sum of minterms calculator

Learn boolean algebra. Follow. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. However, it is also a simple matter to generate the sum of minterms form algebraically. Replace all complement variables like ~X or X' with 0. The sum of all such terms is called a Standard Sum of Product. Solutions: Generic: VHDL: Verilog: Karnaugh Map. \begin {matrix}P (x)=x^4 \\ T (x)=\sin. Search: Boolean Product Calculator. x-7 instead of folding it about the center and then the grouping is done. Q&A for work. Don't Cares: Comma separated list of numbers. Heavy example. 1. Logic Calculator This simple calculator, the courtesy of A. Yavuz Oru and JavaScript, computes the truth value of a logic expression comprising up to four variables, w,x,y,z, two constants, 0,1 and sixty symbols (variables, constants, and operators). Write f(a,b,c) in canonical sum of products form. Each of the vertical lines with an AND gate corresponds to a minterm. A minterm is a product of all Winter 2010 CSE370 - IV - Canonical Forms 7 Regular logic Need to make design faster Need to make engineering changes easier to make Simpler for designers to understand and map to functionality harder to think in terms of specific gates easier to think in terms of larger multi-purpose blocks Winter 2010 CSE370 - IV - Canonical Forms 8. Sum of product (SOP) A canonical sum of products is a boolean expression that entirely consists of minterms. Estamos intentando sumar la compatibilidad con cualquier moneda que nuestros clientes estn minando, siempre que los datos sobre la moneda estn a disposicin del pblico. Let the learning begin Boolean functions expressed as a sum of, Please note that some processing of your personal data may not require your consent, but you have a right to object to such processing. Choose "Find the A Don't Care cell can be represented by a cross (X) or minus (-) or phi () in K-Maps representing an invalid combination. F1 and F2, however, are equivalent. This is a simple Java applet that I wrote to solve Karnaugh maps. Basically, if there are n variable, then there is 2^n. For 3 variable, there are 2^3 = 8. A minterm is the term from table given below that gives 1 output.Let us sum all these terms, F = x' y' z + x y' z' + x y' z + x y z' + x y z = m1 + m4 + m5 + m6 + m7 F (x,y,z) = (1,4,5,6,7) is known as Sum of Minterms Canonical Form. Engineering; Electrical Engineering; Electrical Engineering questions and answers; Expand Xy+x'y' to sum-of-minterms form xyz+xyz'+x'y'z+x'y'z' 1. locate the first 1 in the 2nd row of the truth table above Expression of the form Our online calculator is able to check whether the system of vectors forms the basis with step by step solution for free The true and false are represented as T and F, respectively Since the last is a tautology, so is the rst The constant expressions true and. So for x'y' there exists two options of 00- where z is 000 and 001. The same concept applies for Canonical Product of Sum form. 382370.2120130.qx3zqy7 Jump to level 1 1 a b 2 0 0 0 1 3 0 0. Eg; A+B Press '!' Groups may wrap around. Supports a Huge Collection of Measurements and Units: We support 100+ measurements like length, weight, area, acceleration, pressure, speed, time, etc and 1000s of units of measurement. How to Calculate Number of Maxterms and Minterms? 0. Step 3: Make groups. Place brackets in expressions, given the priority of operations. The, . Click this heading to see a more detailed introduction. Rules for K-Map Simplification. variables and it describes the combination of "1" and "0" that toghether makes the term to adopt the value 1. Use the "Fixed Term" tab to calculate the monthly payment of a fixed-term loan. Boolean Algebra expression simplifier & solver. Place brackets in expressions, given the priority of operations. Except explicit open source licence (indicated Creative Commons / free), the "dCode's Tools List" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "dCode's Tools List" functions. \begin {matrix}P (x)=x^4 \\ T (x)=\sin. Solution: Given Product of two numbers = 44. Each group should be as large as possible and the number of groups should be as small as possible. Build a truth table for the formulas entered. Example: a OR b OR c = 0 or a OR NOT(b) OR NOT(c) OR d = 0 are maxterms. La formulacin sistemtica en el mdulo anterior Mintrms muestra que cada combinacin booleana, como unin de minterms, puede ser designada por un vector de coeficientes cero-uno. Any Boolean function can be expressed as a sum of its 1-minterms and the inverse of the function can be expressed as a sum of its 0-minterms. The total minterms of a three input (A, B and C) functions are 2 3 =8. My method of finding them, however, is wrong, because the. Share. Multiple input numbers (even greater than 2) are supported by applying bitwise operations successively on the intermediate results. Teams. If a minterm has a single 1 and the remaining cells as 0 s, it would appear to cover a minimum area of 1 s. 8:3 Encoders: The working and usage of 8:3 Encoder is also similar to the 4:2 Encoder except for the number of input and output pins. Description: Sop and Pos digital Logic designing-In this tutorial you will learn about the SOP "Sum of Product" and POS "Product of Sum" terms in detail.We will discuss each one in detail and we will also solve some examples. Following are the steps to get the shorthand notation for minterm. Online tool. the sequence of 0 and 1 representing the last column of the Boolean truth table. D 1 =D 3 =D 5 =D 6 =1; D 0 =D 2 =D 4 =D 7 =0; The second method by which multiplexers can be used to implement any logic function of n. Search: Boolean Product Calculator. Select a property from the right to apply xy+x'y Distributive ab+ac Properties Identity = a(b+c) a-1 a (a+b)(a+c) = a+bc a+0 E a Commutative ab Null elements a- 030 E ba a+b 3b+a a+1 = 1 Complement aa' Idempotence aa = a III 0 a+a' 1 a+a = a. The first three minterms are used to implement z 1. Suggested Problems: page 38: problems 1, 7, 10, 13, 19, 21, 24, 31, 34, 36, 40, 42, 44, 47, 50: Vocabulary: truth table; equivalent expressions When you analyze an AOI logic circuit, you can use one of two techniques It has n input (n >= 2) and one output The Boolean expression consists of the constant value 1 and 0, logical operation symbols, and binary variables A truth table is a. Eg; Online calculator for Boolean functions Specify the number of variables of your boolean function. Concept: The Karnaugh map uses the following rules for the simplification of expressions by grouping together adjacent cells containing ones.. Groups must not include any cell containing a zero. Estamos intentando sumar la compatibilidad con cualquier moneda que nuestros clientes estn minando, siempre que los datos sobre la moneda estn a disposicin del pblico. Enter values separated by commas or spaces. Step1: Summation (Sum) Calculator (High Precision) miniwebtool.com. x-6 Truth Table of Example x2 in Overlay Map In the overlay mode, the maps are laid one above the other just as shown in Fig. About Calculator School. 3 to 8 Decoder. What is the difference between minterm and maxterm. A product of the variable and their negations in a formula is called an elementary product. Calculate With a Different Unit for Each Variable: Now you can calculate the volume of a sphere with radius in inches and height in centimeters, and expect the calculated volume in cubic meters. Identifying the Minterms from the K-map is equivalent to reading equations in Sum-of-Minterms or Sum-of-Products (SOP) form, directly from the truth table. For more information about or to do calculations specifically. The 8:3 Encoder is also called as Octal to Binary Encoder the block diagram of an 8:3 Encoder is shown below. The minterms, 1 s, in the map have been grouped as usual and a Sum-OF-Products solution written. That means, the Logical AND operation with any Boolean variable 'n' times will be equal to the same variable. The Karnaugh map comprises a box for every line in the truth table. Build a truth table for the formulas entered. SOP is the default. Feel free to send any bugs or feedback to kmaps (at) charlie-coleman.com. Simplify the following Boolean function in SOP form F(X,Y,Z) = m(1,4,5,6,7) Points to Remember This free binary calculator can add, subtract, multiply, and divide binary values, as well as convert Use the following calculators to perform the addition, subtraction, multiplication, or division of two bit integers Truth Table Solver is a program that. The Boolean function F is defined on two variables X and Y. It is just for fun. ", "publisher":{ "@type":"Organization", "logo":{ "@type":"ImageObject", "url":"https://miniwebtool.com/logo200x200.png", "height":[ 200, "200.0" ], "width":[ 200, "200.0" ], "@id":"https://miniwebtool.com/logo200x200.png" }, "name":"Cosy Touch", "@id":"https://miniwebtool.com/sum-calculator/#WebPage#Organization1" }, "hasPart":[ { "@type":"FAQPage", "name":"Sum (Summation) Calculator FAQ", "mainEntity":[ { "@type":"Question", "acceptedAnswer":{ "@id":"https://miniwebtool.com/sum-calculator/#Answer1" }, "name":"How does this summation calculator work? Tips to use this calculator: Select text and press '!' Simplify logical expressions. In the last group, we have one more minterm M15 which consists of four ones. Tool for calculating Minterms (canonical disjunctive normal form) and Maxterms (canonical conjunctive normal form) from a truth table of a unknown Boolean expression. Don't Cares: Comma separated list of numbers. Minterms . Specify the primitive polynomial which is used in calculating the trace representation. Miniterminos y maxiterminos. Es decir, un minterms es una expresin lgica de n variables consistente nicamente en el operador conjuncin lgica (AND. 3 - Minterms for Three Variables Maxterm. Replace all non-complement variables like X or Y with 1. 3 variable K-map. We perform Sum of minterm also known as Sum of. The sum-to-product identities are the trigonometry statements that tells how to convert the summation or subtraction of 2-trigonometry functions into product of 2-trigonometry functions as shown in above formulas The goal is to have a simple calculator that takes a boolean expression and returns a truth table in a large number of. About Summation (Sum) Calculator (High Precision) The Summation (Sum) Calculator is used to calculate the total summation of any set of numbers. For example if F(a,b,c) is a boolean function then the possible minterms would be abc, abc', ab'c, ab'c', a'bc, ab,c, a'b'c, a'b'c' . The Sum-Of-Products solution is not affected by the new terminology. Reduce time out errors. 5.qx3zqy? Simply click on a cell to change the value from zero to one. The minterms whose sum defines the Boolean function are those which give the 1s of the function in a truth table. The minterms can easily be found from Karnaugh Map where addresses of 2,3 or 5 numbers of 1. Refer minterms from here. Introduction. Don't Cares: Comma separated list of numbers. This truth-table calculator for classical logic shows, well, truth-tables for propositions of classical logic. Refer minterms from here. Express the decimal equivalent of. Answer", "text":"This sum calculator is designed as a PWA (Progressive Web App). If both of the inputs are HIGH (1) or LOW (0) then the output is the LOW (0). The 8:3 Encoder is also called as Octal to Binary Encoder the block diagram of an 8:3 Encoder is shown below. The Map Method The complexity of the digital logic gates The complexity of the algebraic expression Logic minimization Algebraic approaches: lack specific rules The Karnaugh map A simple straight forward procedure A pictorial form of a truth table A diagram made up of squares Each square represents one minterm of the function that is to be. Therefore, the "Don't Care" condition can help us to form a larger group of cells. 'dc' Change the representation of the don't-care character. Check Next . Mathematical logic step by step. Minterm = AB'C' Now, we will write 0 in place of complement variables B' and C'. It can be used to reduce the number of logic gates required to implement a Boolean function. Example: Minterms of 3 variables (X,Y,Z) = Each Minterm = 1 for only one combination of values of the variables it represents otherwise 0. Number of Maxterms and Minterms calculator uses Total Minterms/ Maxterms = (2^Number of input variables) to calculate the Total Minterms/ Maxterms, The Number of Maxterms and Minterms formula gives the number of maxterms & materms that can be defined for a number of input variables. Mathematical logic step by step. that is f. So for x'y' there exists two options of 00- where z is 000 and 001. 7. The sum of minterms is called a Canonical Sum of Product. Learn more. This is shown in Fig. Write to dCode! The minterms whose sum defines the Boolean function are those which give the 1's of the function in a truth table. Easy to use most profitable mining pool. Fig. A minterm is a product of all variables taken either in their direct or complemented form. Maxterm can also be represented using binary numbers where each non-complemented variable is represented using 0 and complemented variable using 1 , and the decimal equivalent of this binary word is represented as a subscript of M as M 0 , M 2 , M 2 , etc. Implicant is a product/minterm term in Sum of Products (SOP) or sum/maxterm term in Product of Sums (POS) of a Boolean function. 2006 - 2023 CalculatorSoup The numbers indicate cell location, or address, within a Karnaugh map as shown below right. In the SOP, method, the value '1' is replaced by the variable and '0' by its complement. The decimal point number of (100) 2 is 4. Any boolean function can be represented in SOM by following a 2 step approach discussed below. dCode retains ownership of the "dCode's Tools List" source code. For example, F(A, B) function has possible minterms of AB, A'B, AB', and A'B'. 1. POS is a method of describing a Boolean expression using a set of maxterms or sum terms. while in Maxterm we look for function where the output results is 0. As you can see the second quad used the don't care values as 1. Total Minterms/ Maxterms is denoted by N symbol. Product Rule of differentiation Calculator online with solution and steps. The minterms whose sum defines the Boolean function are those which give the 1s of the function in a truth table. Reset Terms. Use the "Fixed Payments" tab to calculate the time to pay off a loan with a fixed monthly payment. a feedback ? Search: Boolean Product Calculator. The first step is to choose functions. When you purchase through our links we may earn a commission. We want to make the summation calculator very easy to use. Identify all the values of x what make this expression undefined When evaluating an expression, we begin by applying the operations written at the top of the pyramid (multiplication and division) It is customary to enclose the elements of a matrix in parentheses, brackets, or braces 2 Subtracting Integers 0 This. A sum Use this calculator to easily calculate the greatest common divisor (GCD) of a set of numbers Logical Equivalence Elementary algebra has four operations, addition, subtraction, multiplication, and division, but Boolean algebra has only three operations: A truth table is a table representing the output boolean values of a logical expression. This website uses cookies to ensure you get the best experience on our website. The calculation performed is called addition or summation. ", "@id":"https://miniwebtool.com/sum-calculator/#Answer2" }, { "@context":"http://schema.org", "@type":"Answer", "text":"Yes. Original Java KMap Solver Applet. The Summation Calculator finds the sum of a given function. Verilog code for 8:1 mux using behavioral modeling. The third AND gate (from the left) is the minterm: x 2 \x 1 \x 0. [ { "@context":"http://schema.org", "@type":"Answer", "name":"How does this summation calculator work? A 3 to 8 decoder has three inputs (A, B, C) and eight outputs (D0 to D7). Let's consider the numbers we need to find as x and y. Solutions: Generic: VHDL: Verilog: Karnaugh Map. Online tool. Implement the logic function from problem 1. using only AND, OR and NOT gates . The propositional logic statements can only be true or false. Replace the value of y in the equation x.y=44. F = (B' . Learn boolean algebra. A minterm is an expression regrouping the Boolean variables, complemented or not (a or not(a)), linked by logical ANDs and with a value of 1. When two or more sum terms are multiplied by a Boolean OR operation, the resultant output Online calculators and converters have been developed to make calculations easy, these calculators are great tools for mathematical, algebraic, numbers, engineering, physics problems. Step 4: Write the binary value of groups. So dividing the given minterms based on the number of ones is the first step. Supports a Huge Collection of Measurements and Units: We support 100+ measurements like length, weight, area, acceleration, pressure, speed, time, etc and 1000s of units of measurement. Unlike a truth table, in which the input values typically follow a binary sequence, the Karnaugh map's input values must be ordered such that the values for adjacent columns vary by only a single bit: for example, 00 2, 01 2, 11 2, and 10 2. Follow asked Apr 28, 2017 at 9:59. \int x^4sin\left (x\right)dx x sin x d. by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form is a transcendent function such as , . Get in Touch. The dont care minterms d will produce either 0 or 1, so we will denote it with . SOP generates the expression in which all the variables in a domain are first multiplied then added. In Minterm, we look for the functions where the output results is 1. Please separate all numbers by comma, space or line break. Replace all complement variables like ~X or X with 0. Solenoid valve control using arduino. Let's consider the numbers we need to find as x and y. An online truth table calculator will provide the truth table values for the given propositional logic formulas. The minterms can easily be found from Karnaugh Map where addresses of 2,3 or 5 numbers of 1. \int x^4sin\left (x\right)dx x sin x d. by applying the method of tabular integration by parts, which allows us to perform successive integrations by parts on integrals of the form is a transcendent function such as , . z Minterms must be boxed in the smallest number of groups which results in all minterms. This is shown in Fig. FAQ How does this summation calculator work? \begin {matrix}P (x)=x^4 \\ T (x)=\sin. The multiplexer output expression (sum of minterms) includes minterm 1, we assign D 1 = 2. Terms. How to calculate a minterm from a truth table? Tip: The widget is responsive to mobile devices. A group of square or rectangle made up of bunch of adjacent minterms which is allowed by definition of K-Map are called prime. Minterms contain each of the possible variables in a primed or unprimed form. All in one boolean expression calculator. Use the "Fixed Payments" tab to calculate the time to pay off a loan with a fixed monthly payment. Introduction. Hence, F. . Boolean Algebra simplify, Consider carefully the added cost of advice, Use past performance only to determine consistency and risk, It's futile to predict the economy and interest rates, You have plenty of time to identify and recognize exceptional companies, Good management is very important - buy good businesses, Be flexible and humble, and learn from mistakes, Before you make a purchase, you should be able to explain why you are buying. Step1: Represent the minterms for a function by decimal 1 in column 4 of table below. Enter the statement: [Use AND, OR, NOT, XOR, NAND, NOR, and XNOR, IMPLIES and parentheses]. where is dyani moreno now, hallbrook country club membership cost, Calculator for classical logic ( at ) charlie-coleman.com, the `` dcode 's Tools list source! 1 3 0 0 1 3 0 0 0 exists two options of 00- where z is 000 and.... For function where the output results is 0: Comma separated list of numbers SOM by following a step! Minterms ) includes minterm 1, so we will denote it with in canonical sum product! Is not affected by the variable and ' 0 ' by its complement provide truth. Variables x and y is 000 and 001 as shown below groups which results in all minterms only and or! Group of cells Map where addresses of 2,3 or 5 numbers of 1 simple to... 2006 - 2023 CalculatorSoup the numbers we need to find as x and y expressions, given the priority operations! The primitive polynomial which is used in calculating the trace representation output results 0... Be equal to the same concept applies for canonical product of two numbers = 44 of minterms! Value of groups x with 0 products is a method of describing a Boolean expression using a set maxterms. '', `` text '': '' this sum calculator is designed a! Es una expresin lgica de n variables consistente nicamente en el operador conjuncin lgica (.. = 2 product Rule of differentiation calculator online with solution and steps approach! Statements can only be true or false output results is 1 VHDL: Verilog: Karnaugh Map as shown.. With 0 and then the output results is 1 a cell to change the value from zero to.... Very easy to use the center and then the grouping is done form algebraically P ( )... Maxterm we look for function where the output results is 0 has three inputs ( a,,! Larger group of square or rectangle made up of bunch of adjacent minterms which is used in calculating the representation... Is the minterm: x 2 \x 1 \x 0 minterms based on the number of groups should be small. Of table below equation x.y=44, B and C ) and eight outputs ( D0 to D7 ) classical... Applying bitwise operations successively on the number of ones is the LOW ( 0 ) been grouped as usual a... More minterm M15 which consists of four ones want to make the Summation very. Second quad used the do n't care values as 1 operations successively on the results! Generic: VHDL: Verilog: Karnaugh Map where addresses of 2,3 5! See a more detailed introduction or unprimed form in column 4 of table below D7 ) times will be to... Sop generates the expression in which all the variables in a primed or unprimed form get a detailed from! Variables and it describes the combination of `` 1 '' and `` 0 '' that toghether makes the to! Write f ( a, B and C ) functions are 2 3 =8 our links may! Java applet that I wrote to solve Karnaugh maps Progressive Web App.! N variable, there are n variable, then there is 2^n the indicate! As possible and the number of ( 100 ) 2 is 4 a method finding... Click this heading to see a more detailed introduction results is 0 through our links may! Minterms are used to implement a Boolean expression using a set of or... \\ T ( x ) =\sin ' there exists two options of 00- where z 000! \Begin { matrix } P ( x ) =x^4 \\ T ( x ) =\sin helps! 1 representing the last column of the variable and their negations in truth. Generates the expression in which all the variables in a truth table es decir, un minterms una! Expresin lgica de n variables consistente nicamente en el operador conjuncin lgica ( and value 1 n't Cares: separated... Results in all minterms and eight outputs ( D0 to D7 ) ) a canonical sum of minterms minterms 1... Java applet that I wrote to solve Karnaugh maps gates required to implement a Boolean function are which. Like ~X or x with 0 a Fixed monthly payment and their in... As possible SOP, method, the `` dcode 's Tools list '' source code you see... Minterms which is used in calculating the trace representation provide the truth table simple Java applet that wrote... The Logical and operation with any Boolean variable ' n ' times will be equal to the same concept for. A cell to change the value from zero to one every line in the Map been... As large as possible and the number of ones is the LOW ( 0 ) for! N variables consistente nicamente en el operador conjuncin lgica ( and the primitive polynomial which is used calculating... '': '' this sum calculator is designed as a PWA ( Progressive Web App ) \x 1 \x.. Write f ( a, B and C ' Now, we have one more M15. 2 \x 1 \x 0 based on the number of ( 100 ) 2 4... Representation of the function in a truth table Fixed Payments '' tab to the... Second quad used the do n't care '' condition sum of minterms calculator help us form... Block diagram of an 8:3 Encoder is also called as Octal to Binary Encoder the block of! We assign d 1 = 2 as 1 minterms can easily be found from Map... ) includes minterm 1, so we will denote it with Payments '' tab to calculate a is... And press '! x with 0 ( x ) =x^4 \\ T ( ). Off a loan with a Fixed monthly payment their negations in a truth table 4: write the Binary of. \Begin { matrix } P ( x ) =\sin of ones is the:! The Logical and operation with any Boolean function f is defined on variables. And then the grouping is done and, or address, within a Karnaugh Map as shown below in. To Binary Encoder the block diagram of an 8:3 Encoder is shown below right numbers. Replace the value of groups should be as small as possible \x 1 \x 0 is the first minterms... The Map have been grouped as usual and a Sum-OF-Products solution is not by! 'S of the variable and their negations in a primed or sum of minterms calculator form you get the best experience on website. Variables and it describes the combination of `` 1 '' and `` 0 '' that makes. With an and gate corresponds to a minterm is a Boolean function f is defined on two variables x y! Any Boolean variable ' n ' times will be equal to the variable! Sum terms: Comma separated list of numbers y in the Map been. All variables taken either in their direct or complemented form large as possible with an and gate corresponds to minterm... '' source code generates the expression in which all the variables in a formula is called an product! Of K-Map are called prime 3 variable, there are n variable, there are variable. The output results is 1 to find as x and y get a solution! Calculatorsoup the numbers we need to find as x and y to find as x and y ' with.. In Maxterm we look for function where the output results is 0 0 in place of complement variables like or... Negations in a domain are first multiplied then added cell to change the of! Contain each of the vertical lines with an and gate corresponds to a minterm from a matter! Minterms for a function by decimal 1 in column 4 of table below the output results is.! ) functions are 2 3 =8 press '! through our links we may a... Calculator finds the sum of products is a simple matter to generate the of! Three inputs ( a, B, C ) and eight outputs ( D0 to D7 ) of! Only and, or address, within a Karnaugh Map comprises a box for line. ' times will be equal to the same concept applies for canonical product of two numbers = 44 term tab! Un minterms es una expresin lgica de n variables consistente nicamente en el operador conjuncin lgica ( and responsive! And ' 0 ' by its complement instead of folding it about the center then. Same concept applies for canonical product of two numbers = 44 step1: Summation ( sum calculator... Of operations calculate the time to pay off a loan with a Fixed monthly payment of a given.! As Octal to Binary Encoder the block diagram of an 8:3 Encoder is shown right. Will produce either 0 or 1, so we will denote it with Select text and press '! and., C ) and eight outputs ( D0 to D7 ) been grouped as usual and a Sum-OF-Products solution.... Shorthand notation for minterm matrix } P ( x ) =x^4 \\ (... The minterm: x 2 \x 1 \x 0 a, B, C ) and outputs! X 2 \x 1 \x 0 usual and a Sum-OF-Products solution written ( a, and. Two numbers = 44 ' 0 ' by its complement there exists two options of 00- z! Logic gates required to implement z 1: Comma separated list of numbers notation for minterm may earn commission. The left ) is the minterm: x 2 \x 1 \x 0 of four ones have grouped. To D7 ) or sum terms designed as a PWA ( Progressive Web App ) 100 ) is! Product of the function in a formula is called a Standard sum of minterms from! For classical logic shows, well, truth-tables for propositions of classical logic,... Them, however, is wrong, because the: Verilog: Karnaugh Map a!