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Topic: Minterm

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Sardar Patel

Secular state

	Canonical form (Boolean algebra)
		minterms of n variables - this is true since a variable in the minterm expression can either be in the form of itself or its complement - two choices per n variables.
		For example, minterm 5, a b' c, is true only when a and c both are - the input where a = 1, b = 0, c = 1 results in 1.
		minterms of n variables - this is true since a variable in the maxterm expression also, can either be in the form of itself or its complement - two choices per n variables.
	www.brainyencyclopedia.com /encyclopedia/c/ca/canonical_form__boolean_algebra_.html (657 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		A minterm is that AND function which includes the algebraic symbol for every input to the circuit (usally called input variables, variables or literals) once, and only once, in either true or complemented (inverted) form.
		Further, each minterm corresponds to a single row in the truth table in such a way that the minterm can only have the value 1 when the circuit inputs have the values corresponding to this particular row in the truth table.
		If all the minterms corresponding to an output of 1, and only those are listed, then whenever input conditions exist for which the circuit is required to give an output of 1, one of these listed minterms will have the value 1.
	www.funnyprofessor.com /discrete/dis15.html (605 words)

	Hypercubic Minimization of Logic Circuits (Site not responding. Last check: 2007-10-16)
		A minterm of this Boolean function is represented by one of the 2^n bit strings of length n, corresponding to a vertex of the n-cube.
		The minterms may be reduced to an exact minimal form using the geometry of the hypercube.
		A 0 in the kth bit indicates the complement of variable k in the minterm, and a 1 in the kth bit indicates variable k in the minterm.
	sweb.uky.edu /~jcscov0/hypercubic_minimization_of_logic.htm (545 words)

	Static PLA with state machine controlled by model of both minterm and an output line
		The state of the inputs to the minterm and the state of the other minterms determines the array line output and this output along with the logic signal on line 24 determines the final PLA line output.
		Consider first the minterm 10, charged at the beginning of the evaluate period, if this minterm is not discharged by one of the inputs, a prolonged evaluate period will cause the minterm to discharge because of leakage thereby losing data.
		2, a minterm and output line forming a portion of a data array as used in the currently preferred embodiment of the invention is shown.
	www.freepatentsonline.com /5274281.html (4005 words)

	Dictionary of Meaning www.mauspfeil.net (Site not responding. Last check: 2007-10-16)
		We firstly begin with defining a ''minterm'' as a logical expression of ''n'' variables consisting of only the logical conjunction logical and operator and complements.
		In general, one assigns each minterm (ensuring the variables are written in the same order, usually alphabetic), an index based on the binary value of the minterm.
		If one is given a truth table of a logical function, it is possible to write the function as a "sum of products" (minterms logical conjunction AND'd in series).
	www.mauspfeil.net /Canonical_form_%28Boolean_algebra%29.html (748 words)

	Implicit Transition Relation
		Note that each minterm of the logical formula represents a state of the POM, and each variable of the minterm/state corresponds to an event.
		By least minterms we mean the minterms that represent the initial states of a POM according to the definition 4.
		Note that the completed terms are minterms representing states, whose set of events is contained in the set of events of each other minterm covered by the term.
	www-ti.informatik.uni-tuebingen.de /~moreira/publicat/pom/node11.html (381 words)

	CMSC 313 Lecture 21,
		Remember that a minterm is the input pattern where there is a '1' in the output of a truth table.
		All minterms in a group must have the same number of ones and if any X's, the X's must be in the same position.
		All remaining minterms are prime implicants A B C D __ X 0 X 0 thus F = BD In essence, the Quine McClusky algorithm is doing the same operations as the Karnaugh map.
	www.cs.umbc.edu /~squire/s04-313/cs313_l21.html (964 words)

	Minterm (Site not responding. Last check: 2007-10-16)
		A minterm is composed of every input variable (or its complement) ANDed together
		The truth table for a minterm in an n-variable system has one “1” and 2n - 1 ”0”’s
		A minterm is denoted by a lowercase m and the (equivalent) number of the row on which the “1” occurs
	www.olemiss.edu /courses/EE/ELE_335/Fall1999/335_L09_99/sld008.htm (80 words)

	PHY107 Solved Problems (Site not responding. Last check: 2007-10-16)
		The loop contains both A and B and their complements and so the resulting minterm is NOT C AND D. The green loop is a loop of 2 and so one variable can be eliminated leaving 3 variables in the minterm.
		The K-map shows that this loop is independent of D and so the minterm is given by NOT A AND B AND NOT C. The purple loop is again a loop of 4.
		The corresponding minterm is NOT B AND C. The blue loop is totally redundant as all of the 1s in the blue loop are also contained in another loop.
	www.shef.ac.uk /physics/teaching/phy107/solvekmap.html (313 words)

	Digital Logic - Using Minterms
		Although a minterm expansion will always produce a function you can implement, for any truth table, there are better ways - ways that use fewer gates and which therefore cost less to implement.
		Minterms are often referred to as sum-of-product expressions.
		The minterms are shown to the right of the entries which are ones in the table above.
	www.facstaff.bucknell.edu /mastascu/eLessonsHTML/Logic/Logic2.html (2872 words)

	Static vs. Instance Variables (Site not responding. Last check: 2007-10-16)
		This is the minterm expansion representation of the function.
		Since the minterm expansion is exactly the sum of those minterms, the function will have value 1 iff its minterm expansion has value 1.
		Such an implementation is just a different representation of the minterm expansion, specifically a form of the DAG representation for the syntax of the expression.
	www.cs.hmc.edu /claremont/keller/webBook/ch09/sec05.html (4810 words)

	hypercube (Site not responding. Last check: 2007-10-16)
		These minterms may be referenced in two ways: directly by its gray code or from one of its neighbours.
		The gray code of the minterm is given by the integer pos.
		If the minterm is to be set to present, it is set to false.
	www.ee.iitb.ac.in /uma/~nirmeshs/projects/prog/ee206/assign4/doc/dataStructures/hypercube.html (357 words)

	Topography for sixteen bit CMOS microprocessor with eight bit emulation and abort capability
		The resulting minterm signals are inverted by a row of CMOS inverters, the outputs of which are connected to polycrystalline lines extending into an N-channel sum-of-minterm section.
		A plurality of vertical polycrystalline silicon conductors are connected to the outputs of the respective minterm inverter drivers and run parallel to and the respective vertical vertical diffused lines, intersecting the various horizontal extensions thereof to define the N-channel FETs.
		Making the MOSFET gates even wider decreased the minterm signal propagation time in the vertical direction, but increased the horizontal signal propagation along the polycrystalline silicon lines 176 by increasing the capacitance and the resistance of the polycrystalline silicon lines 176, and hence increasing their RC time constant.
	www.freepatentsonline.com /4739475.html (10267 words)

	Canonical forms of switching functions: (Site not responding. Last check: 2007-10-16)
		Any expression which contains only variables in the minterm (sum of products) form, where each product term contains all the variables, or their complement, exactly once, is a minterm expression.
		Sometimes the minterm and maxterm expression are written in a kind of ``shorthand,'' where the values (0 or 1) of the set of variables is used to form a binary number, the decimal equivalent of which designates the appropriate minterm or maxterm.
		The minterm or maxterm form of the function is not usually the simplest or most concise; e.g.
	www.cs.mun.ca /~paul/cs3724/material/web/notes/node4.html (879 words)

	[No title]
		minterm: is the rows for which the SOP is 1 (any single element has a value
		The rows of a truth are the minterms of the equation
		the minterm is simply all rows for which the truth table yields a true value
	www.sirfsup.com /programmingToolBox/comp_orgI/minterm.txt (311 words)

	ECE3714 Spring 2005 (Site not responding. Last check: 2007-10-16)
		Write each of the following minterm canonical formulas in algebraic form and construct their corresponding truth tables.
		Minterm canonical formula in algebraic form F(x,y,z) = x’y’z’ + x’yz’ + xy’z’ + xy’z + xyz
		Express each of the following functions by a minterm canonical formula without first constructing a truth table.
	www.ece.msstate.edu /~janem/ECE3714/S05/HW/HW4_Maxplus_minterms_KmapsIntro_Solutions.htm (509 words)

	expression (Site not responding. Last check: 2007-10-16)
		This function returns the value of the given variable(or its variable as requested) as represented in the given minterm (1 if present, 0 if complement is present).
		Each minterm is indexed by a number, each digit in its binary representation denoting a particular variable.
		Thus this is a short utility function which is called many times by the evaluate method as well as the main function in assignment class directly.
	www.ee.iitb.ac.in /uma/~nirmeshs/projects/prog/ee206/assign1/ass1/expression.html (410 words)

	CS251 - Computer Organization
		The moral of the story is that SOP gives and easy implementation but it is not always the best.
		MinTerm form is another (more compact) way of expressing a boolean function.
		To get the MinTerm form list the rows of the truth table that contain 1's.
	www.dickinson.edu /~braught/courses/cs251f99/classes/notes10.html (315 words)

	PHY107 Karnaugh Maps (Site not responding. Last check: 2007-10-16)
		Each AND-ed set of variables in the minterm expression is placed in the corresponding cell on the K-map.
		For minterm expressions, the correct labelling for a Karnaugh map corresponding to a 4-input circuit (inputs A, B, C and D) is
		All cells in the K-map set to 1 must be included in at least one loop when developing the minterm or maxterm form.
	www.shef.ac.uk /~phys/teaching/phy107/kmap.html (604 words)

	Untitled Document
		when function is written as a sum of minterms, this is called minterm expansion or a standard sum of products (or canonical sum of products or disjunctive normal form).
		given two different minterms of n varibles, mi and mj at least one variable appears complemented in one of the minterms and uncomplemented in the other.
		so given minterm expansions of f1, f2; the expression f1 f2 contains only these minterms which are present in both f1 and f2.
	optimal.vlsi.uwaterloo.ca /NEW/223-3notes.htm (561 words)

	Finding minimal POS with a K-map
		A'B'C' A minterm is an expression that is 1 for exactly one set of input values.
		The canonical form of an expression is either sum-of-minterms (with a minterm for every element in the onset of the function):
		The structure of a K-map is such that adjacent minterms and maxterms can always be covered by a smaller expression.
	bit-server1.cstp.umkc.edu /vu/course/cs281/lectures/simplification/k-map-pos.html (417 words)

	[No title]
		2) SOP, POS, Minterm and Maxterms (Canonical forms) Canonical means: “Officially approved”, “Orthodox”, “Widely accepted” Lots of ways to write logic expressions: Truth table Schematic (gate) diagram Boolean algebra expressions Only one way to write a truth table but many ways to write a schematic diagram or the Boolean algebra expression.
		Minterm) Need to AND all the zeros in a truth table (POS.
		Boolean cubes: Minterms correspond to a “1” on the cube.
	www-inst.eecs.berkeley.edu /~cs150/fa98/f98section/LECTURES/week3_1.doc (641 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		Given a set of minterm predicates M, there are as many horizontal fragments of relation R as there are minterm predicates.
		A set of simple predicates Pr is said to be complete if and only if the accesses to the tuples of the minterm fragments defined on Pr requires that two tuples of the same minterm fragment have the same probability of being accessed by any application.
		Minterm predicates that form the basis of fragmentation should be mutually exclusive.
	db.uwaterloo.ca /~tozsu/ddbook/notes/Design/outlinee.htm (1625 words)

	ECE 275 Homework #5, Fall 2000
		Since the computer program is designed to operate non-interactively, you need to prepare a data file beforehand that can be input to the program via UNIX redirection.
		The minterm information is usually entered as decimal values, one value per minterm, preceding the very first minterm value with a -1 and following the very last minterm value by -1.
		After all true minterm values are entered, don't cares are entered in the same manner as the true minterms.
	venus.ece.ndsu.nodak.edu /ece/academics/courses/ece275/f2000/assign/hw5f00.htm (958 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		Try to answer all questions on this quiz and when you are done, click on the grade me button at the bottom.
		A'BC If you were to draw a logic circuit corresponding to a minterm expression and fan-in limits were no problem, what would the delay of such a circuit be?
		Many times a minterm expression can be replaced by a much smaller but equivalent one.
	www-cs.canisius.edu /~meyer/253/BOOK/ch2/Quizzes/quiz6.html (305 words)

	ENEE 459Y - Verifier (Site not responding. Last check: 2007-10-16)
		My method is to create a minterm file for each of the 2 blif files.
		The code to create a minterm file....: MinT.c (First command line argument is the input blif file name, second command line argument is the output minterm file.
		The code to compare 2 minterm files: verify.c (First argument is the original minterm file, second is the minterm file generated from the simplified blif.)
	www.enee.umd.edu /courses/enee644.S2000/VerCodes (155 words)

	CS 2513 Week 3 Lectures (Site not responding. Last check: 2007-10-16)
		Given an algebraic expresssion for a function, expand it algebraically to obtain the minterm or maxterm form.
		Write the general form of the minterm and maxterm expansion of a function of n variables.
		The function may be given in minterm, maxterm, or algebraic form.
	www.cs.utsa.edu /~key/courses/cs2514/lectures/Week3.html (294 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		Each minterm corresponds to the unique (only 1) combination of the inputs that give a 1 in a particular row
		Write down the minterm for the combination of A, B and C that is shown:
		How many minterms would there be in the minterm expression at the very most?
	www-cs.canisius.edu /~meyer/253/BOOK/ch2/REVIEW/review2-5njsanswers.html (297 words)

	COURSE NOTES - Boolean Algebra; Minterms and Maxterms (Site not responding. Last check: 2007-10-16)
		A truth table is often used initially to find a solution to a logic problem.
		In this example, the maxterm solution contains only one term, whereas the minterm solution contains three, so clearly the maxterm solution is simpler in this case.
		In the next section, we will see how the sum of products or product of sums can be used to simplify a logic circuit, using a technique known as Karnaugh Maps.
	dragon.herts.ac.uk /course_details/1ELE0023/digital/minterm.htm (280 words)

	EE 270 Homework #5, Fall 1995 (Site not responding. Last check: 2007-10-16)
		The true minterm (and don't care) values should be entered starting on a new line following the last program control parameter value.
		The minterm information should be entered as decimal values, one value per minterm, preceding the very first minterm value with a -1 and following the very last minterm value by -1.
		After all true minterm values are entered, any don't cares should be entered in the same manner as the true minterms.
	venus.ece.ndsu.nodak.edu /ece/academics/courses/ece270/f1995/assign/hw5f95.html (800 words)

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