:. 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,
3015:
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
1071:
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
77:, 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.
1089:
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.
295:, 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.
2452:. 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).
862:
1338:
1022:
4049:
3728:, 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)
1187:
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.
2600:
1898:
1354:
249:
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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63:
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3132:
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2345:= 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
2337:
389:
184:
4205:. 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.)
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1049:
889:
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3035:
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.
4253:
3842:
2991:
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.
4220:
80:
Do not translate text that appears unreliable or low-quality. If possible, verify the text with references provided in the foreign-language article.
3134:
must be added to the inverse to eliminate another potential race hazard. Applying De Morgan's laws creates another product of sums expression for
4423:
4566:
KV-Diagramme in der
Schaltalgebra - Verknüpfungen, Beweise, Normalformen, schaltalgebraische Umformungen, Anschauungsmodelle, Paradebeispiele
740:
4689:
1278:
900:
268:
of the logic in the original truth table. These terms can be used to write a minimal
Boolean expression representing the required logic.
2360:(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.
1197:
is the same and is equal to 1 throughout the box, therefore it should be included in the algebraic representation of the red minterm.
4321:
4571:
KV diagrams in
Boolean algebra - relations, proofs, normal forms, algebraic transformations, illustrative models, typical examples
3681:
3189:
The following are all the possible 2-variable, 2 × 2 Karnaugh maps. Listed with each is the minterms as a function of
718:
Following are two different notations describing the same function in unsimplified
Boolean algebra, using the Boolean variables
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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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4015:
271:
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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2571:{\displaystyle {\overline {f(A,B,C,D)}}={\overline {A}}\,{\overline {B}}+{\overline {A}}\,{\overline {C}}+{\overline {A}}D}
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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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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
101:
Content in this edit is translated from the existing German
Knowledge article at ]; see its history for attribution.
4453:
4112:
3908:
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265:
4647:
4022:
3700:, 1963) by Matthew V. Mahoney (a reflection-symmetrical extension of Karnaugh maps for larger numbers of inputs)
4470:
4104:
3763:
3736:(MRM, 1990) by Thomas R. McCalla (a three-dimensional extension of Karnaugh maps for larger numbers of inputs)
1869:{\displaystyle {\overline {f(A,B,C,D)}}={\overline {A}}\,{\overline {B}}+{\overline {A}}\,{\overline {C}}+BCD}
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17:
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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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45:
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After the Karnaugh map has been constructed, it is used to find one of the simplest possible forms — a
288:
276:
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3062:
3851:
Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics
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292:
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1711:
The three terms to cover the inverse are all shown with grey boxes with different colored borders:
96:
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assigned 1s and 0s to the squares and their labels and deduced the numbering scheme in common use.
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304:
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but now with a focus set on its utility for switching circuits. Veitch charts are also known as
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This should not be confused with the negation of the result of the previously found function.
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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.
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It would also have been possible to derive this simplification by carefully applying the
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are true, i.e. the cells numbered 13, 9, 15, 11 in the diagram above. On the other hand,
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4368:
4073:(NB. Quite many secondary sources erroneously cite this work as "A logical diagram for
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Karnaugh maps also allow easier minimizations of functions whose truth tables include "
140:
An example Karnaugh map. This image actually shows two Karnaugh maps: for the function
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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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3755:(BDD), a data structure that is a compressed representation of a Boolean function
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1700:, but the time it takes to do that grows exponentially with the number of terms.
307:
functions. For example, consider the Boolean function described by the following
203:
4438:
Lind, Larry Frederick; Nelson, John Christopher Cunliffe (1977). "Section 2.3".
2356:
The example on the right is the same as the example above but with the value of
1708:
The inverse of a function is solved in the same way by grouping the 0s instead.
1262:. Note that it is acceptable that the green grouping overlaps with the red one.
4637:
POCKET–PC BOOLEAN FUNCTION SIMPLIFICATION, Ledion Bitincka — George E. Antoniou
4147:(1 ed.). Binghamton, New York, USA: Litton Educational Publishing, Inc. /
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4050:
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
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onto a two-dimensional grid where, in Karnaugh maps, the cells are ordered in
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4201:(NB. The two page sections taken together say that K-maps are labeled with
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1063:
K-map drawn on a torus, and in a plane. The dot-marked cells are adjacent.
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3900:. The Bell Laboratories Series (1 ed.). Princeton, New Jersey, USA:
3688:
308:
272:
257:
4762:
4311:
1076:
99:
to the source of your translation. A model attribution edit summary is
4581:(e-book) (in German) (1 ed.). Berlin, Germany: viademica Verlag.
3957:
Proceedings of the 1952 ACM national meeting (Pittsburgh) on - ACM '52
857:{\displaystyle f(A,B,C,D)=\sum _{}m_{i},i\in \{6,8,9,10,11,12,13,14\}}
4532:
4202:
1094:
1059:
261:
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1225:
Thus the first minterm in the Boolean sum-of-products expression is
4419:
3939:(viii+635 pages) (NB. This book was reprinted by Chin Jih in 1969.)
3097:
in terms of the static logic of the system, but such redundant, or
1333:{\displaystyle A{\overline {C}}+A{\overline {B}}+BC{\overline {D}}}
1067:
1052:
1017:{\displaystyle f(A,B,C,D)=\prod _{}M_{i},i\in \{0,1,2,3,4,5,7,15\}}
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4166:
3955:(1952-05-03) . "A chart method for simplifying truth functions".
284:
149:
145:
4387:
74:
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3051:
Above diagram with consensus terms added to avoid race hazards.
3843:"The Map Method for Synthesis of Combinational Logic Circuits"
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3101:, are often needed to assure race-free dynamic performance.
4479:
1080:
In three dimensions, one can bend a rectangle into a torus.
303:
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).
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to map (i.e., rows that have output 1 in the truth table).
156:() signifies a sum of minterms, denoted in the article as
4654:
4254:
Erik Jonsson School of Engineering and Computer Science
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Karnaugh maps are useful for detecting and eliminating
3195:
4145:
Introduction to the Methodology of Switching Circuits
3144:
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Thus the Karnaugh map has guided a simplification of
1281:
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743:
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162:
256:
The required Boolean results are transferred from a
70:
4628:, Circuit design project to control traffic lights.
4366:Wickes, William E. (1968). "3.5. Veitch Diagrams".
3020:(a momentary transition of the output to 0) exists.
148:(colored rectangles) and for its complement, using
66:
a machine-translated version of the German article.
4367:
4005:Boolean Reasoning - The Logic of Boolean Equations
3898:A new approach to the design of switching circuits
3210:
3173:
3126:
3081:
2962:
2570:
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1265:In the same way, the blue grouping gives the term
1117:would mean a cell which covers the 2x2 area where
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1016:
883:
856:
383:
178:
4441:Analysis and Design of Sequential Digital Systems
4345:Switching Theory: Insight Through Predicate Logic
238:-(albeit only rarely)- and even Karnaugh maps as
4774:
4529:Computer Arithmetic and Verilog HDL Fundamentals
4343:Vingron, Shimon Peter (2004) . "Karnaugh Maps".
4143:(May 1972). "Reference Notations to Chapter 2".
3653:Related graphical minimization methods include:
131:Graphical method to simplify Boolean expressions
4243:"Simplifying Logic Circuits with Karnaugh Maps"
4031:
4029:
3833:
3831:
4089:
4087:
4007:(reissue of 2nd ed.). Mineola, New York:
3174:{\displaystyle \left(A+{\overline {D}}\right)}
2431:{\displaystyle f(A,B,C,D)=A+BC{\overline {D}}}
95:accompanying your translation by providing an
57:Click for important translation instructions.
44:expand this article with text translated from
4683:
4626:Using Karnaugh maps in practical applications
3947:
3945:
4097:(1958). "6. Marquand's Machine and Others".
4026:
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3996:
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1011:
963:
851:
803:
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4135:
4133:
4084:
3649:Logic optimization § Graphical methods
2455:The inverse case is simplified as follows:
4690:
4676:
4437:
4234:
4208:
4183:Digital Design: Principles & Practices
3942:
3889:
3184:
107:{{Translated|de|Karnaugh-Veitch-Diagramm}}
4632:K-Map Tutorial for 2,3,4 and 5 variables
4539:
4274:
4217:"Karnaugh Maps – Rules of Simplification"
3983:
3808:
3043:Race hazards are present in this diagram.
2999:, a potential race condition exists when
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2755:
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2707:
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2517:
2123:
2085:
2029:
2005:
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210:introduced it in 1953 as a refinement of
4526:
4464:Holder, Michel Elizabeth (March 2005) .
4409:
4322:The Benjamin/Cummings Publishing Company
4130:
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3046:
3038:
2285:
1177:
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135:
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14:
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4655:California State University San Marcos
4463:
4365:
4283:"Using Karnaugh Maps to Simplify Code"
4214:
3951:
3895:
2363:This yields the new minimum equation:
279:(SOP) can always be implemented using
4697:
4671:
4562:
4370:Logic Design with Integrated Circuits
4240:
4002:
3882:(NB. Also contains a short review by
4733:Propositional directed acyclic graph
4542:Switching and Finite Automata Theory
4410:Maxfield, Clive "Max" (2006-11-29).
4310:
4139:
4077:terms" or "On a logical diagram for
3776:(1905), a similar diagram in biology
218:, which itself was a rediscovery of
26:
4540:Kohavi, Zvi; Jha, Niraj K. (2009).
4466:"A modified Karnaugh map technique"
4241:Dodge, Nathan B. (September 2015).
3961:Association for Computing Machinery
3059:In our case, an additional term of
1170:, which includes the four corners.
24:
4648:"Guide To The K-Map (Karnaugh Map"
4304:
3759:Espresso heuristic logic minimizer
3708:(RKM) techniques (from 1969) like
25:
4809:
4613:
4250:The University of Texas at Dallas
4041:"XXXIII: On Logical Diagrams for
3221:
3104:Similarly, an additional term of
2441:Note that the first term is just
152:(gray rectangles). In the image,
4761:
4347:. Berlin, Heidelberg, New York:
4280:
3622:
3595:
3568:
3540:
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3466:
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3333:
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3282:
3254:
3234:
3127:{\displaystyle {\overline {A}}D}
3082:{\displaystyle A{\overline {D}}}
31:
4598:from the original on 2022-11-12
4426:from the original on 2017-04-19
4289:from the original on 2017-04-18
4263:from the original on 2017-04-18
4223:from the original on 2017-04-18
2973:
1243:maintain the same state, while
1084:
4609:(282 pages with 14 animations)
4471:IEEE Transactions on Education
4105:McGraw-Hill Book Company, Inc.
4003:Brown, Frank Markham (2012) .
3896:Curtis, Herbert Allen (1962).
3866:. Paper 53-217. Archived from
3764:List of Boolean algebra topics
3205:
3202:
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2671:
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2471:
2400:
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1969:
1945:
1928:
1904:
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1773:
1384:
1360:
931:
907:
771:
747:
378:
354:
105:You may also add the template
13:
1:
4620:Detect Overlapping Rectangles
4103:(1 ed.). New York, USA:
3902:D. van Nostrand Company, Inc.
3821:
3722:variable-entered Karnaugh map
2996:
202:) is a method of simplifying
4215:Belton, David (April 1998).
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1977:
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7:
4753:Method of analytic tableaux
4738:Sentential decision diagram
4579:-capable browser on CD-ROM)
4575:(Windows/Mac executable or
4100:Logic Machines and Diagrams
3740:
3138:, but with a new factor of
3056:considering clocked logic.
1221:changes, so it is excluded.
1173:
1132:would mean the cells where
1101:
10:
4814:
4546:Cambridge University Press
3646:
3218:and the race hazard free (
2332:{\displaystyle f(A,B,C,D)}
1703:
384:{\displaystyle f(A,B,C,D)}
315:Truth table of a function
298:
289:product-of-sums expression
277:sum-of-products expression
179:{\displaystyle \sum m_{i}}
69:Machine translation, like
4798:Logic in computer science
4759:
4703:
4527:Cavanagh, Joseph (2008).
4317:Contemporary Logic Design
4181:Wakerly, John F. (1994).
4063:10.1080/14786448108627104
3780:Quine–McCluskey algorithm
3724:(VEKM) by G. W. Schultz,
3643:Related graphical methods
1757:This yields the inverse:
1698:axioms of Boolean algebra
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436:
416:
396:
46:the corresponding article
4793:Electronics optimization
4009:Dover Publications, Inc.
3953:Veitch, Edward Westbrook
3864:10.1109/TCE.1953.6371932
3801:
1235:For the green grouping,
232:Marquand–Veitch diagrams
4728:Binary decision diagram
4189:. pp. 48–49, 222.
4149:D. van Nostrand Company
4125:. ark:/13960/t5cc1sj6b.
3937:. ark:/13960/t56d6st0q.
3753:Binary decision diagram
3185:2-variable map examples
116:For more guidance, see
4563:Grund, Jürgen (2011).
4496:10.1109/TE.2004.832879
3212:
3175:
3128:
3083:
3052:
3044:
2964:
2572:
2432:
2346:
2333:
2272:
1870:
1687:
1334:
1190:For the red grouping:
1184:
1081:
1073:
1064:
1045:
1018:
885:
858:
385:
293:conditional statements
187:
180:
4622:, by Herbert Glarner.
4376:John Wiley & Sons
3969:10.1145/609784.609801
3785:Reed–Muller expansion
3747:Algebraic normal form
3714:map-entered variables
3647:Further information:
3213:
3211:{\textstyle \sum m()}
3176:
3129:
3084:
3050:
3042:
2965:
2573:
2433:
2334:
2289:
2273:
1871:
1688:
1335:
1181:
1079:
1070:
1062:
1046:
1044:{\displaystyle M_{i}}
1019:
886:
884:{\displaystyle m_{i}}
859:
386:
181:
139:
118:Knowledge:Translation
89:copyright attribution
4713:Square of opposition
4392:a refinement of the
3963:. pp. 127–133.
3796:Zhegalkin polynomial
3718:variable-entered map
3710:infrequent variables
3705:Reduced Karnaugh map
3193:
3142:
3108:
3063:
2596:
2462:
2370:
2296:
1894:
1764:
1350:
1279:
1028:
901:
868:
741:
734:and their inverses.
348:
240:Karnaugh–Veitch maps
160:
4488:2005ITEdu..48..206H
4412:"Reed-Muller Logic"
4185:. New Jersey, USA:
3698:designation numbers
2589:can be determined:
2581:Through the use of
1887:can be determined:
1879:Through the use of
1215:should be included.
1154:bottom. Therefore,
1140:is false (that is,
316:
4642:K-Map troubleshoot
4351:. pp. 57–76.
4312:Katz, Randy Howard
4285:. Quantum Rarity.
4107:pp. 104–116.
3884:Samuel H. Caldwell
3841:(November 1953) .
3769:Logic optimization
3208:
3171:
3124:
3079:
3053:
3045:
2960:
2958:
2568:
2428:
2347:
2329:
2268:
2266:
1866:
1683:
1681:
1330:
1185:
1082:
1074:
1065:
1041:
1014:
943:
881:
854:
783:
381:
314:
188:
176:
97:interlanguage link
4770:
4769:
4698:Diagrams in logic
4588:978-3-939290-08-7
4555:978-0-521-85748-2
4374:. New York, USA:
4171:(xvi+573+1 pages)
4141:Klir, George Jiří
4017:978-0-486-42785-0
3959:. New York, USA:
3839:Karnaugh, Maurice
3726:Thomas E. Osborne
3164:
3119:
3077:
2949:
2876:
2866:
2845:
2839:
2828:
2807:
2801:
2790:
2763:
2753:
2740:
2729:
2716:
2705:
2682:
2678:
2563:
2550:
2539:
2526:
2515:
2502:
2426:
2257:
2244:
2231:
2164:
2138:
2132:
2121:
2100:
2094:
2083:
2056:
2038:
2027:
2014:
2003:
1980:
1976:
1852:
1841:
1828:
1817:
1804:
1677:
1658:
1642:
1618:
1593:
1574:
1563:
1538:
1515:
1502:
1483:
1472:
1456:
1445:
1434:
1418:
1402:
1328:
1309:
1293:
937:
777:
716:
715:
129:
128:
58:
54:
16:(Redirected from
4805:
4765:
4748:Sequent calculus
4692:
4685:
4678:
4669:
4668:
4664:
4662:
4661:
4652:
4606:
4604:
4603:
4597:
4580:
4559:
4536:
4523:
4459:
4434:
4432:
4431:
4406:
4373:
4362:
4339:
4320:. Vol. 26.
4298:
4297:
4295:
4294:
4278:
4272:
4271:
4269:
4268:
4262:
4247:
4238:
4232:
4231:
4229:
4228:
4212:
4206:
4200:
4178:
4172:
4170:
4137:
4128:
4126:
4091:
4082:
4072:
4070:
4069:
4033:
4024:
4021:
4000:
3981:
3980:
3949:
3940:
3938:
3935:978-0-44201794-1
3893:
3887:
3881:
3879:
3878:
3872:
3847:
3835:
3815:
3812:
3733:Minterm-ring map
3672:Edward W. Veitch
3658:Marquand diagram
3626:
3599:
3572:
3544:
3516:
3493:
3470:
3439:
3408:
3384:
3360:
3337:
3310:
3286:
3258:
3238:
3222:previous section
3217:
3215:
3214:
3209:
3180:
3178:
3177:
3172:
3170:
3166:
3165:
3157:
3133:
3131:
3130:
3125:
3120:
3112:
3088:
3086:
3085:
3080:
3078:
3070:
2969:
2967:
2966:
2961:
2959:
2955:
2951:
2950:
2942:
2929:
2925:
2910:
2906:
2885:
2881:
2877:
2872:
2867:
2859:
2856:
2850:
2846:
2841:
2840:
2832:
2829:
2821:
2818:
2812:
2808:
2803:
2802:
2794:
2791:
2783:
2780:
2768:
2764:
2759:
2754:
2746:
2741:
2733:
2730:
2722:
2717:
2709:
2706:
2698:
2695:
2687:
2683:
2674:
2642:
2641:
2583:De Morgan's laws
2577:
2575:
2574:
2569:
2564:
2556:
2551:
2543:
2540:
2532:
2527:
2519:
2516:
2508:
2503:
2498:
2466:
2451:
2450:
2444:
2437:
2435:
2434:
2429:
2427:
2419:
2340:
2338:
2336:
2335:
2330:
2277:
2275:
2274:
2269:
2267:
2263:
2259:
2258:
2250:
2245:
2237:
2232:
2224:
2217:
2213:
2198:
2194:
2173:
2169:
2165:
2160:
2149:
2143:
2139:
2134:
2133:
2125:
2122:
2114:
2111:
2105:
2101:
2096:
2095:
2087:
2084:
2076:
2073:
2061:
2057:
2052:
2039:
2031:
2028:
2020:
2015:
2007:
2004:
1996:
1993:
1985:
1981:
1972:
1940:
1939:
1881:De Morgan's laws
1875:
1873:
1872:
1867:
1853:
1845:
1842:
1834:
1829:
1821:
1818:
1810:
1805:
1800:
1768:
1753:
1749:
1744:
1743:
1739:
1738:
1733:
1728:
1727:
1723:
1722:
1717:
1692:
1690:
1689:
1684:
1682:
1678:
1670:
1659:
1651:
1643:
1635:
1628:
1619:
1611:
1594:
1586:
1575:
1567:
1564:
1556:
1539:
1531:
1525:
1521:
1516:
1508:
1503:
1495:
1484:
1476:
1473:
1465:
1457:
1449:
1446:
1438:
1435:
1427:
1419:
1411:
1403:
1395:
1391:
1339:
1337:
1336:
1331:
1329:
1321:
1310:
1302:
1294:
1286:
1271:
1270:
1261:
1260:
1231:
1230:
1214:
1213:
1169:
1168:
1165:
1160:
1159:
1145:
1144:
1139:
1135:
1131:
1130:
1124:
1120:
1116:
1050:
1048:
1047:
1042:
1040:
1039:
1023:
1021:
1020:
1015:
953:
952:
942:
890:
888:
887:
882:
880:
879:
863:
861:
860:
855:
793:
792:
782:
733:
729:
725:
721:
392:
390:
388:
387:
382:
317:
313:
283:feeding into an
228:Marquand diagram
212:Edward W. Veitch
208:Maurice Karnaugh
185:
183:
182:
177:
175:
174:
108:
102:
75:Google Translate
56:
52:
35:
34:
27:
21:
4813:
4812:
4808:
4807:
4806:
4804:
4803:
4802:
4783:Boolean algebra
4773:
4772:
4771:
4766:
4757:
4718:Porphyrian tree
4699:
4696:
4659:
4657:
4650:
4646:
4616:
4601:
4599:
4595:
4589:
4574:
4556:
4456:
4446:Macmillan Press
4429:
4427:
4359:
4349:Springer-Verlag
4336:
4307:
4305:Further reading
4302:
4301:
4292:
4290:
4279:
4275:
4266:
4264:
4260:
4245:
4239:
4235:
4226:
4224:
4213:
4209:
4197:
4179:
4175:
4159:
4138:
4131:
4115:
4095:Gardner, Martin
4092:
4085:
4067:
4065:
4057:(75): 266–270.
4037:Marquand, Allan
4034:
4027:
4018:
4001:
3984:
3950:
3943:
3911:
3894:
3890:
3876:
3874:
3870:
3845:
3836:
3829:
3824:
3819:
3818:
3813:
3809:
3804:
3743:
3682:Antonín Svoboda
3651:
3645:
3638:
3627:
3618:
3600:
3591:
3573:
3564:
3545:
3536:
3517:
3508:
3494:
3485:
3471:
3462:
3440:
3431:
3409:
3400:
3385:
3376:
3361:
3352:
3338:
3329:
3311:
3302:
3287:
3278:
3259:
3250:
3239:
3194:
3191:
3190:
3187:
3156:
3149:
3145:
3143:
3140:
3139:
3111:
3109:
3106:
3105:
3099:consensus terms
3069:
3064:
3061:
3060:
2995:In the example
2985:race conditions
2981:
2976:
2957:
2956:
2941:
2934:
2930:
2915:
2911:
2896:
2892:
2883:
2882:
2858:
2857:
2855:
2851:
2831:
2820:
2819:
2817:
2813:
2793:
2782:
2781:
2779:
2775:
2766:
2765:
2745:
2732:
2721:
2708:
2697:
2696:
2694:
2685:
2684:
2643:
2640:
2633:
2599:
2597:
2594:
2593:
2587:product of sums
2555:
2542:
2531:
2518:
2507:
2467:
2465:
2463:
2460:
2459:
2448:
2446:
2442:
2418:
2371:
2368:
2367:
2297:
2294:
2293:
2291:
2284:
2265:
2264:
2249:
2236:
2223:
2222:
2218:
2203:
2199:
2184:
2180:
2171:
2170:
2150:
2148:
2144:
2124:
2113:
2112:
2110:
2106:
2086:
2075:
2074:
2072:
2068:
2059:
2058:
2030:
2019:
2006:
1995:
1994:
1992:
1983:
1982:
1941:
1938:
1931:
1897:
1895:
1892:
1891:
1885:product of sums
1844:
1833:
1820:
1809:
1769:
1767:
1765:
1762:
1761:
1751:
1747:
1741:
1740:
1736:
1735:
1731:
1725:
1724:
1720:
1719:
1715:
1706:
1680:
1679:
1669:
1650:
1634:
1629:
1627:
1621:
1620:
1610:
1585:
1566:
1555:
1530:
1523:
1522:
1520:
1507:
1494:
1475:
1464:
1448:
1437:
1426:
1410:
1394:
1392:
1390:
1353:
1351:
1348:
1347:
1320:
1301:
1285:
1280:
1277:
1276:
1268:
1266:
1258:
1256:
1228:
1226:
1211:
1210:
1176:
1166:
1163:
1162:
1157:
1155:
1142:
1141:
1137:
1133:
1128:
1126:
1122:
1118:
1114:
1104:
1087:
1035:
1031:
1029:
1026:
1025:
948:
944:
941:
902:
899:
898:
875:
871:
869:
866:
865:
788:
784:
781:
742:
739:
738:
731:
727:
723:
719:
349:
346:
345:
343:
305:Boolean algebra
301:
251:race conditions
224:logical diagram
204:Boolean algebra
170:
166:
161:
158:
157:
132:
125:
124:
123:
106:
100:
59:
53:(February 2018)
36:
32:
23:
22:
15:
12:
11:
5:
4811:
4801:
4800:
4795:
4790:
4785:
4768:
4767:
4760:
4758:
4756:
4755:
4750:
4745:
4740:
4735:
4730:
4725:
4720:
4715:
4710:
4704:
4701:
4700:
4695:
4694:
4687:
4680:
4672:
4666:
4665:
4644:
4639:
4634:
4629:
4623:
4615:
4614:External links
4612:
4611:
4610:
4587:
4560:
4554:
4544:(3 ed.).
4537:
4531:(1 ed.).
4524:
4461:
4454:
4435:
4407:
4390:. p. 36:
4363:
4357:
4340:
4334:
4306:
4303:
4300:
4299:
4273:
4233:
4207:
4195:
4173:
4169:. C4463-000-3.
4157:
4151:. p. 84.
4129:
4113:
4083:
4025:
4016:
3982:
3941:
3909:
3888:
3858:(5): 593–599.
3826:
3825:
3823:
3820:
3817:
3816:
3806:
3805:
3803:
3800:
3799:
3798:
3793:
3787:
3782:
3777:
3774:Punnett square
3771:
3766:
3761:
3756:
3750:
3742:
3739:
3738:
3737:
3729:
3701:
3685:
3675:
3665:
3662:Allan Marquand
3644:
3641:
3640:
3639:
3628:
3621:
3619:
3601:
3594:
3592:
3574:
3567:
3565:
3546:
3539:
3537:
3518:
3511:
3509:
3495:
3488:
3486:
3472:
3465:
3463:
3441:
3434:
3432:
3410:
3403:
3401:
3386:
3379:
3377:
3362:
3355:
3353:
3339:
3332:
3330:
3312:
3305:
3303:
3288:
3281:
3279:
3260:
3253:
3251:
3240:
3233:
3207:
3204:
3201:
3198:
3186:
3183:
3169:
3163:
3160:
3155:
3152:
3148:
3123:
3118:
3115:
3076:
3073:
3068:
3037:
3036:
3021:
2980:
2977:
2975:
2972:
2971:
2970:
2954:
2948:
2945:
2940:
2937:
2933:
2928:
2924:
2921:
2918:
2914:
2909:
2905:
2902:
2899:
2895:
2891:
2888:
2886:
2884:
2880:
2875:
2871:
2865:
2862:
2854:
2849:
2844:
2838:
2835:
2827:
2824:
2816:
2811:
2806:
2800:
2797:
2789:
2786:
2778:
2774:
2771:
2769:
2767:
2762:
2758:
2752:
2749:
2744:
2739:
2736:
2728:
2725:
2720:
2715:
2712:
2704:
2701:
2693:
2690:
2688:
2686:
2681:
2677:
2673:
2670:
2667:
2664:
2661:
2658:
2655:
2652:
2649:
2646:
2639:
2636:
2634:
2632:
2629:
2626:
2623:
2620:
2617:
2614:
2611:
2608:
2605:
2602:
2601:
2579:
2578:
2567:
2562:
2559:
2554:
2549:
2546:
2538:
2535:
2530:
2525:
2522:
2514:
2511:
2506:
2501:
2497:
2494:
2491:
2488:
2485:
2482:
2479:
2476:
2473:
2470:
2439:
2438:
2425:
2422:
2417:
2414:
2411:
2408:
2405:
2402:
2399:
2396:
2393:
2390:
2387:
2384:
2381:
2378:
2375:
2328:
2325:
2322:
2319:
2316:
2313:
2310:
2307:
2304:
2301:
2283:
2280:
2279:
2278:
2262:
2256:
2253:
2248:
2243:
2240:
2235:
2230:
2227:
2221:
2216:
2212:
2209:
2206:
2202:
2197:
2193:
2190:
2187:
2183:
2179:
2176:
2174:
2172:
2168:
2163:
2159:
2156:
2153:
2147:
2142:
2137:
2131:
2128:
2120:
2117:
2109:
2104:
2099:
2093:
2090:
2082:
2079:
2071:
2067:
2064:
2062:
2060:
2055:
2051:
2048:
2045:
2042:
2037:
2034:
2026:
2023:
2018:
2013:
2010:
2002:
1999:
1991:
1988:
1986:
1984:
1979:
1975:
1971:
1968:
1965:
1962:
1959:
1956:
1953:
1950:
1947:
1944:
1937:
1934:
1932:
1930:
1927:
1924:
1921:
1918:
1915:
1912:
1909:
1906:
1903:
1900:
1899:
1877:
1876:
1865:
1862:
1859:
1856:
1851:
1848:
1840:
1837:
1832:
1827:
1824:
1816:
1813:
1808:
1803:
1799:
1796:
1793:
1790:
1787:
1784:
1781:
1778:
1775:
1772:
1755:
1754:
1745:
1729:
1705:
1702:
1694:
1693:
1676:
1673:
1668:
1665:
1662:
1657:
1654:
1649:
1646:
1641:
1638:
1633:
1630:
1626:
1623:
1622:
1617:
1614:
1609:
1606:
1603:
1600:
1597:
1592:
1589:
1584:
1581:
1578:
1573:
1570:
1562:
1559:
1554:
1551:
1548:
1545:
1542:
1537:
1534:
1529:
1526:
1524:
1519:
1514:
1511:
1506:
1501:
1498:
1493:
1490:
1487:
1482:
1479:
1471:
1468:
1463:
1460:
1455:
1452:
1444:
1441:
1433:
1430:
1425:
1422:
1417:
1414:
1409:
1406:
1401:
1398:
1393:
1389:
1386:
1383:
1380:
1377:
1374:
1371:
1368:
1365:
1362:
1359:
1356:
1355:
1327:
1324:
1319:
1316:
1313:
1308:
1305:
1300:
1297:
1292:
1289:
1284:
1223:
1222:
1216:
1204:
1198:
1175:
1172:
1108:canonical form
1103:
1100:
1086:
1083:
1057:
1056:
1038:
1034:
1013:
1010:
1007:
1004:
1001:
998:
995:
992:
989:
986:
983:
980:
977:
974:
971:
968:
965:
962:
959:
956:
951:
947:
940:
936:
933:
930:
927:
924:
921:
918:
915:
912:
909:
906:
896:
878:
874:
853:
850:
847:
844:
841:
838:
835:
832:
829:
826:
823:
820:
817:
814:
811:
808:
805:
802:
799:
796:
791:
787:
780:
776:
773:
770:
767:
764:
761:
758:
755:
752:
749:
746:
714:
713:
710:
707:
704:
701:
698:
694:
693:
690:
687:
684:
681:
678:
674:
673:
670:
667:
664:
661:
658:
654:
653:
650:
647:
644:
641:
638:
634:
633:
630:
627:
624:
621:
618:
614:
613:
610:
607:
604:
601:
598:
594:
593:
590:
587:
584:
581:
578:
574:
573:
570:
567:
564:
561:
558:
554:
553:
550:
547:
544:
541:
538:
534:
533:
530:
527:
524:
521:
518:
514:
513:
510:
507:
504:
501:
498:
494:
493:
490:
487:
484:
481:
478:
474:
473:
470:
467:
464:
461:
458:
454:
453:
450:
447:
444:
441:
438:
434:
433:
430:
427:
424:
421:
418:
414:
413:
410:
407:
404:
401:
398:
394:
393:
380:
377:
374:
371:
368:
365:
362:
359:
356:
353:
341:
336:
331:
326:
321:
300:
297:
266:canonical form
236:Svoboda charts
220:Allan Marquand
173:
169:
165:
130:
127:
126:
122:
121:
114:
103:
81:
78:
67:
60:
41:
40:
39:
37:
30:
9:
6:
4:
3:
2:
4810:
4799:
4796:
4794:
4791:
4789:
4786:
4784:
4781:
4780:
4778:
4764:
4754:
4751:
4749:
4746:
4744:
4741:
4739:
4736:
4734:
4731:
4729:
4726:
4724:
4721:
4719:
4716:
4714:
4711:
4709:
4706:
4705:
4702:
4693:
4688:
4686:
4681:
4679:
4674:
4673:
4670:
4656:
4649:
4645:
4643:
4640:
4638:
4635:
4633:
4630:
4627:
4624:
4621:
4618:
4617:
4608:
4594:
4590:
4584:
4578:
4572:
4568:
4567:
4561:
4557:
4551:
4547:
4543:
4538:
4534:
4530:
4525:
4521:
4517:
4513:
4509:
4505:
4501:
4497:
4493:
4489:
4485:
4481:
4477:
4473:
4472:
4467:
4462:
4457:
4451:
4447:
4443:
4442:
4436:
4425:
4421:
4417:
4413:
4408:
4405:
4403:
4399:
4395:
4389:
4385:
4381:
4377:
4372:
4371:
4364:
4360:
4358:3-540-40343-4
4354:
4350:
4346:
4341:
4337:
4335:0-8053-2703-7
4331:
4327:
4323:
4319:
4318:
4313:
4309:
4308:
4288:
4284:
4281:Cook, Aaron.
4277:
4259:
4255:
4251:
4244:
4237:
4222:
4218:
4211:
4204:
4198:
4196:0-13-211459-3
4192:
4188:
4187:Prentice Hall
4184:
4177:
4168:
4164:
4160:
4158:0-442-24463-0
4154:
4150:
4146:
4142:
4136:
4134:
4127:(x+157 pages)
4124:
4120:
4116:
4110:
4106:
4102:
4101:
4096:
4090:
4088:
4080:
4076:
4064:
4060:
4056:
4052:
4051:
4046:
4044:
4038:
4032:
4030:
4023:
4019:
4013:
4010:
4006:
3999:
3997:
3995:
3993:
3991:
3989:
3987:
3978:
3974:
3970:
3966:
3962:
3958:
3954:
3948:
3946:
3936:
3932:
3928:
3924:
3920:
3916:
3912:
3906:
3903:
3899:
3892:
3885:
3873:on 2017-04-16
3869:
3865:
3861:
3857:
3853:
3852:
3844:
3840:
3834:
3832:
3827:
3811:
3807:
3797:
3794:
3791:
3788:
3786:
3783:
3781:
3778:
3775:
3772:
3770:
3767:
3765:
3762:
3760:
3757:
3754:
3751:
3748:
3745:
3744:
3735:
3734:
3730:
3727:
3723:
3719:
3715:
3711:
3707:
3706:
3702:
3699:
3695:
3691:
3690:
3686:
3683:
3679:
3678:Svoboda chart
3676:
3673:
3669:
3666:
3663:
3659:
3656:
3655:
3654:
3650:
3636:
3632:
3625:
3620:
3617:
3613:
3609:
3605:
3598:
3593:
3590:
3586:
3582:
3578:
3571:
3566:
3562:
3558:
3554:
3550:
3543:
3538:
3534:
3530:
3526:
3522:
3515:
3510:
3507:
3503:
3499:
3492:
3487:
3484:
3480:
3476:
3469:
3464:
3461:
3457:
3453:
3449:
3445:
3438:
3433:
3430:
3426:
3422:
3418:
3414:
3407:
3402:
3398:
3394:
3390:
3383:
3378:
3374:
3370:
3366:
3359:
3354:
3351:
3347:
3343:
3336:
3331:
3328:
3324:
3320:
3316:
3309:
3304:
3300:
3296:
3292:
3285:
3280:
3276:
3272:
3268:
3264:
3257:
3252:
3248:
3244:
3237:
3232:
3231:
3230:
3226:
3224:
3223:
3199:
3196:
3182:
3167:
3158:
3153:
3150:
3146:
3137:
3121:
3113:
3102:
3100:
3096:
3091:
3071:
3066:
3057:
3049:
3041:
3034:
3030:
3026:
3022:
3019:
3014:
3010:
3006:
3002:
2998:
2994:
2993:
2992:
2990:
2986:
2952:
2943:
2938:
2935:
2931:
2926:
2922:
2919:
2916:
2912:
2907:
2903:
2900:
2897:
2893:
2889:
2887:
2878:
2869:
2860:
2852:
2847:
2833:
2822:
2814:
2809:
2795:
2784:
2776:
2772:
2770:
2756:
2747:
2742:
2734:
2723:
2718:
2710:
2699:
2691:
2689:
2668:
2665:
2662:
2659:
2656:
2653:
2650:
2644:
2637:
2635:
2627:
2624:
2621:
2618:
2615:
2612:
2609:
2603:
2592:
2591:
2590:
2588:
2584:
2565:
2557:
2552:
2544:
2533:
2528:
2520:
2509:
2504:
2492:
2489:
2486:
2483:
2480:
2477:
2474:
2468:
2458:
2457:
2456:
2453:
2420:
2415:
2412:
2409:
2406:
2403:
2397:
2394:
2391:
2388:
2385:
2382:
2379:
2373:
2366:
2365:
2364:
2361:
2359:
2354:
2352:
2344:
2323:
2320:
2317:
2314:
2311:
2308:
2305:
2299:
2290:The value of
2288:
2260:
2251:
2246:
2238:
2233:
2225:
2219:
2214:
2210:
2207:
2204:
2200:
2195:
2191:
2188:
2185:
2181:
2177:
2175:
2166:
2157:
2154:
2151:
2145:
2140:
2126:
2115:
2107:
2102:
2088:
2077:
2069:
2065:
2063:
2049:
2046:
2043:
2040:
2032:
2021:
2016:
2008:
1997:
1989:
1987:
1966:
1963:
1960:
1957:
1954:
1951:
1948:
1942:
1935:
1933:
1925:
1922:
1919:
1916:
1913:
1910:
1907:
1901:
1890:
1889:
1888:
1886:
1882:
1863:
1860:
1857:
1854:
1846:
1835:
1830:
1822:
1811:
1806:
1794:
1791:
1788:
1785:
1782:
1779:
1776:
1770:
1760:
1759:
1758:
1746:
1730:
1714:
1713:
1712:
1709:
1701:
1699:
1671:
1666:
1663:
1660:
1652:
1647:
1644:
1636:
1631:
1624:
1612:
1607:
1604:
1601:
1598:
1595:
1587:
1582:
1579:
1576:
1568:
1557:
1552:
1549:
1546:
1543:
1540:
1532:
1527:
1517:
1509:
1504:
1496:
1491:
1488:
1485:
1477:
1466:
1461:
1458:
1450:
1439:
1428:
1423:
1420:
1412:
1407:
1404:
1396:
1387:
1381:
1378:
1375:
1372:
1369:
1366:
1363:
1357:
1346:
1345:
1344:
1341:
1322:
1317:
1314:
1311:
1303:
1298:
1295:
1287:
1282:
1273:
1263:
1254:
1250:
1246:
1242:
1238:
1233:
1220:
1217:
1208:
1205:
1202:
1199:
1196:
1193:
1192:
1191:
1188:
1180:
1171:
1152:
1147:
1111:
1109:
1099:
1096:
1091:
1078:
1069:
1061:
1054:
1036:
1032:
1008:
1005:
1002:
999:
996:
993:
990:
987:
984:
981:
978:
975:
972:
969:
966:
960:
957:
954:
949:
945:
938:
934:
928:
925:
922:
919:
916:
913:
910:
904:
897:
894:
876:
872:
848:
845:
842:
839:
836:
833:
830:
827:
824:
821:
818:
815:
812:
809:
806:
800:
797:
794:
789:
785:
778:
774:
768:
765:
762:
759:
756:
753:
750:
744:
737:
736:
735:
711:
708:
705:
702:
699:
695:
691:
688:
685:
682:
679:
675:
671:
668:
665:
662:
659:
655:
651:
648:
645:
642:
639:
635:
631:
628:
625:
622:
619:
615:
611:
608:
605:
602:
599:
595:
591:
588:
585:
582:
579:
575:
571:
568:
565:
562:
559:
555:
551:
548:
545:
542:
539:
535:
531:
528:
525:
522:
519:
515:
511:
508:
505:
502:
499:
495:
491:
488:
485:
482:
479:
475:
471:
468:
465:
462:
459:
455:
451:
448:
445:
442:
439:
435:
431:
428:
425:
422:
419:
415:
411:
408:
405:
402:
399:
395:
375:
372:
369:
366:
363:
360:
357:
351:
342:
340:
337:
335:
332:
330:
327:
325:
322:
319:
318:
312:
310:
306:
296:
294:
290:
286:
282:
278:
274:
269:
267:
263:
259:
254:
252:
247:
245:
241:
237:
233:
229:
225:
221:
217:
213:
209:
206:expressions.
205:
201:
197:
193:
171:
167:
163:
155:
151:
147:
143:
138:
134:
119:
115:
112:
104:
98:
94:
90:
86:
82:
79:
76:
72:
68:
65:
62:
61:
55:
49:
47:
42:You can help
38:
29:
28:
19:
18:Karnaugh maps
4723:Karnaugh map
4722:
4708:Venn diagram
4658:. Retrieved
4600:. Retrieved
4570:
4565:
4541:
4528:
4475:
4469:
4455:0-33319266-4
4440:
4428:. Retrieved
4415:
4394:Venn diagram
4391:
4369:
4344:
4316:
4291:. Retrieved
4276:
4265:. Retrieved
4236:
4225:. Retrieved
4210:
4182:
4176:
4144:
4114:1-11784984-8
4099:
4078:
4074:
4066:. Retrieved
4054:
4048:
4042:
4004:
3956:
3910:0-44201794-4
3897:
3891:
3875:. Retrieved
3868:the original
3855:
3849:
3810:
3790:Venn diagram
3731:
3721:
3717:
3713:
3709:
3703:
3697:
3693:
3687:
3677:
3668:Veitch chart
3667:
3657:
3652:
3634:
3630:
3615:
3611:
3607:
3603:
3588:
3584:
3580:
3576:
3560:
3556:
3552:
3548:
3532:
3528:
3524:
3520:
3505:
3501:
3497:
3482:
3478:
3474:
3459:
3455:
3451:
3447:
3443:
3428:
3424:
3420:
3416:
3412:
3396:
3392:
3388:
3372:
3368:
3364:
3349:
3345:
3341:
3326:
3322:
3318:
3314:
3298:
3294:
3290:
3274:
3270:
3266:
3262:
3246:
3242:
3227:
3219:
3188:
3135:
3103:
3093:The term is
3092:
3058:
3054:
3032:
3028:
3024:
3017:
3012:
3008:
3004:
3000:
2988:
2982:
2974:Race hazards
2580:
2454:
2440:
2362:
2357:
2355:
2348:
2342:
1878:
1756:
1710:
1707:
1695:
1342:
1274:
1264:
1252:
1248:
1244:
1240:
1236:
1234:
1224:
1218:
1206:
1200:
1194:
1189:
1186:
1149:The grid is
1148:
1136:is true and
1112:
1105:
1092:
1088:
1085:Construction
717:
338:
333:
328:
323:
302:
270:
255:
248:
243:
239:
235:
231:
227:
223:
216:Veitch chart
215:
199:
195:
192:Karnaugh map
191:
189:
153:
141:
133:
93:edit summary
84:
51:
43:
4743:Truth table
4577:Adobe Flash
4482:: 206–207.
4460:(146 pages)
4378:. pp.
4324:. pp.
3689:Mahoney map
3684:(1907–1980)
3674:(1924–2013)
3664:(1853–1924)
3633:(1,2,3,4);
2979:Elimination
2282:Don't cares
309:truth table
273:logic gates
258:truth table
4777:Categories
4660:2023-12-18
4602:2022-11-26
4430:2017-04-19
4422:. Part 3.
4293:2012-10-07
4267:2017-04-18
4227:2009-05-30
4068:2017-05-15
3919:1036797958
3877:2017-04-16
3822:References
3680:(1956) by
3670:(1952) by
3660:(1881) by
3011:is 1, and
2351:don't care
1151:toroidally
1146:is true).
4533:CRC Press
4512:0018-9359
4504:1557-9638
4416:Logic 101
4314:(1998) .
4203:Gray code
4167:72-181095
3720:(VEM) or
3606:(2,3,4);
3579:(1,3,4);
3551:(1,2,4);
3523:(1,2,3);
3197:∑
3162:¯
3117:¯
3095:redundant
3075:¯
3027:is 0 and
3003:is 1 and
2947:¯
2874:¯
2864:¯
2843:¯
2837:¯
2826:¯
2805:¯
2799:¯
2788:¯
2761:¯
2751:¯
2738:¯
2727:¯
2714:¯
2703:¯
2680:¯
2676:¯
2561:¯
2548:¯
2537:¯
2524:¯
2513:¯
2500:¯
2424:¯
2255:¯
2242:¯
2229:¯
2162:¯
2136:¯
2130:¯
2119:¯
2098:¯
2092:¯
2081:¯
2054:¯
2036:¯
2025:¯
2012:¯
2001:¯
1978:¯
1974:¯
1850:¯
1839:¯
1826:¯
1815:¯
1802:¯
1675:¯
1656:¯
1640:¯
1616:¯
1591:¯
1572:¯
1561:¯
1536:¯
1513:¯
1500:¯
1481:¯
1470:¯
1454:¯
1443:¯
1432:¯
1416:¯
1400:¯
1326:¯
1307:¯
1291:¯
1183:maxterms.
1095:Gray code
961:∈
939:∏
801:∈
779:∑
281:AND gates
262:Gray code
164:∑
111:talk page
48:in German
4788:Diagrams
4593:Archived
4520:25576523
4424:Archived
4420:EE Times
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