On a piece of paper, create the minterm expansion formula for this truth table. Consider the following functions min-term list: Determine the min-term expression for function, . A switching circuit has three inputs (A, B, C) and one output Z. Minterm 與 Maxterm 是表達一個函式的標準式（Standard form），標準式是一種唯一的表示法，當函式 f 與函式 g 結果相同時，就能找到一個相同的表達式。. (a) Find the minterm expansion for F (both decimal and algebraic form). d. Rather, it should be built by combining four instances of your Full Adder circuit. Z = ∑ (c) Find the maxterm expansion for Z in both decimal form in terms of. Step 1 of 5. Z + X. Write the complete minimized Boolean expression in sum-of-products form. Write the general form of the minterm and maxterm expansion of a function of n variables. , xk, where yi = xi if δi = 1 and yi = ¯ xi if δi = 0. Find the maxterm expansion of f2(a,b,c,d)= bc + ac’ + abd’ 7. b. EENG 2710 - Digital Logic Design Assignment #4 (Due on 9/29/2023) (Include details for full credit) 1. Show transcribed image text. Step 1 of 3. See solution. Answered 2 years ago. Z' +. ) [5 Points] Not the question you’re looking for? Post any question and get expert help quickly. Question: Build a 4x1 multiplier in the space provided. 3. 3 a Ми використовуємо шаблони, відображені на карті minterm, щоб допомогти в алгебраїчному розв'язанні для різних мінтермальних ймовірностей. Question: 36 and 37. The Tables below represent a three variable input (A,B,C) and single Zoutput. Create a free account to view solutions for this book. (25 Points) 4. For this truth table the minterm of row (a) is • The minterm for row (b) is • The expression y= (as a minterm expansion). Computer Science questions and answers. The given expression can be written as: F (A, B, C) = AB (C + C̅) + (A + A̅) BC̅ + A (B + B̅)C̅. See Answer See Answer See Answer done loadingEngineering. VWXYZ represents a 2-out-of-5 coded number whose value equals the number of O's. The Gray Code belongs to a class of code called minimum-change. Kirchhoff’s current law states that a. The output is1 only if the product M×N is <=2. ) Show transcribed image text. Given: f(a, b, c) = a(b + c’) (a) Express F as a minterm expansion (Use m-notation): F = ∑ . (a) Consider the function. Who are the experts? Experts are tested by Chegg as specialists in their subject area. The minterm is described as a sum of products (SOP). Use maxterms that aren’t in minterm expansion F(A,B,C) = ∑m(1,3,5,6,7) = ∏M(0,2,4) Maxterm to minterm Use minterms that aren’t in maxterm. A logic circuit realizing the function f has four inputs A, B, C, and D. (17 points) X = (c) Find the maxterm expansion for Y. (a) Minterm expansion of is: To expand the given into a standard sum of products (minterm expansion) then introduce the missing variables in each term as. Find the. (a) Find the truth table for Z. , F(A,B,C) = ΠM(0,1,2) = Σm(3,4,5,6,7) 3. If a minterm has a single 1 and the remaining cells as 0 s, it would. ) [5 Points] (b) Express F as a maxterm expansion. Download Solution PDF. minterm (standard product term) A product (AND) of n Boolean variables, uncomplemented or complemented but not repeated, in a Boolean function of n variables. Who are the experts?Question: 2. Log in to add comment. Find a) the minterm expansion for b0 and b1 b1=m(0,1,2,4); b0=m(0,3,5,6) and b) the maxterm expansion for b0 =M(1,2,4,7) and b1=M(3,5,6,7). Rather, it should be built by combining four instances of your Full Adder circuit. 5 as the initial value. g. 5. = a’b’ +a’d + acd’ = a’b’(c+c’)(d+d’) + a’d(b+b’)(c+c’) + acd’(b+b’) = a’b’c’d’ + a’b’c’d + a’b’cd’ +a’b’cd + a’bc’d + a’bcd + abcd’ +ab’cd’ = Σm(0,1,2,3,5,7,10,14) What is the maxterm expansion for f? Minterm maps and the minterm expansion. Fundamentals of Logic Design (7th Edition) Edit edition Solutions for Chapter 4 Problem 5SG: Study Section 4. the algebraic sum of the currents around any closed. . XY represents a binary number whose value equals the number of O's at the input. ) (d) Express F' as a maxterm expansion. (a) Any Boolean expression may be expressed in terms of either minterms or maxterms. Step 1 of 5. Write the complete minimized Boolean expression in sum-of-products form. If A = 0, the output Z is the equivalence of B AND C. Fla, b, c) M(0,3,4,6,7) a) Construct an Implicant chart to determine all the prime implicants b) Construct a Prime Implicant (Pl) chart and find all the essential prime implicants. Derive Equations of Cout and Sum for a half adder and a full adder using truth tables. Question: 16. This product is not arithmetical. ,, a product term in which each of the variables appears once (either in its complemented or uncomplemented form) is called a minterm. Prove your answer by using the general form of the minterm expansion. Note: If a truth table is given, and if the output is 1 then it corresponds to minterm and in case the output is 0 then it corresponds to 0. Be sure to include the image of your. Prove your answer by using the general form of the minterm expansion. Remember that a Full Adder adds a single column of digits from the bitwise sum of two binary numbers. Example: a OR b OR !c = 1 or (a AND NOT (b)) OR (NOT (c) AND d) = 1 are minterms. Q3. d) F′ as a max term expansion is . The output of the minterm functions is 1. , the value of D is such that A, B, C, and D always contain an odd number of 1’s. ZMinterm and MAXTERM Expansions 350151 – Digital Circuit 1 ChoopanRattanapoka. The Gray Code belongs to a class of code called minimum-change. Minterm | Maxterm 1. 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. 최소항 전개(minterm expansion)는 정규형 중 논리 함수의 모든 변수들을 곱의 합 형태로 표현한 것이다. . From the Digital. Simplify further. c) F′ as a min term expansion is . Question: 1) Given: F (a,b,c) = a'bc + (a) Express F as a minterm expansion. (Use M-notation. See below for information about how to import your Full Adder, as well as for the steps needed to export Ripple-Carry Adder. 20 A bank vault has three locks with a different key for each lock. (b) Express f as maxterm expansion (use M-notation). 이를 활용해서 minterm expansion(최소항 전개) 또는 standard sum of products(표준 논리곱의 합)으로 표현할 수 있습니다. The three inputs A, B, and C are the binary representation of the digits 0 through 7 with A being the most-significant bit. For each remaining row, create a minterm as follows: For each variable that has a 1 in that row, write the name of the variable. (a) Write the minterm expansion for F. g. Express F as a minterm expansion in m-notation. Design a binary adder which takes three inputs: A, B and C ( C is the carry bit, A and B are the two binary numbers), there are two outputs S and X ( S is the sum and X is carry bit to next column) and the table is given as below: a) Write down the minterm expansion for S (in terms of A, B and C) b) Write down the minterm expansion for X (in. a and b represents the 1st and 2 nd bits of a binary number M. General Minterm and Maxterm Expansions general function of n variablesA 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. Otherwise, F = 0. ”. f = A'BC + AB'C' + AB'C + ABC + ABC의 식을 표현한다고 했을 때 각 항이 의미하는 것을 찾아 옮겨 적으면 f(A, B, C) = m 3 + m 4 + m 5 + m 6 + m 7 으로 표현이 됩니다. Simplify further. Who are the experts? Experts are tested by Chegg as specialists in their subject area. 6. Using postulates and theorems of Boolean algebra, simplify the minterm expansion of F to a form with as few occurrences of each as possible. State a general rule for finding the expression for F1 F2 given the minterm expansions for F and F2. The point to review is that the address of the cell corresponds directly to the minterm being mapped. First, we will write the minterm: Maxterm = A+B'. Find the minterm expansion equation for F using Quine-McCluskey method and prime chart. 100% (42 ratings) for this solution. Also, Boolean functions can be simplified using Karnaugh map ( K - map) without using Boolean theorems, by transferring a function to K-map and reading simplified function from K-map. Design a combinational logic circuit which has one output Z and a 4. For a 6-input logic circuit, possible number of combinations for designing the truth table are _____?? Both OR and AND gate can have only 2 inputs. Rather, it should be built by combining four instances of your Full Adder circuit. Minterm expansion = ∑ m (0, 1, 2, 4, 8) \text{Minterm expansion}=\sum m(0,1,2,4,8) Minterm expansion = ∑ m (0, 1, 2, 4, 8) The minterm expansion will consist of a sum of n n n products when the truth table contains n n n ones in the last column. Express F as a minterm expansion in m-notation. A minterm is a Boolean expression resulting in 1 for the output of a single cell, and 0s for all other cells in a Karnaugh map, or truth table. The general rule for finding the expression, is that all the terms present in either or will be present in . 1) F 1 ( x, y) = x ⋅ y ′ + x ′ ⋅ y + x ⋅ y. Express F as a minterm expansion in boolean expression. schedule) No labs this week; 10/11: last day to drop without a ‘W’. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 9, which involves an independent class of ten events. Each of three coins has two sides, heads and tails. The minterm expansion of f(P,Q,R) =P Q+Q¯¯¯¯R +P ¯¯¯¯R is. r. (b) Write the minterm expansion for Z in decimal form and in terms of A,B,C. Maxterm is the sum of N distinct literals where each literals occurs exactly once. 2. It takes three inputs: x and y, the two bits being added from this column of the addition; c_in, the carry bit into this column of the addition Discuss. See below for information about how to import your Full Adder, as well as for the steps needed to export Ripple-Carry Adder. Minterm is represented by m. Given: F (a, b, c) = abc’ + b’. For each row with a 1 in the final column, the corresponding product to add to the minterm expansion is obtained as:COE/EE 243 Digital Logic Session 9; Page 5/9 Spring 2003 x y x y 3. (~Y) is a minterm we can express complement ~Y as Y’ so, the above minterm can be expressed as XY’ So, if we have two variables then the minterm will consists of product of both the variables. If a minterm has a single 1 and the. It is sometimes convenient to express a Boolean function in its sum of minterm form. -5 in 4-bit = 1011. 100% (27 ratings) for this solution. . For example, , ′ and ′ are 3. 0 × 21 . Note that the function is unchanged if the exclusive OR is replaced with inclusive OR. Given expression is. 100% (42 ratings) for this solution. For each row with a 1 in the final column, the corresponding product to add to the minterm expansion is obtained as: COE/EE 243 Digital Logic Session 9; Page 5/9 Spring 2003 x y x y 3. Example (PageIndex{12}) A hybrid approach. Note that, in addition to the input and output columns, the truth table also has a column that gives the decimal equivalent of the input binary combination, which makes it easy for us to arrive at the minterm or maxterm expansion for the given problem. Minterm Minterm is a product of all the literals (with or without complement). the operation is or. are those nos. Question: Using kmap to find the SOP format for the Boolean function below, Z, Z = (A + B' + C)(A' +B+ C') choose the closet answer from the multiple choice hint: Z expressed in POS format so find Maxterm expansion using truth table. 1. Expert Answer. (5 POINTS EACH) Four chairs are placed in a row: Each chair may be occupied (1) or empty (O). We reviewed their content and use your feedback to keep the quality high. 1. Find the minterm and maxterm expansion for f in decimal and algebraic form. 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∏M 0 3 5 6 so the minterm expansion is. Any Boolean function can be expressed as a sum (OR) of. The minterm expansion for \(E \cap F\) has only those minterms in both sets. Find step-by-step solutions and answers to Exercise 27 from Fundamentals of Logic Design - 9781133628477, as well as thousands of textbooks so you can move forward with confidence. the algebraic sum of the currents flowing into any point in a circuit must equal zero. b) simplify the resulted Boolean expression in part a c) Construct circuits for the resulted Boolean expressions F and G. 1. Minterms and Maxterms are important parts of Boolean algebra. . Who are the experts? Experts have been vetted by Chegg as specialists in this subject. Do this repeatedly to eliminate as many literals as possible. 5. Stuck at simplifying boolean expression. Write the minterm expansion for Z in decimal form and in terms of A,B,C. Joyligolf8693 is waiting for your help. Fundamentals of Logic Design (6th Edition) Edit edition Solutions for Chapter 4 Problem 3SG: Study Section 4. Write out the full Boolean expressions. What does minterm mean? Information and translations of minterm in the most comprehensive. So, the shorthand notation of A+B' is. Question 2. 1-minterms = minterms for which the function F = 1. of F list minterms not present in F maxterm nos. . The relationships between the inputs and the outputs are shown below: x3 x2. Minterm is represented by m. )3) Assume that the input combinations of ABC=011 and ABC=110 will never occur. The output is1 only if the product M×N is <=2. (17 points) X = duha (b) Find the minterm expansion for X. Without using a truth table, find. Question: Fill in the blanks: . In the above truth table, the minterms will be m 2, m 5, m 6 and m. From the Digital Design course. Show the pin diagram. Express F’ as a minterm expansion (Use m-notation): F’ = ∑ Express F’ as a maxterm expansion (Use M -notation): F’ = ∏ There are 2 steps to solve this one. 자세하게 알아보자. Suggest. The point to review is that the address of the cell corresponds directly to the minterm being mapped. Write out the full Boolean expressions. 0 × 29 and c = 1. A and B represe bits of a binary number N,. Minterm to maxterm " Use maxterms that aren™t in minterm expansion " F(A,B,C) = ∑m(1,3,5,6,7) = ∏M(0,2,4)! Maxterm to minterm " Use minterms that aren™t in maxterm expansion " F(A,B,C) = ∏M(0,2,4) = ∑m(1,3,5,6,7) ! Minterm of F to minterm of F’ " Use minterms that don™t appear " F(A,B,C) = ∑m(1,3,5,6,7) F’(A,B,C) = ∑m(0,2,4)!A switching circuit has four inputs as shown. For each row with a 1 in the final column, the corresponding product to add to the minterm. 민텀을가진다. E. the algebraic sum of the currents entering and leaving any point in a circuit must equal zero. Given a minterm expansion, the minimum sum-of products form can often be obtained by the following procedure: (i) Combine terms by using 𝑋𝑌′+ 𝑋Y =(𝑌′+𝑌)=𝑋. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Minimum Forms of Switching Functions Given a minterm expansion, the minimum sum-of-products format can often be obtained by the following procedure: • Combine terms by using XY′ + XY = X. Chegg Products & Services. A B C D 3. (TCO 2) What is a VLAN? (Points : 5) It is a physical segmentation of a layer 2 network. (17 points) Y = Not the question you’re looking for? Post any question and get expert help quickly. Simplified Boolean Function (Minimum SOP): Let's simplify the. But is it necessary to search in f x′? Remember that because of unateness of f w. If A = 1, the output is the XOR of B and C. (Use M-notation. A switching circuit had 4 inputs a,b,c, and d and output f. + b 0 2 0 Same adder works for both unsigned and signed numbers To negate a number, invert all bits and add 1 As slow as add in worst caseD, and D next to A. m2+m4+m6+m7. Minterm is a product of all the literals (with or without complement). (b) Find the minterm expansion for Z in decimal form in terms of A, B, C. The output is to be 1 only if the product N1 times N2 is less than or equal to 2. (11 points) (b) Draw the corresponding two-level AND-OR circuit. Question: Find the minterm expansion of f(a,b,c,d)=a’(b’+d)+acd’ and then design the result. (b) Express f as maxterm expansion (use M-notation). Note: If a truth table is given, and if the output is 1 then it corresponds to minterm and in case the output is 0 then it corresponds to 0. Expert-verified. (a) Write the minterm expansion for F. Question: Given: f (a, b, c) = a (b + c’). Simplify if desired F = (B +C)(A+C) – Typeset by FoilTEX – 29. To understand better about SOP, we need to know about min term. Example if we have two boolean variables X and Y then X. (a) Given expression is. A combinational switching circuit has four inputs and one output as shown. The minterm expansion will consist of a sum of n n n products when the truth table contains n n n ones in the last column. Given the following truth table: ABCF 0001 0011 0101 0110 1000 1011 1101 1111 a) Write down the minterm expansion for the function F b) Draw the K-Map using the minterm expansion c) Determine all the essential prime implicants. Step 2. No need to simplify on. Express F as a minterm expansion in boolean expression. Write the complete minimized Boolean expression in sum-of-products form. (~Y) is a minterm we can express. Add answer 5 pts. Expert-verified. Express F as a minterm expansion (standart sum of products). Determine the minterm and maxterm for each of the following: a). Minterm expansion of F to Minterm expansion of F': in minterm shorthand form, list the indices not already used in FQuestion: Build a 4x1 multiplier in the space provided. a. If A=1, the output is the equivalence of B and C. Problem 3: (a) Plot the following function on a Karnaugh map. That is, the cell 111 corresponds to the minterm ABC above left. a) Express F as a minterm expansion (use m-notation) b) Express F as a maxterm expansion (use M-notation) Build Logisim circuits for b) and c) and show that they give same output. Answer to Solved Homework 2 Due 9/22/2022 P-4. g. Y'. Need help with this problem . If S and T are two different trees with ξ (S) = ξ (T),then. 3. If A=1, the output is the equivalence of B and C. Q3. Minterm expansion for a function is unique. (a) Express F as a minterm expansion (Use m-notation): F = ∑ (b) Express F as a maxterm expansion (Use M-notation): F = ∏ (c) Express F’ as a minterm expansion (Use. Remember that a Full Adder adds a single column of digits from the bitwise sum of two binary numbers. Solution. 1. Equation (4-1) can be rewritten in terms of m-notation as: This can be further abbreviated by listing only the decimal subscripts in the. i. N1 B F N2 D O Find the minterm expansion for F. Each chair may be occupied (1) or empty (0). A minterm, denoted as mi, where 0 ≤ i < 2n, is a product (AND) of the n variables in which each variable is complemented if the value assigned to it is 0, and uncomplemented if it is 1. Express F as a maxterm expansion (standard product of sum) 4. c. This is a differential equation problem involving a Taylor expansion series. 즉 F=x+yz라는 것은 곱의 합 형태이므로 최소항 전개 형태이다. The minterm expansion for (E cup F) has all the minterms in either set. Design a binary adder which takes three inputs: A, B and C ( C is the carry bit, A and B are the two binary numbers), there are two outputs S and X ( S is the sum and X is carry bit to next column) and the table is given as below: a) Write down the minterm expansion for S (in terms of A, B and C) b) Write down the minterm expansion for X (in. Show the pin diagram. How to express a digital logic function in minterm (sum of products) form. 3, Minterm and Maxterm Expansions. Question: A combinational circuit has three inputs (A, B, C) and two outputs (X,Y). 🔗. 2. 5. This means the \(j\)th element of the vector for \(E \cup F\) is the maximum of the \(j\)th elements for the two vectors. (a) Write the minterm expansion for F. Ці дані наведені на карті minterm на малюнку 2. b) F as a max term expansion is . If S and T are two different trees with ξ (S) = ξ (T),then. the minterm/maxterm expansions can be obtained from truth tables as described above (or can also obtain minterm expansion by using sum of products and by interoducing the missing variables in each term, X + X' = 1) or for maxterm expression by using X X' =0 and factoring. 1. Given a truth table for a Boolean function, the minterm (also known as standard product) expansion could be constructed by taking an OR of products, where each product represents an instance. and Mi drops out of the expansion; however, Mi is present if ai = 0. 2. A) B) So from the given information, we find that: A) The. (a) Find the truth table for Z. c. Consider the following function, which is stated in minterm expansion form: F(W,X,Y,Z)=Σm(0,4,5,7,12)+∑d(2,9,11,13,15) Using Karnaugh maps, a. State a general rule for finding the expression for F1+F2 given the minterm expansions for F1 and F2. Prove your answer by using the general form of. Convert between a minterm and a maxterm expansion If f = Σm i, then f = ΠM j, where each m j is not in f There is a 1-to-1 mapping between a truth table and the minterm/maxterm expansion Minterm & maxterm expansions 16. An excess-3 code is obtained by adding 3 to a decimal number. Review: Binary Encoding of Numbers Unsigned numbers b n-1 2n-1 + b n-2 2 n-2 + . (a) Express f as a minterm expansion (use m-notation). If A=1, the output is the equivalence of B and C. Express F as a minterm expansion in boolean expression. Do this repeatedly to eliminate as many literals as possible. 2. 100% (73 ratings) for this solution. (Use M-notation. The decimal point number of (10) 2 is 2. Given the following truth table: A B C F 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 a) Write down the minterm expansion for the function F b. Minterm expansion; No lecture on 10/10 (holiday) Lecture on 10/11 (Mon. Simplification in a Boolean algebra. Find step-by-step solutions and answers to Exercise 28 from 논리설계기초 - 9788962183948, as well as thousands of textbooks so you can move forward with confidence. (use M-notation) Expert Solution. What does MINTERM mean as an abbreviation? 1 popular meaning. Give the minterm and maxterm expansion for each of the following logic functions: (a) F(A, B, C, D. F(A, B, C). Who are the experts? Experts have been vetted by Chegg as specialists in this subject. Final answer. e. . 2. Slide 1 Boolean Algebra and Logic Simplification BY UNSA SHAKIR. Computer Science questions and answers. Step 1. Question: Due Date: Friday, 3/31/2023 Show your complete work for each problem - Write down the algebraic expression for minterm and maxterms for the following cases. Number of Minterms: The function has 4 minterms. 문제를 많이 풀어보시길 바랍니다. Question 1: For the truth table below; a. b. Write the maxterm expansion for Z in. Minterm is the product of N distinct literals where each literal occurs exactly once. Given F1-Im (0,4,5,6) and F2 -2m (0,3,6,7) find the minterm expression for F1 + F2. EE/CompE 243 Digital Logic Session 10; Page 2/4 Spring 2003 (c) F A B C. 5. engineering. A. The result is an another canonical expression for this set of variables. , xk that has the form. From SOP to POS and back Minterm of F to minterm of F' Use minterms that don’t appear F(A,B,C) = ∑m(1,3,5,6,7) F' = ∑m(0,2,4) Maxterm of F to maxterm of F' Use maxterms that don’t appear F. 1-minterms = minterms for which the function F = 1. 我们首先开始于定义极小项(minterm)为只由逻辑与和补运算符组成的 n 个变量的逻辑表达式。 例如，下列是极小项的例子: a b'c a' b c. This observation makes it clear that one can represent any Boolean function as a sum-of-products by taking Boolean sums of all minterms corresponding to the elements of Bn that are assigned the value 1 by the function. The output of the minterm functions is 1. Minterm. 1. Computer Science. Task 1: Given that F(a, b, c) = ac' + a'c+b' a) Create a truth table for the function b) Express F as a minterm expansion (use m-notation) c) Express F as a maxterm expansion (use M-notation) d) Express F' as a minterm expansion (use m-notation) e) Express F' as a maxterm expansion (use M-notation) f) Build Logisim circuits for b) and c) and show that. This circuit should not be built using the minterm expansion principle. 1. 1. A logic circuit realizing the function f has four inputs A, B, C, and D. (b) Express F as a maxterm expansion (use M-notation). 🔗. f = A'BC + AB'C' + AB'C + ABC + ABC의 식을 표현한다고 했을 때 각 항이 의미하는 것을 찾아 옮겨 적으면 f(A, B, C) = m 3 + m 4 + m 5 + m 6 + m 7 으로 표현이 됩니다. Express F as a maxterm expansion in boolean expression. Algebraic Simplification ( #2 ) Find the consensus term in each expression and delete it : a) abc'd+a'be+bc'de ; b) (x'+y+z)(x+w)(y+z+w) Simplify each expression by. (Use M-notation. Fill in the truth table below with the minterm expansion for f= m (1,3,5,6,7) and the maxterm expansion for g= II M (0,1,2,3,4,6) 09 ABCf 0 0 0 0 0 1 0 1 0 011 1 0 0 101 110 1 1 1 Use a 3-variable Karnaugh map to determine a Boolean expression in terms of A, B, and Cfor function f as. General Minterm and Maxterm Expansions We can write the minterm expansion for a general function of three variables as follows: Section 4. Find the minterm and maxterm expansion for f in decimal and algebraic form. Canonical Form – In Boolean algebra,Boolean function can be expressed as Canonical Disjunctive Normal Form known as minterm and some are expressed as Canonical Conjunctive Normal Form known. ABC indicates. Example if we have two boolean variables X and Y then X. Find the truth table for Z. (c) Express f' as a minterm expansion (use m-notation).