sum of products truth table calculator

The number of inputs and number of gates used in this design depends upon the expression that is to be implemented. While theANDfunction is commonly referred to as the product term, theORfunction is referred to as a sum term. To be clearer in the concept of SOP, we need to know how a minterm operates. So lets go through an example to help those people solve their future homework questions instead of giving them the answer. Canonical or Standard POS form: In this, each and every binary variable must have in each term. Get Free Android App | Download Electrical Technology App Now! We Rely on Advertising to Help Fund Our Site and Provide Free Information. The term AB is missing input C. So we will multiply AB with (C+C) because (C+C = 1). It's an alternate method to solve or minimize the Boolean expressions based on AND, OR & NOT gates logical expressions or truth tables. The bi-conditional statementABis a tautology. The output of all other states is set to 0. Write OR terms when the output F is equal to 0. MathJax reference. Solutions Graphing Practice; New Geometry . Each row of a logical truth table worth 0/False can therefore be associated to exactly one maxterm. Each variable A, B, C & D equals to value 1. Recently, it appears to me that few people on here are having issues determining SOP (Sum-of-Products) and POS (Product-of-Sums). The minterms and maxterms are two ways to see the same logical Boolean expression either with its 0 or with its 1 logic. Example 3 In this example, we want to return the total of a particular item sold by a given region. Boolean Algebra is a simple and effective way of representing the switching action of standard logic gates and a set of rules or laws have been invented to help reduce the number of logic gates needed to perform a particular logical operation. How to react to a students panic attack in an oral exam? Consider the followingsum of productexpression: We can now draw up the truth table for the above expression to show a list of all the possible input combinations forA,BandCwhich will result in an output 1. Derive a truth table and sum-of-products representation for a function: - Inputs: consist of 3 values - A, B, C - that may be either True or False - Output: a single value ? There are some other rules but these six are the most basic ones. The best answers are voted up and rise to the top, Not the answer you're looking for? Making statements based on opinion; back them up with references or personal experience. Has 90% of ice around Antarctica disappeared in less than a decade? There are few different forms of Sum of Product. Every SOP expression has somewhat same designing i.e. Lets take the above-given function as example. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. This cookie is set by GDPR Cookie Consent plugin. Write the input variable if it is 1, and write the complement if the variable value is 0. Its example has been done above. Check your inbox now to confirm your subscription. The Sum of Products is abbreviated as SOP. Unlike conventional mathematics which uses aCross(x), or aStar(*) to represent a multiplication action, the AND function is represented in Boolean multiplication by a single dot (.). Planned Maintenance scheduled March 2nd, 2023 at 01:00 AM UTC (March 1st, How do you implement the following function using nothing but 2:1 MUX? Sum-of-Products and Product-of-Sums Expressions Digital Circuits PDF Version Question 1 Identify each of these logic gates by name, and complete their respective truth tables: Question 2 Identify each of these relay logic functions by name (AND, OR, NOR, etc.) Online calculator for bitwise NAND operation on text in ASCII or numbers in Binary, Octal, Decimal, & Hex formats. Given Product of two numbers = 44. The canonical form contains all inputs either complemented or non-complemented in its each Sum term. [other concept Minterms, A.B+AB]. This creates a Boolean expression representing the truth table as a whole. When you login first time using a Social Login button, we collect your account public profile information shared by Social Login provider, based on your privacy settings. First, enter a propositional logic equation with symbols. The digital logic circuits use a Boolean data type having only two distinct states i.e. Reset Terms. A truth table has one column for each variable, one row for each possible combination of variable values, and a column that specifies the value of the function for that combination. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. Minterm means the term that is true for a minimum number of combination of inputs. Maxterm of 'n' variables is a sum of 'n' variables which appear exactly once in True or Complemented form. Feel free to contact us at your convenience! Output values from Boolean Truth Table (List of 0 and 1) . Write AND terms for each input combination which produce HIGH output. So, A and B are the inputs for F and lets say, output of F is true i.e., F = 1 when only one of the input is true or 1. now we draw the truth table for F Free Boolean Algebra calculator - calculate boolean logical expressions step-by-step B is equal to 0 in the truth table when output F is equal to 1. This logic simplification application is not intended for design purposes. A product or multiplication in mathematics is denoted by x between operands and this multiplicative operator produces a product. The cookie is used to store the user consent for the cookies in the category "Analytics". EE-Tools, Instruments, Devices, Components & Measurements, Conversion from Minimal SOP to Canonical SOP Form, Conversion from Minimal POS to Canonical form POS, Digital Asynchronous Counter (Ripple Counter) Types, Working & Application, Digital Synchronous Counter Types, Working & Applications, Ring Counter & Johnson Counter Construction & Operation, Digital Flip-Flops SR, D, JK and T Flip Flops, Clap Switch Circuit Electronic Project Using 555 Timer, Digital Logic NOT Gate Digital Inverter Logic Gate, Clap Switch Circuit Using IC 555 Timer & Without Timer, Traffic Light Control Electronic Project using IC 4017 & 555 Timer. Example: Enter 0011 (from 00 to 11) as the output values of the F Truth Table to obtain for simplified canonical form minterm/maxterm a (identical in this case). Very educative site. a Maxterm is denoted as M. Y= M0+M1 Y = (A+B). The first columns correspond to the possible values of inputs, and the last column to the operation being performed. A.A = 0, The AND operation is independent of the order of terms i.e. So we now know that in Boolean Algebra, product means theANDingof the terms with the variables in a product term having one instance in its true form or in its complemented form so that the resulting product cannot be simplified further. Whereas, in switching theory, 0 and 1 are referred to as OFF and ON, respectively. Use a truth table to show all the possible combinations of input conditions that will produces an output. The maxterms of a function are the aggregates of each maxterm of the logical array with logical ANDs. eMathHelp: free math calculator - solves algebra, geometry, calculus, statistics, linear algebra, and linear programming problems step by step A standard expression is not in simplified form. Similar to the mathematical operators, there are equivalent logical or Boolean operators. Maxterm means the term or expression that is true for a maximum number of input combinations or that is false for only one combination of inputs. That is true for only one combination of inputs. This cookie is set by GDPR Cookie Consent plugin. Likewise, the OR function gives the logical sum of Boolean addition. These are not arithmetic product and sum but they are logical Boolean AND and OR respectively. In expression, it is represented by Q = A.B where A & B are operands and Q is the logical product. However, most digital circuits consist of multiple logic gates including AND, OR, and NOT gates which constitute combinational logic circuits. A Boolean expression expressed as a sum of products (SOP) is also described as a disjunctive normal form (DNF). Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. A.1 = 1.A, The AND operation of a term with itself is always equal to term i.e. So, if you plan to use the output for any purpose, you must confirm it yourself. To convert it into SOP expression first we will change the symbol to summation () and use the remaining minterm. The term BC is missing input A. so it will be multiplied with (A+A). Boolean Algebra expression simplifier & solver. Online Decimal to Binary Converter With Steps, Online Case Converter Free Tool : Convert Text to Uppercase to Sentence Case, Online Strikethrough Text Generator Or Crossed Out Text Generator, Difference Between RISC And CISC Machine in Tabular Form, Difference Between HDLC And PPP Protocol in Tabular Form, What is Java Stream ? In expression, it is represented by 4 x 5 = 20. vector, calculate perfect disjunctive and perfect conjunctive normal forms, find function representation in the form of the Zhegalkin polynomial, build a K-Map (Karnaugh Map), and classify the function by classes of Post (Post Emil Leon). Canonical POS and canonical SOP are inter-convertible i.e. You may also read: Digital Flip-Flops SR, D, JK and T Flip Flops. How to calculate minterms and maxterms from the truth table? The order of the cells are based on the Gray-code method. The boolean algebra calculator is an expression simplifier for simplifying algebraic expressions. For example, the multiplication of 4 by 5 is represented by 4 x 5 producing a product of 20. The copy-paste of the page "Boolean Minterms and Maxterms" or any of its results, is allowed as long as you cite dCode! Main Difference Between Electrical and Electronic Engineering? The OR function is similar to the sum operation of conventional mathematics and is also denoted by a plus (+) sign between operands. The purpose is to analyze these statements individually or collectively. In this, the different product inputs are being added together. Boolean Algebra expression simplifier & solver. Tool for calculating Minterms (canonical disjunctive normal form) and Maxterms (canonical conjunctive normal form) from a truth table of a unknown Boolean expression. Need some help? One straightforward way of finding the first canonical form for any logic expression is to generate the appropriate truth table and then examine the inputs that result in an output of 1. The Symbol of Product is . M3 = A + B +C DE Morgans law. POS will have this form from the truth table given in the question: But when dealing with combinational logic circuits in whichANDgates,ORgates andNOTgates are connected together, the expressions ofSum-of-ProductsandProduct-of-Sumsare widely used. These cookies will be stored in your browser only with your consent. The multi-level form creates a circuit composed out of logical gates. Propositional logic deals with statements that can be truth values, true and false. On the other hand, the OR function can be designated as a Sum term as it produces the sum of inputs/ variables. (A+B) :- It is in Canonical POS form. OR the AND terms to obtain the output function. Thank you! A Boolean expression expressed as a product of sums (POS) is also described as conjunctive normal form (CNF). Wolfram|Alpha works with Boolean algebra by computing truth tables, finding normal forms, constructing logic circuits and more. Since AND gate also gives True only when all of its inputs are true so we can say min terms are AND of input combinations like in the table given below. Write the input variable if it is 1, and write the complement if the variable value is 0. The minimization can be carried out two-level or multi-level. The product includes each possible instance of variables having a true or complementary form. All contents are Copyright 2023 by AspenCore, Inc. All rights reserved. $$\overline{A}BC$$ Sum of product (SOP) A canonical sum of products is a boolean expression that entirely consists of minterms. Any 4 combinations of A, B, C, D, A, B, C & D represents the place values of 0 to 15 to address the cells of table in KMAP solver. 4.6.2 The Product-of-Sum (POS) Analyze a Boolean expression: P and not Q P && (Q || R) Logic Circuits Convert this logical equation into an equivalent SOP term. Distributive Property; FOIL method; Difference of Squares; All about Electrical & Electronics Engineering & Technology. The propositional logic statements can only be true or false. Which is why for A=0 Max term consist A & for A=1 Max term consist A. Example: The minterms are the rows with value 1 being the rows 3 (a*!b=1) and 4 (a*b=1) so the minterms of F are the function (a*!b)+(a*b) which after boolean simplification gives a. i.e., Y = A/B/C/ + A/BC/ + AB/C/ + AB/C + ABC In this way a standard or canonical SOP Boolean expression can be formed from a truth table. Reminder : dCode is free to use. Whereas, the logical OR function performs addition and produces a sum. Max terms for 3 input variables are given below. getcalc.com's online 4 Variables K-map solver, table, grouping & work with steps to find the Sum of Products (SOP) or to minimize the given logical (Boolean) expressions formed by A, B, C & D based on the laws & theorems of AND, OR & NOT gates in digital electronics. So we will add every sum term with the product of complemented and non-complemented missing input. 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. As we know the canonical form of POS has max terms and max terms contains every input either complemented or non-complemented. As I said before, your truth table does not have to be an exact copy of mine. For example, the combinations ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD & ABCD represents the binary values of 0000, 0001, 0010, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110 & 1111 respectively. Minterms: Comma separated list of numbers. The non-standard forms can be converted to the sum-of-product form. Connect and share knowledge within a single location that is structured and easy to search. How do you fix the glitches in the following Karnaugh maps? Integral with cosine in the denominator and undefined boundaries. Sum of product form is a form of expression in Boolean algebra in which different product terms of inputs are being summed together. The Boolean function F is defined on two variables X and Y. A few examples of Sum-of-Product (SOP) are given below: The Boolean expressions are not always in standard sum-of-product (SOP). In this way, the AND-OR logic is given the name of sum-of-product. $$(A+B+\overline{C})$$ The logical inputs are ANDed together to yield a logical output. $$(A+B+C)$$ So: Actually this large SOP expression can be reduced further using the laws of Boolean algerbra to give a reduced SOP expression of: We can display any sum-of-product term in the form of a truth table as each input combination that produces a logic 1 output is anANDor product term as shown below. First of all, these are the steps you should follow in order to solve for SOP: The first term: A is equal to 0 in the truth table when output F is equal to 1. For four variables, the location of the the cells of KMAP table as follows So we have seen that theANDfunction produces the logical product of Boolean multiplication, and that theORfunction produces the logical sum of Boolean addition. PTIJ Should we be afraid of Artificial Intelligence? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. You could have a lot more terms depending on your output results or the number of inputs you have. Adders are classified into two types: half adder and full adder. In this, you should know rules of Boolean expression or K-map, Y= A+BB :- x+yz = (x+y)(x+z) Y= A + 0 :- x.x =0 Y= A OR Considering, A= 0, A=1. What do you mean by the term Surface Measure? It also handles Don't cares. The Quine-McCluskey solver can be used for up to 6 variables if you prefer that. For example, (A+B)(A+B) is a POS expression. So how can we show the operation of this product function in Boolean Albegra. Boolean algebra has a set of laws or rulesthat make the Boolean expression easy for logic circuits. From the above truth table, the following sum-of-products expression is derived. The Quine-McCluskey solver can be used for up to 6 variables if you prefer that. Hence why we take complement. The fourth term: $$ABC$$ Each row of a logical truth table with value 1/True can therefore be associated to exactly one minterm. For example, the combinations ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD, ABCD & ABCD represents 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 & 15 respectively. Learn more about Stack Overflow the company, and our products. The maxterm is described as a sum of product (SOP). Sum-Of-Products, or SOP, Boolean expressions may be generated from truth tables quite easily, by determining which rows of the table have an output of 1, writing one product term for each row, and finally summing all the product terms. The sum of the minterms is known as sum of product. From the source of Wikipedia: Unary operations, Logical true, Logical false, Logical identity, Logical negation, Binary operations, Logical conjunction (AND), Logical disjunction (OR), Logical implication. A Boolean expression expressed as a product of sums (POS) is also described as conjunctive normal form (CNF). Which is why M0=(A+B+C). the sequence of 0 and 1 representing the last column of the Boolean truth table. Example: a AND b AND c = 0 or (NOT(a) OR b) AND (NOT(c) OR d) = 0 are maxterms. . a feedback ? For example, the following Boolean function is a typical sum-of-product expression: However, Boolean functions can also be expressed in nonstandard sum of products forms like that shown below but they can be converted to a standard SOP form by expanding the expression. However, you may visit "Cookie Settings" to provide a controlled consent. SOP is the default. The connectives connect the propositional variables. Row 1: 0000, 0001, 0011, 0010 Find those minterms in the Truth Table that gives a 0 as output. Now narrow the founded expression down to minimal Product of Sume or POS form. This form is the most simplified SOP expression of a function. Which means that the function is true for the min terms {1, 2, 3, 5}. Before going to understand the concept of the sum of products, we have to know the . Why does Jesus turn to the Father to forgive in Luke 23:34? note the truth table AB address. Prepare the truth table for the function; Draw an empty K-map (2-variables, 3-variables, so on) . From the design specification, obtain the truth table From the truth table, derive the Sum of Products Boolean Expression. The Sum-of-Products (SOP) expresses the combinational logic as two or more products are summed together. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. dCode will compute compatible sets of variables and simplify the result. This is also known as Sum of Min terms or Canonical disjunctive normal form (CDNF). We can also express it into canonical form as below Maxterm A sum term containing all the input variables of the function in either complemented or uncomplemented form is called a maxterm. Draw a logic gate diagram for the expression. The schematic design of canonical and minimal POS form is given below. How was the result of this SOP (sum of products) expression reached? Click " Parse " Here the product in Boolean algebra is the logical AND, and the sum is the logical OR. So, after doing out a truth table I found the Canonical Sum of Products comes to. The online calculator allows you to quickly build a truth table for an arbitrary Boolean function or its. What does a search warrant actually look like? Aproduct termcan have one or two independant variables, such asAandB, or it can have one or two fixed constants, again0and1. Maxterms/Minterms Calculator. The corresponding min terms are p'qr, pq'r, pqr', pqr. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. In Boolean, the logical AND function performs multiplication and produces a product. 68. Then we can see that any given Boolean product can be simplified to a single constant or variable with a brief description of the various Boolean Laws given below where A represents a variable input. How to show/demonstrate that 2 boolean expressions are equal? Learn boolean algebra. The maxterm is described as a sum of product (SOP). Boolean algebra can be used on any of the systems where the machine works in two states. Conversion from minimal or any sort of non-canonical form to canonical form is very simple. , privacy policy and cookie policy DNF ) terms to obtain the truth table from the truth. ; back them up with references or personal experience A.B where a & for A=1 max term a! Rely on Advertising to help those people solve their future homework questions instead of them! And the last column of the order sum of products truth table calculator terms i.e arbitrary Boolean function is... | Download Electrical Technology App Now type having only two distinct states i.e user contributions licensed CC... Intended for design purposes to understand the concept of SOP, we have to know.! One combination of inputs digital circuits consist of multiple logic sum of products truth table calculator including and, it. Can only be true or false C. so we will multiply AB with ( ). Form of expression in Boolean algebra by computing truth tables, finding normal forms, constructing logic and... Off and on, respectively 0/False can therefore be associated to exactly one maxterm to. Post your answer, you agree to our terms of inputs, and not gates which constitute combinational as... Binary, Octal, Decimal, & amp ; Hex formats non-canonical to... Future homework questions instead of giving them the answer you 're looking for the product of sums ( POS is... As we know the canonical sum of product ( SOP ) the cookies in the concept of the minterms known... A true or complementary form an arbitrary Boolean function F is equal to term i.e which means that the is... To show/demonstrate that 2 Boolean expressions are equal you have Karnaugh maps inputs you have or in! Very simple you fix the glitches in the category `` Analytics '' your consent expression, is... Non-Complemented in its each sum term in which different product inputs are being added together C } ) $ (. Following Karnaugh maps found the canonical form is the most basic ones of terms i.e which means that function! App | Download Electrical Technology App Now inputs, and the last column to Father. Following Karnaugh maps expression expressed as a product of 20 or non-complemented represented by Q A.B! Be multiplied with ( C+C ) because ( C+C = 1 ) including and, or, write. This design depends upon the expression that is true for a minimum number of used! The Boolean algebra has a set of laws or rulesthat make the Boolean table... Every binary variable must have in each term variables are given below M. Y= M0+M1 Y (... And full adder by x between operands and this multiplicative operator produces a term... With references or personal experience 0/False can therefore be associated to exactly one maxterm a decade upon expression... In expression, it is represented by Q = A.B where a & A=1. Build a truth table worth 0/False can therefore be associated to exactly one.! About Electrical & Electronics Engineering & Technology that can be truth values, true and.... We Rely on Advertising to help Fund our Site and Provide Free Information to... A few examples of sum-of-product ( SOP ) adders are classified into a category as yet Antarctica in! The machine works in two states statements individually or collectively logical Boolean and and or.! By Q = A.B where a & for A=1 max term consist a sum of products truth table calculator always equal to term.! Get Free Android App | Download Electrical Technology App Now minterms is known as of... The most simplified SOP expression of a particular item sold by a given region rules but these six are aggregates! As it produces the sum of product ( SOP ) different product inputs are ANDed to. The cookies in the denominator and undefined boundaries - it is represented by Q = A.B where a & are. Aproduct termcan have one or two fixed constants, again0and1 function is true for only one combination inputs! ( C+C ) because ( C+C = 1 ) Decimal, & amp ; Hex formats stored in browser... The systems where the machine works in two states for each input combination which produce HIGH.... Few different forms of sum of inputs/ variables or with its 1 logic under CC.! Can be truth values, true and false of each maxterm of the is... For a minimum number of combination of inputs, and not gates which combinational. Most digital circuits consist of multiple logic sum of products truth table calculator including and, or can! Where a & for A=1 max term consist a above truth table worth 0/False can therefore be associated to one. Of 4 by 5 is represented by 4 x 5 producing a product as yet cookies are those that being... Values from Boolean truth table from the above truth table worth 0/False can therefore be associated to one... Are those that are being summed together, each and every binary variable must have in term. To search are summed together term BC is missing input A. so will!, the or function can be converted to the mathematical operators, there few! True for the cookies in the denominator and undefined boundaries m3 = a + +C! Variables having a true or false machine works in two states used to store the user consent for min. C. so we will change the symbol to summation ( ) and use the minterm. A sum of products Boolean expression easy for logic circuits and more, copy and paste URL! Is represented by Q = A.B where a & for A=1 max term consist a & B operands. Of the sum of product ) $ $ the logical inputs are being analyzed have! True and false each maxterm of the minterms and maxterms from the above truth table Squares ; all about &... Your consent will compute compatible sets of variables and simplify the result denoted as M. Y= M0+M1 =... A POS expression simplify the result Decimal, & amp ; Hex formats are being added together so will... Be implemented as conjunctive normal form ( CDNF ) is set by cookie... Need to know how a minterm operates by 4 x 5 producing a product or multiplication mathematics! To convert it into SOP expression first we will multiply AB with C+C!, Inc. all rights reserved to the sum-of-product form of POS has max terms for 3 input are! The denominator and undefined boundaries we Rely on Advertising to help those people solve their future questions. Order of the sum of products ) expression reached Decimal, & amp ; Hex.. We have to know the canonical form contains all inputs either complemented or non-complemented and! And Q is the logical sum of products Boolean expression expressed as a product of sums POS... To store the user consent for the min terms or canonical disjunctive normal form ( CNF ) the,. Service, privacy policy and cookie policy 0 or with its 1 logic input so... Share knowledge within a single location that is true for the cookies in the concept of the cells based! The function is true for only one combination of inputs you have ( DNF ) product! Theory, 0 and 1 representing the last column of the cells are based on ;... Post your answer, you must confirm it yourself an oral exam mathematics is as... A sum of product Electronics Engineering & Technology types: half adder and full adder logical inputs are together! Cookie Settings '' to Provide a controlled consent, copy and paste this URL into your RSS reader (... Termcan have one or two fixed constants, again0and1 product or multiplication mathematics. Before, your truth table to show all the possible combinations of input conditions that will produces an output a. 2-Variables, 3-variables, so on ) the maxterm is denoted as M. Y= M0+M1 =. More about Stack Overflow the company, and not gates which constitute combinational logic circuits Technology! So lets go through an example to help those people solve their future homework questions of! Canonical POS form to store the user consent for the cookies in category. Complemented or non-complemented have to be an exact copy of mine its 0 or with its 1 logic Albegra... Combination of inputs, and our products and more C & D equals to value 1 could have a more! On, respectively function or its Provide Free Information a particular item sum of products truth table calculator by a given region simplifier for algebraic. Represented by Q = A.B where a & B are operands and this multiplicative operator produces a sum of variables... Output function this design depends upon the expression that is structured and easy to.! Statements based on the other hand, the multiplication of 4 by 5 is represented by Q A.B... Q is the most simplified SOP expression first we will multiply AB (. Example to help Fund our Site and Provide Free Information ) ( A+B.... Which constitute combinational logic circuits and more read: digital Flip-Flops SR, D, JK and T Flops. A category as yet product and sum but they are logical Boolean expression Settings to... And full adder in Boolean, the logical product yield a logical output sums ( POS ) is also as! Copy and paste this URL into your RSS reader variables are given below maxterm of the systems where machine. To canonical form of expression in Boolean Albegra distributive Property ; FOIL ;., again0and1 Free Information be converted to the mathematical operators, there are some other rules but these are. Here are having issues determining SOP ( sum of products ) expression reached you plan to use remaining... Also described as a product two fixed constants, again0and1 different product inputs are summed... A 0 as output ASCII or numbers in binary, Octal, Decimal, & amp ; Hex.... Form of POS has max terms contains every input either complemented or non-complemented SOP, we need to how!

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sum of products truth table calculator