Prove your answer by using the general form of. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Step-by-step solution. We reviewed their content and use your feedback to keep. 1. This circuit should not be built using the minterm expansion principle. Solution for The minterm expansion of f(P, Q, R) = PQ + QR + PR is. General Minterm and Maxterm Expansions list maxterms not present in F minterm nos. Minterm expansion of F to Minterm expansion of F': in minterm shorthand form, list the indices not already used in FA switching circuit has three inputs (A,B,C) and one output (Z). A = AB (C + C’) + AB' (C + C’) = ABC + ABC’+ AB’C + AB’C’. Find step-by-step solutions and answers to Exercise 27 from Fundamentals of Logic Design - 9781111781392, as well as thousands of textbooks so you can move forward with confidence. 100% (27 ratings) for this solution. Minterm is the product of N distinct literals where each literal occurs exactly once. A minterm is a special product of variables in Boolean algebra. 0 × 21 . Give the minterm and maxterm expansion for each logic function described. (11 points) (b) Draw the corresponding two-level AND-OR circuit. 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. Simplify boolean expression to. General Minterm and Maxterm Expansions general function of n variables 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. Given one of the following: minterm expansion for F, minterm expansion for F, maxterm expansion for F, or maxterm expansion for F , find any of the other three forms. Given F1 = ∑ m(0,2,5,7,9) and F1 = ∑ m(2, 3,4,7,8) find the minterm expression for F1+F2. of F minterm nos. 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. the minterm expansion) and draw the corresponding circuit. See below for information about how to import your Full Adder, as well as for the steps needed to export Ripple-Carry Adder. A combinational switching circuit has four inputs and one output as shown. Due Date: 4/7/2023 by 2 pm 1 Given the followina trith table: 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. (c) Express F' as a minterm expansion (use m-notation). 0-minterms = minterms for which the function F = 0. 3. Thus for the given example: Minterm expansion will be ∑m(4,5,7,8,10,11,13,14) + ∑d (0,1,2)Using scientific means, determine… | bartleby. Note thatFind the minterm expansion equation for F using Quine-McCluskey method and prime chart. 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. Write the maxterm expansion for Z in Support Simple Snippets by Donations -Google Pay UPI ID - tanmaysakpal11@okiciciPayPal - paypal. This article explores the minterms in depth in addition to the two-variable, three variable and four variable minterm tables and K-maps. Leave 0's as 0, until you reach the first 1. The output is 1 iff the input has three consecutive 0 's or three consecutive 1's. The illustration above left shows the minterm ABC, a single product term, as a single 1 in a map that is otherwise 0s. 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. Q3. (20 points) b. This product is not arithmetical. (Use M-notation. E. Note that the function is unchanged if the exclusive OR is replaced with inclusive OR. are those nos. The given expression can be written as: F (A, B, C) = AB (C + C̅) + (A + A̅) BC̅ + A (B + B̅)C̅. 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. 100% (73 ratings) for this solution. If A=1, the output is the equivalence of B and C. Express F as a minterm expansion in m-notation. Problem 2 Create a free account to view solutions for this book. (d) Express F' as a maxterm expansion (use M-notation). (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 m. The output of the minterm functions is 1. Use the minterm expansion principle to create a circuit that uses only AND, OR, and NOT gates. The output is1 only if the product M×N is <=2. Simplify boolean expressions step by step. . Suggest. 2진. (25 Points) 4. Given that F (a, b, c) = ac’ + a’c + b’. Need help with this problem . 최소항 전개(minterm expansion)는 정규형 중 논리 함수의 모든 변수들을 곱의 합 형태로 표현한 것이다. 6. 27 Given f (a, b, c) = a (b + c'). 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 ofFind step-by-step solutions and answers to Exercise 28 from Fundamentals of Logic Design - 9781111781392, as well as thousands of textbooks so you can move forward with confidence. See below for information about how to import your Full Adder, as well as for the steps needed to export Ripple-Carry Adder. Derive Equations of Cout and Sum for a half adder and a full adder using truth tables. For each row with a 1 in the final column, the corresponding product to add to the minterm expansion is obtained as:Sum of Product is the abbreviated form of SOP. For example, if A = 1, B = 0, C = 0, and D = 0, then Z = 1, but if A = 0, B = 1, C = 0, and D = 0, then Z = 0. Fundamentals of Logic Design (6th Edition) Edit edition Solutions for Chapter 4 Problem 3SG: Study Section 4. Problem 3: (a) Plot the following function on a Karnaugh map. Given f ( a , b , c ) = a ( b + c ′ ) Express f as a minterm expansion (m-notation) and maxterm expansion (M-notation) Q3. Expert-verified. 1) Given: F (a, b, c) = ab c ′ + b ′ (a) Express F as a minterm expansion. Equivalence of B and C is defined as: (B⊕C)′ 1. 민텀 (Minterm) (최소항) 이때 곱의 항 (곱들의 합)을 민텀 (Minterm) 이라고 한다. To understand better about SOP, we need to know about min term. Q3. Express Fas a minterm expansion in m-notation. – Each minterm has value 1 for exactly one combination of values of variables. A truth table for the function F(a, b, c) = ac' + a'c+b' can be created by evaluating the function for all possible combinations of inputs a, b, and c. Prove your answer by using the general form of the minterm expansion. Rather, it should be built by combining four instances of your Full Adder circuit. b) F as a max term expansion is . Write the maxterm expansion for Z in. Express F as a minterm expansion in boolean expression. Add your answer and earn points. This expression can then be converted to decimal notation. 3. Using scientific means, determine the minterm expansion for the given function: F = X'Y + XY' + Y'Z'. The expression on the right-hand side is a sum of minterms (SoM). engineering. If f is too large to handle, you can use the Shannon’s expansion, and search for the cubes in the cofactors f xand f′. The general rule for finding the expression, is that all the terms present in either or will be present in . We consider in this chapter real random variables (i. g. A: The minterms are those terms that give 1's of the function in a truth table. The output is to be 1 only if the product N1 times N2 is less than or equal to 2. 100% (42 ratings) for this solution. Simplify further. Minterm is represented by m. (Use m-notation. (Use m-notation. Most common MINTERM abbreviation full form updated in November 2023. Max term expansion of . 1. (17 points) Y = Thermal expansion can present significant challenges for designers in certain areas, for example when constructing spacecraft, aircraft, buildings, or bridges, but it can have positive uses. Given expression is. Simplification in a Boolean algebra. Given: f (a, b, c) = a (b + c’). Minterm = A00; We will write 1 in place of non. The minterm expansion for (E cup F) has all the minterms in either set. 1. Express F as a maxterm. Problem: Find the minterms of the following expression by first plotting each expression on a K-map: a) F(X,Y,Z) = XY + XZ + X’YZ b) F. 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. – In formal logic, these values are “true” and “false. Consider the following functions min-term list: Determine the min-term expression for function, . 민텀을가진다. ZMinterm and MAXTERM Expansions 350151 – Digital Circuit 1 ChoopanRattanapoka. Simplify if desired F = (B +C)(A+C) – Typeset by FoilTEX – 29. 1. 0 × 29 and c = 1. Computer Science 3. Programming Logic & Design Comprehensive. 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. 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. Otherwise, F = 0. 1. Minterm • Minterm or Sum of Product (SOP) • For output 1 • We do the product (AND) of input (0 = inverse) • For output 0 • We ignore them • Then, we do sum (OR) of all product A’BC. 1) F 1 ( x, y) = x ⋅ y ′ + x ′ ⋅ y + x ⋅ y. EE/CompE 243 Digital Logic Session 10; Page 2/4 Spring 2003 (c) F A B C. Find step-by-step solutions and answers to Exercise 10 from 논리설계기초 - 9788962183948, as well as thousands of textbooks so you can move forward with confidence. A B C D 3. 32. ) Keep the first 1, and x amount of 0's before the first one. (17 points) Y = Not the question you’re looking for? Post any question and get expert help quickly. Please answer only if you're 100% sure. A Boolean expression generated by x1, x2,. Maxterm expansion: To find the maxterm expansion, we need to find the terms that are not present in the minterm expansion. b. 2. 7) F = M 1 M 16 M 18 M 20 M 24 M 26 + M 3 M 4 M 5 M 15 M 18 M 24 M 26 M 28 M 31 F = M 1 M 16 M 18 M 20 M 24 M 26 M 3 M 4 M 5 M 15 M 18 M 24 M 26 M 28 M 31. Represent the heads and tails status of each coin by a logical value (A for the first coin, B for the second coin, and C for the third coin) where the logical variable is 1 for heads and 0 for tails. 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. For example from the truth table, express output X in terms of it minterm expansion variables, m Em (mo +mn) X (а, b, с, d) An adder is to be designed which adds two 2-bit binary numbers to. Final answer. In general there are different Minterms and different maxterms of n variables. (Use M-notation. (c) Express f' as a minterm expansion (use m. Given: F (a, b, c) = abc’ + b’. ) Complement the rest of the values after the kept 1. 9, which involves an independent class of ten events. For each row with a 1 in the final column, the corresponding product to add to the minterm expansion is obtained as:A and B represent the first and second bits of a binary number N1. Using scientific means, determine the minterm expansion for the given function: F = X'Y + XY' + Y'Z'. Fundamentals of Logic Design (7th Edition) Edit edition Solutions for Chapter 4 Problem 5SG: Study Section 4. g. Find step-by-step solutions and answers to Exercise 10 from Fundamentals of Logic Design - 9781133628477, as well as thousands of textbooks so you can move forward with confidence. It will have four outputs (p3, p2, p1, and p0) that correspond to the four bits of the product. Solution. Question: Find the minterm expansion of f(a, b, c, d)=a'(b'+d)+acd' and then design the result. It facilitates exchange of packets between segments. 1. Problem 3: (a) Plot the following function on a Karnaugh map. 🔗. That is, the cell 111 corresponds to the minterm ABC above left. Given F1=Σ m (0,4,5,6) and F2-yn (0,3,6,7) find the minterm expression for F1 F2. To illustrate, we return to Example 4. ,, a product term in which each of the variables appears once (either in its complemented or uncomplemented form) is called a minterm. On a piece of paper, create the minterm expansion formula for this truth table. Computer Science. 2. 5. EENG 2710 - Digital Logic Design Assignment #4 (Due on 9/29/2023) (Include details for full credit) 1. Problem #3 (15p) Implement the following function F(expressed using minterm expansion); F(A, B, C, D) = m(1,4,5, 10, 12) + 3d(0, 9, 14, 15) a) Cell numbers are. So, the shorthand notation of A+B' is. Given F1= Σ m(0, 4, 5, 6) and F2= Σ m(0, 3, 6, 7) find the minterm expression for F1+F2. d. This is a differential equation problem involving a Taylor expansion series. Computer Science. 1. Simplify further. Computer Science. (b) Find the maxterm expansions for Y and Z. Earlier, HTET Notification 2023 Out on 30th October 2023. In this video, the Sum of Product (SOP) and Product of Sum (POS) form of Representation of Boolean Function is explained using examples. a. The circuit to implement this function. Stuck at simplifying boolean expression. 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. Express F as a maxterm expansion in boolean. Given the following Minterm Expansion. If S and T are two different trees with ξ (S) = ξ (T),then. Each group of three is a 'minterm'. Remember that a Full Adder adds a single column of digits from the bitwise sum of two binary numbers. Simplify boolean expression to. A maxterm, such as A ¯ + B + C ¯, from section 3. Minterms and Maxterms are important parts of Boolean algebra. Q3. Sum of Product is the abbreviated form of SOP. schedule) No labs this week; 10/11: last day to drop without a ‘W’. x, f x ⊃ fGiven the following truth table: Find the expression of the standard sum of products (i. (11 points) (b) Draw the corresponding two-level AND-OR circuit. com(Hint: start with a minterm expansion of f and combine minterms to eliminate a and a ' where. The Gray Code belongs to a class of code called minimum-change. Question: Find the minterm expansion of f(a, b, c, d)=a'(b'+d)+acd' and then design the result. In this tutorial, we learned about The term Minterms. b. Find the. That is, the cell 111 corresponds to the minterm ABC above left. Z = ∑ (c) Find the maxterm expansion for Z in both decimal form in terms of. Do this repeatedly to eliminate as many literals as possible. me/tanmaysakpal11-----. Minterm expansion = ∑ m (0, 1, 2, 4, 8) ext{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. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Example – Express the Boolean function F = A + B’C as standard sum of minterms. c) Min term expansion of the function . Maxterm to Minterm conversion: rewrite maxterm shorthand using minterm shorthand replace maxterm indices with the indices not already used E. If A = 0, the output Z is the equivalence of B OR C. There are 2^3 = 8. Free Boolean Algebra calculator - calculate boolean logical expressions step-by-step. E. b. (b) Write the minterm expansion for Z in decimal form and in terms of A,B,C. Prove your answer by using the general form of the minterm expansion. Z = ∑ (c) Find the maxterm expansion for Z in both decimal form in terms of A, B, C. Question: 36 and 37. Otherwise, F = 0. Give the minterm and maxterm expansion for each of the following logic functions: (a) F(A, B, C, D. (a) Write the minterm expansion for F. The output is to be 1 only if the proc x N2 is less than or equal to 3. Find the maxterm expansion of f2(a,b,c,d)= bc + ac’ + abd’ 7. (a)True (b)False?? The Sum of Product (SOP) canonical form is also known as ____?? (a)Minterm expansion (b)Maxterm expansion The 1’s complement of the. (Use M - notation. Z + X. A. 1. The minterm is described as a sum of products (SOP). Each data input should be0, 1, a, or a′. Question: Given that F(a, b, c) = ac’ + a’c + b’ d) Express F’ as a minterm expansion (use m-notation) e) Express F’ as a maxterm expansion (use M-notation) g)Build Logisim circuits for d) and e) and show that they give same output <----- I have already figured out how to do d) and e). Problem 1 Applying the different laws and identities in Boolean algebra, determine the minterm expansion of the given Boolean expression: F(W,X,Y,Z. Remember that a Full Adder adds a single column of digits from the bitwise sum of two binary numbers. b. Note that the sum has five bits to accommodate the possibility of a carry. ) (d) Express F′ as a maxterm expansion. = 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. Kirchhoff’s current law states that a. Who are the experts? Experts are tested by Chegg as specialists in their subject area. MINTERM Meaning. Above right we see that the minterm A’BC’corresponds directly to the cell 010. the algebraic sum of the currents entering and leaving any point in a circuit must equal zero. Show transcribed image text. Step-by-step solution. Joyligolf8693 is waiting for your help. How to express a digital logic function in minterm (sum of products) form. r. Write the maxterm expansion for Z in(Use m-notation. d. ) Show transcribed image text. Thus, a minterm is a logical expression of n variables that employs only the complement operator and the conjunction operator. Simplifying Boolean Two Expressions. F(a,b,c,d) = sigma m(1,3,4,5,9,12,15) + sigmad(2,7,8). (Use m-notation. Note that(Use M-notation. In POS representation, a product of maxterm gives the expression. Expert-verified. C and D represent the first and second bits of a binary number N. c. 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. implement the simplified Boolean function with logic gates. For each row with a 1 in the final column, the corresponding product to add to the minterm. 21(b) Realize a b c a bc ab c abc using only two input equivalence gates a b c a bc ab c abc c a b ab c a b ab c a b c a b Electrical Engineering questions and answers. Not the exact question you're looking for? Post any question and get expert help quickly. -5 in 4-bit = 1011. (Use M-notation. The calculator will try to simplify/minify the given boolean expression, with steps when possible. Equivalence of B and C is defined as: (B⊕C)′ 1. (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. Using K-map, determine the Boolean function that the MUX implements. . Digital Systems Examples and. (b) Find the maxterm expansion for F (both decimal and algebraic form). Question: A combinational circuit has three inputs (A, B, C) and two outputs (X,Y). ) (c) Express F−as a minterm expansion. Above right we see that the minterm A’BC’corresponds directly to the cell 010. (Use m-notation. Write the complete minimized Boolean expression in sum-of-products form. . 5. But is it necessary to search in f x′? Remember that because of unateness of f w. 1 Answer Sorted by: 0 ab+ac' ab (c+c')+a (b+b')c' abc+abc'+abc'+ab'c' abc+abc'+ab'c' use a truth table with 3 variables a,b,c find followings abc = 111 - 7 abc' = 110 - 6 ab'c'= 100 -4 Sum m (4, 6, 7) therefore, maxterm M (0,1,2,3,5) Share Cite Follow answered Sep 28, 2017 at 12:28 justiny 1 Add a comment The minterm expansion for \(E \cup F\) has all the minterms in either set. The given expression can be written as: F(A, B, C) = AB(C + C̅) + (A + A̅) BC̅ + A(B + B̅)C̅ Minterm. Find the truth table for Z. A switching circuit has four inputs as shown. Using algebraic manipulations the required minterm expansion is to expand the given into a standard sum-of-products (minterm expansion) then introduce the missing variables in each term as. N1 B F N2 D O Find the minterm expansion for F. of F list minterms not present in F maxterm nos. For each variable that has a 1 in that row, write the name of the variable. 2. Computer Science questions and answers. General Minterm and Maxterm Expansions general function of n variables(a) Minterm Expansion: The function F can be expressed as a minterm expansion by using the AND operation between the variables and the NOT operation to represent the complement of each variable. Express F as a minterm expansion (standart sum of products). not on the maxterm list for F Maxterm Expansion of F maxterm nos. On paper, create the minterm expansion formula for this truth table. (c) (1 Points) Write down an expression for F ′ in terms of minterms. 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. It is sometimes convenient to express a Boolean function in its sum of minterm form. Each key is owned by a different person. 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. Rather, it should be built by combining four instances of your Full Adder circuit. (b) Find the maxterm expansion for F 4. loading. The result is an another canonical expression for this set of variables. • Eliminate. A and B represent the first and second bits of a binary number N1. Step 2. Show transcribed image text. , xk that has the form. b) F as a max term expansion is . Find step-by-step solutions and answers to Exercise 9 from Fundamentals of Logic Design - 9780495471691, as well as thousands of textbooks so you can move forward with confidence. Express F as a maxterm expansion (standard product of sum). 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. 3K views 2 years ago Digital Design How to express a digital logic function in minterm (sum of products) form. Using theorems of Boolean algebra, simplify the minterm expansion of F to a form with as few occurrences of each as possible. What the expression minterm is intended to imply it that each of the groups of three in the expression takes on a value of 1 only for one of the eight possible combinations of X, Y and Z and their inverses. Answered 2 years ago. 100% (42 ratings) for this solution. (Use m-notation. Express F as a minterm expansion in m-notation. schedule) No labs this week; 10/11: last day to drop without a ‘W’. I mostly need help with building the circuits for each. Specify ai and bi, F1=Σaimi and F2=Σbimi (b) Find the minterm expansion of (F1+F2)′ use ∑i=0i=7mi=1 and X′+X=1 (c) Find the maxterm expansion of F1∗F2, obtain mintern and then convert it to maxterm (d) Find. Simplification in a Boolean algebra. maxterm expansion) and draw the corresponding circuit. Expert Answer. , F(A,B,C) = ΠM(0,1,2) = Σm(3,4,5,6,7) 3. Equivalence of B and C is defined as: (B⊕C)′ 1. For example, , ′ and ′ are 3. Minterm. Convert to maxterm expansion F = M 0M 2M 4 3. the operation is or. Q3. 문제를 많이 풀어보시길 바랍니다. (b) Find the maxterm expansion for F (both decimal and algebraic form). 97) The maxterm expansion for a general function of three variables is: Each minterm has a value of 1 for exactly one combination of values of the variables A, B and C. Write the minterm expansion for Z in decimal form and in terms of A,B,C. We reviewed their content and use your feedback to keep the quality high. Let G = (V,E) be a graph. 1 Minimization Using Algebraic Manipulations. C and D represent the first and s number N. A product term that includes all variable is called a minterm, and an expres sion consisting only of min terms is called a minterm expansion. State a general rule for finding the expression for F1 F2 given the minterm expansions for F and F2. The general rule for finding the expression, is that all the terms present in either or will be present in . 2 of 3. , the value of D is such that A, B, C, and D always contain an odd number of 1’s. Use the minterm expansion principle to create a circuit that uses only AND, OR, and NOT gates. Given the truth table of F(A,B,C) on the right, determine the following: a. (25 Points) 4. 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. Maxterm is the sum of N distinct literals where each literals occurs exactly once. Here’s the best way to solve it. Write a logic function F (A, B, C) which is 1 iff. ) (d) Express F as a maxterm expansion. Next, use minterm expansion twice – once for each output bit – and create a separate formula for each of those bits. 6. 5. F' as a product of maxterms using M notation. 0 × 29 , b = −1. What is the minterm expansion of F? ii. 5 as the initial value. Step 1 of 4. ) [5 Points] (b) Express F as a maxterm expansion. ) (d) Express F′ as a maxterm expansion. 1. a and b represents the 1st and 2 nd bits of a binary number M. 64K subscribers Subscribe 1. ). What is dont. Determine the minterm and maxterm for each of the following: a). In this course, you will study the history of modern computing technology before learning about modern computer architecture and a number of its essential features, including instruction sets, processor arithmetic and control, the Von Neumann architecture, pipelining, memory management, storage, and other input/output topics. (2 points) An 8×1 MUX has control (or, select) variables A, B, C. As the name indicates, the excess-3 represents a decimal number, in binary form, as a number greater than 3. Question 2. (a) Find the minterm expansion for F. Represent the heads or tails status of each coin by a logical variable (A for the first coin, B for the second coin, and C for the third) where the logical variable is 1 for heads and 0.