What are minterms and maxterms in Boolean function? Minterms are called products because they are the logical AND of a set of variables, and maxterms are called sums because they are the logical OR of a set of variables. Electrical Engineering questions and answers. See Answer See Answer See Answer done loadingDigital Circuits Questions and Answers – Karnaugh Map. (c) List the minterms of E + F and EF. 3. Draw a cicult from the eanimured sop equation on the paper you sutems on eleaning h Determine the liferal canchical sum of minterms 7 roe your answer h equaton forn in the space provided – A maxterm of n variables = sum of n literals in which each variable appears exactly once in T or F from, but not in both. F (W, X, Y, Z) = (1, 3, 4, 9, 11, 14, 15) + d (2, 8) a)Obtain the list of all prime. W. Computer Science. Both have their uses depending on the situation. Example. It mainly involves in two Boolean terms, “minterms” and “maxterms”. List the minterms of E + F and E F. a) extbf{a)} a) F. F(A,B,C)=Σm(0,1,3,4) (a) Construct the truth table. Digital Circuits Questions and Answers – Karnaugh Map. The SOP equation uses the summation symbol ∑ to suggest the summing of terms, and the POS equation uses the symbol ∏ to suggest taking the product of terms. Reset Terms. Computer Science questions and answers. This is also referred to as a sum of products. b) Find the minimal sum of products expression. Place ‘1’ in the minterms (cell) which are covered by each prime implicant. These output lines can provide the minterms of input variables. Engineering. Electrical Engineering questions and answers. A minterm is a product of all variables taken either in their direct or complemented form. The numbers indicate cell location, or address, within a Karnaugh map as shown below right. The SOP (Sum of Product) and POS (Product of Sum) are the methods for deducing a particular logic. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Find the output function of each truth table a. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. View the full answer. For example, consider the truth table in Figure 3. Then for Z it's --1, where the values can be 001, 011, 101, 111. A prime implicant is an implicant of minimal size (i. The complement of a canonical product becomes a sum. A Karnaugh map (K-map) is an abstract form of ____________ diagram organized as a matrix of squares. Who are the experts? Experts are tested by Chegg as specialists in their subject area. Previous question Next question. Refer minterms from here. E). This is something I was confused with as well. (10 points) 3. Write a function f(x) to represent the cost of water as a function of x, amount used. (Digital_design-__morris_mano-fifth_edition) Boolean functions expressed as a sum of minterms or product of. Note: Type x for x 385678 25595020 Jump to. Each of these three product statements is a minterm—a term that is True (1) for exactly one combination of inputs. Expert Answer. (a) List the minterms and maxterms of each function. Convert 𝐹 to canonical sum-of-minterms form. A sum-of-products form must be a sum of minterms and a minterm must have each variable or its compliment as a factor. ) Simplify the following function F, together with its don't care conditions d, and express the simplified function in sum of minterms and sum of products forms:Note that Consensus is a combination of Reduction and Distribution: PQR + PQ′ = P(QR +Q′) = P(R +Q′) = PR + PQ′ P Q R + P Q ′ = P ( Q R + Q ′) = P ( R + Q ′) = P R + P Q ′. 2. (d) Derive the product of maxterms expression. Develop a truth table for a 1-bit full subtractor that has a borrow input ºn and input * and, and produces a difference, d, and a borrow output, Pout. Obtain the truth table of the following functions, and express each function in sum-of-minterms and product-of-maxterms form: (a) (XY + Z) (Y + XZ) b) (A bar + B) (B + C) (c) WxY bar + WXZ bar + WXY + YZ For the Boolean functions E and F, as given in the following truth table: List the minterms and maxterms of each function. Solutions: Generic: In this video, the Sum of Product (SOP) and Product of Sum (POS) form of Representation of Boolean Function is explained using examples. ). x’ and y’. A. It is impossible to represent the minterms x1' x2' x3 x4 and x1 x2 x3' x4'. " The term "Sum of Products" is widely used for the canonical form that is a disjunction (OR) of minterms. 0. B (A,D,W)=A′D′W+AA′D′W+AD′W′+ADW+ADWB (A,D,W)=A′DW+A′DW+ADW′+AD′W+ADWB (A,D,W)=A′DW+AD′W. Maxterm. Sum of Minterms or SOM is an equivalent statement of Sum of Standard products. Sum of product expressions (SOP) Product of sum expressions (POS) Canonical expressions Minterms Maxterms Conversion of canonical forms Conversion from. The boolean algebra calculator is an expression simplifier for simplifying algebraic expressions. (a) List the minterms and maxterms of each function. Sum of product (SOP) A canonical sum of products is a boolean expression that entirely consists of minterms. 0-minterms = minterms for which the function F. All these MCQs will help you prepare for the various Competitive Exams and University Level Exams. The Boolean function G=F1F2 contains only the minterms that are common to F1 and F2. Assume the company has a capacity of 400 hours of processing time available each month and it makes two types of. 4. I have a question regarding the process of finding minterms. 1: Write in sum-of-minterms form. Support Simple Snippets by Donations -Google Pay UPI ID - tanmaysakpal11@okiciciPayPal - paypal. F (a,b,c,d)=a′b′+d′c′+ad+bc. Sum of the Minterms = Sum-of. by making the n-1 select variables as most significant inputs). – A maxterm of n variables = sum of n literals in which each variable appears exactly once in T or F from, but not inQuestion: Express the following function as a sum of minterms and as a product of maxterms using Boolean algebra theorems. DLD 2. 8000 2. 2 pg. also how fo we find "F". F (d) Express E and Fin sum-of-minterms algebraic form. Write the following expression as a sum of minterms: f(x,y,z)=xyz^'+x^' z+y, then simplify. Chap 4 C-H6. The minterm evaluates to 1 if and only if the values of the variables are set according to the corresponding row of the table. In order to accurately use the Quine-McCluskey, the function needs to be given as a sum of minterms (if the Boolean function is not in minterm form, the minterm expansion can be found) to determine a minimum sum-of-products (SOP) expression for a function. 4: let F = A'C + A'B + AB'C + BC a) Express it in sum of minterms. 2. Draw circuit in Logisim. Each of the sum terms in the canonical POS form is called a maxterm. Here is an outline of a possible approach: First, you should create a more convenient representation of the expression - for example, the expression could be a list of instances of a Minterm class, and Minterm could contain a list of instances of an Atom class, each of which could contain a char that tells which variable it is and a boolean that tells. Since any boolean function can be expressed as a sum of minterms, a decoder that can generate these minterms along with external OR gates that form their logical sums, can be used to form a circuit of any boolean function. Example: The maxterm for the Boolean variables A and B will be:A truth table defines a Boolean function. (a). Minterm is the product of N distinct literals where each literal occurs exactly once. Question: Find the output function of each truth table: (a) As the sum of minterms (b) As the product of maxterms2. 2 is the complement of the corresponding minterm A B ¯ C Plotting a maxterm on a Karnaugh map requires further consideration. There are 4 steps to solve this one. 17 Obtain the truth table for the following functions, and express each function in sum-of minterms and product-of-maxterms form: (a)" (b + cd) (c + bd) (b) (cd + b'c + bd' (b + d) (d) bd'+ acd'+ ab'c+ a'c. Obtain logical expression in sum-of-minterms and simplify it. (b) Draw the logic diagram, using the original Boolean expression. Question: в с be BC 00 01 001111 al AC ABC Using the following truth tables, write out both the Sum of Minterms and optimized Boolean expression (optimore with Kamaugh mape) for each B lalalalala ABC F 000 0 0 0 1 0. 1 Using truth tables, express each one of the following functions and their complements in terms of sum of minterms and product of maxterms. Obviously, this requires a methodology. 1 2 Points Find the Sum-of-Minterms canonical Boolean expression for the output signal B. What is Minterm? Minterms are the product of various distinct literals in which each literal occurs exactly once. 1 Answer. It has been seen earlier that each individual term (Ā, B,. There are 3 steps to. 15 Simplify the following Boolean function F, together with the don't care conditions d, and then express the simplified function in sum-of-minterms form: (a) F(x. Sum-of-minterms form is refered to as the canonical form of a Boolean equation such that the right-side expression is the sum-of-products. Engineering. The complement of this map (i. F(a,b,c) = a + b + c Is the given equation in the canonical sum of minterms form? If not, convert it into this form. Table 1. as well as the minterms they are covering need to be taken out of the prime implicants chart. 4. Express the Boolean function F = x + y z as a sum of minterms. 1. For the input/output table, give a Boolean expression that is a sum of minterms and is equivalent to the function defined by the table. Maxterm is the sum of N distinct literals where each literals occurs exactly once. Equivalent functions will have the same sum-of-minterms representation. . Select a property from the right to apply Properties Distributive Identity WX ab+ac = a (b+c) a:1 a (a+b) (a+c) = a+bc a+0 a Commutative Null elements ab ba a:0 0 a+b b+a a+1 1 Complement. 2. Answered 2 years ago. Th. Step1: Represent the minterms for a function by decimal 1 in column 4 of table below. 2 Points. Concept: Canonical Form: Any Boolean function that expressed as a sum of minterms or as a product of max terms is said to be in its canonical form. Electrical Engineering questions and answers. • They are marked with an ´ in the K-map. – Each maxterm has a value of 0 for exactly one combination of values of variables. Minterm and sum-of-products is mean to realize that. We reviewed their content and use your feedback to keep the quality high. The Boolean expression, containing only the sum of minterms, is called Canonical Sum- of –Product Form of an expression. Who are the experts? Experts have been vetted by Chegg as specialists in this subject. Simplify the following Boolean expressions to a minimum number of literals. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site-SUM OF MINTERMS-MAXTERMS-PRODUCT OF MAXTERMS • Given an arbitrary Boolean function, such as how do we form the canonical form for: • sum-of-minterms • Expand the Boolean function into a sum of products. Fig. See Answer. Question: Write the following Boolean expression in sum-of-minterms form F= X+YZ' Select one: a. Sum of Minterms or SOM is an equivalent statement of Sum of Standard products. hat Describes how to derive the Sum of minterms from a three variable Truth Table A product is called a minterm because it has minimum-satisfiability where as a sum is called a maxterm because it has maximum-satisfiability among all practically interesting boolean functions. For example: F = m (2. These are used in POS. Check out a sample Q&A here. The sum of minterms (SOM) form; The product of maxterms (POM) form; The Sum of Minterms (SOM) or Sum of Products (SOP) form. minterm 0, then minterm 1 etc. Given the constraint matrix where columns correspond to prime implicants and rows correspond to minterms in the on. The calculator will try to simplify/minify the given boolean expression, with steps when possible. Min and Max terms for two literal binary expressions. 10, then from the table we get F = 1 for minterms m3, m4, m5, m6, and m7. To construct the product of maxterms, look at the value of Not f. Referring to the above figure, Let’s summarize the procedure for writing the Sum-Of-Products reduced Boolean equation from a K-map: Form largest groups of 1s possible covering all minterms. Simplify the Boolean function F using the don’t careTherefore G has only common minterms. Step2: Add (or take binary OR) all the minterms in. Question: Expand wy to sum-of-minterms form wyz+wyz' 1. A maxterm is any sum of n literals where each of the n variable appears once in the sum. (c) List the minterms of E + F and E F (d) Express E and F in sum-of-minterms algebraic form. Computer Science. Express f (x, y, z) = x ˉ + y ˉ z as a canonical SOM. This product is not arithmetical multiply but it is Boolean logical AND and the Sum is Boolean logical OR. For the Boolean functions F(X,Y,Z) and E(X,Y,Z), as given in the following truth table: (a) List the minterms of F(b) List the maxterms of E(c) List the minterms of E' (d) List the maxterms of F⋅E(e) Express the Standard Sum of Product (SSOP) form of F(f) Express the Standard Product of Sum (SPOS) of F⋅EThis problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Solution: First, we derive the truth table 3. The following questions refer to the Truth Table below Q7. 2. Type your answer in the space provided In addbon yeui must show your work on the paper you submt on el earning to get credt. (b) Derive the sum of minterms expression. Select the a in the identity property a *15 a, so that a 1-a. So the minterms would come out to be 0, 1, 1, 3, 5, and 7. Mano, 3rd Edition 3. Example 2. For the following input/output table, give a Boolean expression that is a sum of minterms and is equivalent to the function defined by the table. Implement the sum of minterms of this function and connect a, b, c and d to clock. F (a,b,c) = a'c' + a'c + bc'. • This happens, for example, when we don’t input certain minterms to the Boolean function. 1: Convert the table to a sum-of-minterms. Each row of a logical truth table with value 1/True can therefore be. List the minterms of E- and F-. (c) Using Boolean algebra, derive a simplified sum of products expression. 1: Convert the table to a sum-of-minterms. View the full answer. Answer to Solved 1. Draw the truth table. b. For the terms, just write the numbers separated by commas, no space (For example: 1,2,3,4) Sum of Minterms = Product of Maxterms = QUESTION 11 Simplify the following Boolean function, using three-variable maps: F(x,y,z) = (0,2,4,5) Choose the correct answer below, and show the work on the submitted worksheet. A. For maxterms this is the location of 0 s, as shown below. . F(x,y,z) = xyz Is the given equation in the canonical sum of minterms form? If not, convert it into this form. This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Karnaugh Map”. 9. b) Cycle Diagram. UPSC IES Final Result 2023 Out on 22nd November 2023! A total of 401 candidates have been recommended for appointment based on written exam and interview marks. . Minterms are single 1s in a map, maxterms are 0s in a map. m₂ + m + M6 - M7 + ma c. 0 1 02 03. Simplify the sum of minterms to a minimum number of literals. Analysis: F(A, B, C) = AB + BC̅ + AC̅. 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. It is often referred to as minterm expansion or standard sum of products. (b) List the minterms of E and F (e) List the minterms of E+ Fand F. 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. Steps to expand 1. Learn how to map minterms and maxterms for logic reduction problems using Karnaugh maps and Product-Of-Sums expressions. Using truth table find sum-of-minterms and product-of- maxterms form for function F1 b. Previous question Next question. Then make sure that every term contains each of a, b, and c by using the fact that x + x ′ = 1. After identifying the minterms, the logical OR is used to find the Boolean expression equivalent to the output variable. Each row of a table defining a Boolean function corresponds to a minterm. Show an algebraic expression in sum of minterms form for both out and d, respectively. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. This widget allows to get some helpful information about an arbitrary minterm based on its number and amount of logic variables. If each product term is a minterm, the expression is called a canonical sum of products for the function. Express the following function as the sum of minterms. It is calculated as the. A device used in cases where only 2 people work in a business where A. When the SOP form of a Boolean expression is in canonical form, then each of its product term is called ‘minterm’. For maxterms this is the location of 0 s, as shown below. This page titled 8. 19: Express the following function as a sum of minterms and as a product of maxterms: F(A,B,C,D) = B'D + A'D + BDPlease subscribe to my channel. A sum-of-products form must be a sum of minterms and a minterm must have each variable or its compliment as a factor. Generally, Maxterms are represented as complements of Minterms. This set of Digital Electronics/Circuits Multiple Choice Questions & Answers (MCQs) focuses on “Karnaugh Map”. 11, Problem 23E is solved. Maxterm. Minterms and Maxterms: Canonical Form • Each individual term in the POS form is called Maxterm. See solution. Final answer. In Boolean logic, each minterm would have had just two inputs, but here, we added a third input to each, a constant indicating the value of. Canonical Sum of Products. F(A, B, C, D)= B′ D + A′ D +B D b) Directly. B+C + A•B. The resulting expression should include two 2-variable product terms, 3. e. Electrical Engineering questions and answers. 1 2 Points Find the Sum-of-Minterms canonical Boolean expression for the output signal B. Cox – Spring 2010 The University Of Alabama in HuntPetrick's Method is used for determining minimum sum-of-product (SOP) solutions in a given prime implicants chart. 1 . So, this is represented by the sign Σ and all the minterms are enclosed in brackets. Given that f1(a,b,c)=∑m(1,4,5) and f2(a,b,c)=∏M(0,2,3), derive the sum of minterms form of thefunction f1+f2. Express the following Boolean function as a sum of minterms. Here’s the best way to solve it. (b). Electrical Engineering questions and answers. A maxterm is a sum. UPSC IES Exam Date 2024 was declared earlier. Suppose Limor Fried expands her business, Adafruit Industries, to make electric scooters. In the canonical sum of products, there could have been as many as 9 minterms, because there are two 3-valued inputs. Sum of Minterms -- Sum of Products (SOP) Product of Maxterms - Product of Sums (POS) Explain Minterms. Canonical Sum of Products; Non-Canonical Sum of Products; Minimal Sum of Products; 1). Question: Given the function y=ab+a′ a) What's the sum-of-minterms form? b) Construct the truth. k. Question: Identify the Boolean function that is defined by the following input/output table. 2. Show your steps. Sum of minterms formMake a prime implicant table that consists of the prime implicants (obtained minterms) as rows and the given minterms (given in problem) as columns. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. This product is not arithmetical multiply but it is Boolean logical AND and the Sum is Boolean logical OR. A*B = A and B. One way to get the SoP form starts by multiplying everything out, using the distributive law: (ac + b)(a + b ′ c) + ac = ac(a + b ′ c) + b(a + b ′ c) + ac = aca + acb ′ c + ba + bb ′ c + ac = ac + ab ′ c + ab + ac = ac + ab ′ c + ab. f. ) F (x,y,z)= x'y + x + xyz. Find the Sum-of-Minterms canonical Boolean expression for the output signal B. • Each individual term in the SOP form is called Minterm. Ex. Show transcribed image text. Any boolean function can be represented in SOM by following a 2 step approach discussed below. Its De Morgan dual is a " Product of Sums " ( PoS or. The expression can contain operators such as conjunction (AND), disjunction (OR) and negation (NOT). Hence, we can say that it shows the PDNF. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 1) Properties Distributive Identity ab+ac a (b+c) a:1 (a+b) (a+C) = a+bc a+0 = Commutative Null. b Show sum of minterms 0011 1 01000. Step1: Represent the minterms for a function by decimal 1 in column 4 of table below. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Calculate the cost. Step 2. Question: Express the following function as a sum of minterms and as a product of maxterms: F(A,B,C,D) = B'D + A'D + BD For example: (1,2,3,4) Sum of Minterms. Show a minimum SOP expression ( a: 2 terms, 5 literals; b: 1 term, 1 literal). Express the following function as a sum ofsum of minterms. It uses minterms. Note: For n-variable logic function there are 2 n minterms and 2 n maxterms. This is a normal form of SOP, and it can be formed with grouping the minterms of the function for which the o/p is high or true, and it is also called as the sum of minterms. and that "A compact notation is to write only the numbers of the minterms included in F" which is $\sum (1,2,4,7)$ I don't understand this because the rows in the truth table are interchangeable; 0,0,0,0 could be the last row instead of the first. However, the inverse function will be directly expressed as a sum of minterms (‘sum of products’, ‘S-of-P’ or ‘SOP’ form) which can then be plotted immediately. O Multiplying a term by (v + v') changes the term's functionality. A 2-variables function has 2 2 =4 possible maxterms. combined all minterms for which the function is equal to 1. ) Convert the following Boolean function from a sum-of-minterms form, to a product-of-sums form: F (w,x,y,z) = ∑(0,1,2,5,8,10,13) 2. Here’s the best way to solve it. F(a, b, c) = (A & B & C) | (A & B & (~C)) | (A & (~B) & C) | (A & (~B) & (~C)) which is then perfectly simplified to F(a, b, c) = AWe generally use the ∑ (sigma) notation to represent minterms. Show the minterms of f' (complement of f) in numeric form. Electrical Engineering questions and answers. Show transcribed image text. Who are the experts? Experts have been vetted by Chegg as specialists in this subject. Maxterm. Since the function can be either 1 or 0 for each minterm, and since there are 2^n minterms, one can calculate all the functions that can be formed with n variables to be (2^(2^n)). Answered: Q2. I want to ask that if we are told to express an Boolean Expression in sum of min-terms which is already in non-standard SOP form. . The answer should list the minterms as m0+m1+m2. Key points: Minterms are values giving the output 1. It should be noted that the minterms whose sum helps in defining the Boolean function will be the ones that give the 1's with regards to the functions in the truth table. Groups must be a power of 2. . Once again, the numbers indicate K-map cell address locations. Generate truth table for the following functions. Why do we need minterms in the first place? We do not need minterms, we need a way to solve a logic design problem, i. 2. egin {tabular} {|c|c|c|} hlinex & y & f (x,y) hline 0 & 0 & 1. 1. and B workers work, gives "logic 1" output if there are only 2 people in the workplace, first obtain the truth table to create the circuit that expresses this situation, then POS Write the function (according to the maxterms) and then draw the circuit of this function. Solution: = x + y z = x + (y z) AND (multiply) has a higher precedence than OR (add) = x(y+y')(z+z') +. There are 2 cases when f is false: Not f = (Row 3) Or (Row 4) = AB¯¯¯¯C Or AB¯¯¯¯C¯¯¯¯. Show a minimum POS expression (f: 2 solutions, 3 terms, 6 literals; g: 1 term. Provide both the algebraic expression and the sum of indices (Sum (. Customized Logic FunctionThe customized function: F = Σ (1, 2, 3, 6, 7,10,13)1. Expert Answer. 4000 The number of minterms is 8 The number of available minterms is 2 Available minterm probabilities are in vector pma To view available minterm probabilities, call for PMA DV = [DV; Ac&B&C; Ac&B]; % Modified data. A maxterm, such as A ¯ + B + C ¯, from section 3. Step 1. Boolean Algebra simplify minterms. Y 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Expert Solution. • while in Maxterm we look for function where the output results is “0”. 2: Boolean functions CHALLENGE ACTIVITY 5. F=x'yz'+xy'z'+xy'Z+xyz'+xyz' d. It is also possible to find a Boolean expression that represents a Boolean function by taking a Boolean product of Boolean sums (maxterms, i. A sum of minterms is a valid expression of a function, while a product of maxterms is not. These are used in POS. Key points: Minterms are values giving the output 1. Who are the experts? Experts have been vetted by Chegg as specialists in this subject. Convert the Boolean function F = x + y z into a sum of minterms by using a truth table. Determine the Sum of Minterms expression for the function F (A,B,C). (b) List the minterms of E and F . (e) Simplify E and F to expressions with a minimum of literals. Select the 1 in the Complement property ata': 1, so that ata' - 1 5. Then make sure that every term contains each of a, b, and c by using the fact that x + x ′ = 1. 1. A Product-OF-Sums solution is completed in the usual manner. In addition, you must show your work on the paper you submit on eLearning to get credit. For the Boolean functions E and F, as given in the following truth table: List the minterms and maxterms of each function. Get the free "Minterm" widget for your website, blog, Wordpress, Blogger, or iGoogle. 1. 19It helps represent Boolean expressions as product of sum terms. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have -SUM OF MINTERMS-MAXTERMS-PRODUCT OF MAXTERMS • Given an arbitrary Boolean function, such as how do we form the canonical form for: • sum-of-minterms • Expand the Boolean function into a sum of products. (cd+b′c+bd′) (b+d) 3. The boolean algebra calculator is an expression simplifier for simplifying algebraic expressions. 1. -P+Q = Definition of impliy. 2. 9: Sum and Product Notation is shared under a GNU Free. See Answer See Answer See Answer done loading Final answer. The given expression can be written as:Question: Consider a function with three variables: a, b, c. e. (flip) Convert A to base 10. ) and D. Thus we place our sole 0 for minterm (A+B+C) in cell A,B,C=000 in the K-map, where the inputs are all 0 . F (a,b,c) = a'c' + a'c + bc'. Step 4. If E represents the sum of all minterms of a function of n variables, then the sum of all minterms of a function of n+1 variables will be E(z'+z), which is equal to 1. So, every minterm has three literals. So for x'y' there exists two options of 00- where z is 000 and 001. Go through each of the possible inputs with both circuit outputs on the same waveform and explain how the waveform indicates the equations are the same. Obtain the truth table for the following functions, and express each function in sum-of-minterms and product-of-maxterms form: ( b + c d ) ( c + b d ) Expert Solution. They are called terms because they are used as the building-blocks of various canonical representations of arbitrary boolean functions. Click Apply property 4. Sum of Minterms or SOM is an equivalent statement of Sum of Standard products.