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0000 0sum of minterms  In other words, A Boolean function F may be expressed algebraically as a sum of minterms fromLooking at the 3 variable map on the left in Fig

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. B. Convert 𝐹 to canonical sum-of-minterms form. We form a mintable for three variables. The following are examples of “simplifying” that changes a. ) a. , logical-AND) of all of the signals, using the complement of any signal that needs to be False for that combination of inputs. F(x,y,z) = xyz Is the given equation in the canonical sum of minterms form? If not, convert it into this form. 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. 7. View the full answer. ) 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. There are two types of canonical forms: SOP: Sum of products or sum of minterms. )). Question: Given the function y=ab+a′ a) What's the sum-of-minterms form? b) Construct the truth. See Answer See Answer See Answer done loading Final answer. Question: Write the following Boolean expression in sum-of-minterms form F= X+YZ' Select one: a. a) Expand the Boolean function F(a, b, c) = a'b + ac', by using Boolean algebra, to get sum-of-minterms and product-of-maxterms representations (Don't use truth table, just use Boolean equations). • We perform Sum of minterm also known as Sum of. Show all steps. A 2-variables function has 2 2 =4 possible maxterms. Identify minterms or maxterms as given in the problem. A Product-OF-Sums solution is completed in the usual manner. Complement function will be equal to the sum of minterms missing from the given function. 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. The functions: f(u,v,w,z)=π(0,4,8,12,9) d(u,v,w,z)=E(1,5,3) π represents the product of sums(pos) a. 4: let F = A'C + A'B + AB'C + BC a) Express. You'll get a detailed solution from a subject matter expert that helps you learn core concepts. So how can we show the operation of this “product” function in Boolean Albegra. Minterm is represented by m. Show a minimum POS expression (f: 2 solutions, 3 terms, 6 literals; g: 1 term. Question: 4. It uses maxterms. In addition, you must show your work on the paper you submit on eLearning to get credit. Each of these three product statements is a minterm—a term that is True (1) for exactly one combination of inputs. There are 2 steps to solve this one. To represent a function, we perform the sum of minterms which is called the Sum of Product (SOP). A function is given by f (x,y,z)= (x) (y+z) Write this expression as a sum of minterms. Step 2. Using DeMorgan’s law, write an expression for the complement of F. (a). Electrical Engineering questions and answers. 7. Example 2. Step1: Represent the minterms for a function by decimal 1 in column 4 of table below. Since all the variables are present in each minterm, the canonical sum is unique for a given problem. ms + m + m² Cdim - m₂ + m7. . The Boolean function E=F1+F2 contains the sum of the minterms of F1 and F2. Expert Answer. (d) Draw the AND-OR circuit for the expression in part (c). Electrical Engineering. So a 4-variable k-map will have 16. Sum-of-products canonical forms Also known as disjunctive normal form Also known as minterm expansion F = 001 011 101 110 111 A’B’C + A’BC + AB’C + ABC’ + ABC Winter 2010 CSE370 - IV - Canonical Forms 10 short-hand notation for minterms of 3 variables A B C minterms 0 0 0 A’B’C’ m0The only equation in sum-of-minterms form is d. Show the un-simplified logic equation for the customizedfunction, expressed as a sum of minterms. Digital Circuits Questions and Answers – Karnaugh Map. 0. 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. #Minterms #Maxterms #Representhegivenbo. 19It helps represent Boolean expressions as product of sum terms. . 2. (c) Using Boolean algebra, derive a simplified sum of products expression. b) Cycle Diagram. (e) Simplify E and F to expressions with a minimum number of literals. Express the following Boolean functions in the canonical sum-of-minterms (SOM) or the canonical product-ofmaxterms (POM) form, as indicated. b) Find the minimal sum of products expression. Step2: Add (or take binary OR) all the minterms in. b) (cd + b'c + bd' ) (b + d) Expanding it we get : =>. We form the minterms as intersections of members of the class, with various. Select the a in the identity property a *15 a, so that a 1-a. Find the Sum-of-Minterms canonical Boolean expression for the output signal B. a) 3 Variables: A(x,y,z)=m3+m4+m6+m7 b) 3 Variables: B(x,y,z)=m0+m2+m4+m5+m6 c) 4 Variables: C. In SOP (sum of product) form, a minterm is represented by 1. 2. -P+Q = Definition of impliy. • product-of-maxterms • Expand the Boolean function into a product of. There are 4 steps to solve this one. (b) Draw the logic diagram, using the original Boolean expression. Question: Q3. A Boolean function can be expressed, canonically, as a sum of minterms, where each minterm corresponds to a. A function that defines the solution to a problem can be expressed as a sum of minterms (SoM) in which each of the minterms evaluates to. Draw the truth table. The Sum-Of-Products solution is not affected by the new terminology. The representation of the equation will be Thus, the minterms form a partition. Express the Boolean Function F= A + BC as a sum of minterms or canonical form. Show and explain the completed circuit. A Karnaugh map (K-map) is an abstract form of ____________ diagram organized as a matrix of squares. Product-of-maxterms 3. Find the sum-of-products expansion of the Boolean function F(w;x;y;z) that has the value 1 if and only if an odd number of w;x;y, and z have the value 1. , logical-AND) of all of the signals, using the complement of any signal that needs to be False for that combination of inputs. 4: let F = A'C + A'B + AB'C + BC a) Express it in sum of minterms. The following multiple-choice options contain math elements, so you may need to read them in your screen reader's “reading” or “browse” mode instead of “forms” or. [c] Write the short form Sum of Products (SOP) expression (list minterms). Here’s the best way to solve it. Reset Terms. 2. (b) Determine the sum of minterms expression. Answer to Solved 2. by making the n-1 select variables as most significant inputs). 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. The minterm evaluates to 1 if and only if the values of the variables are set according to the corresponding row of the table. (b) List the minterms of E bar and F bar. This page titled 8. Also, it appears the first row is starting from 0, not 1?The Boolean equation description of unsimplified logic, is replaced by a list of maxterms. Describes how to derive the Sum of minterms from a three variable Truth TableIn Sum of Products (what you call ANDs) only one of the minterms must be true for the expression to be true. 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. 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)). 0000 0. We tabulate Maxterm combinations. Since the number of literals in such an expression is usually high, and the complexity of the digital logic gates that implement a Boolean function is directly related to the complexity of the. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Sorted by: 2. . These support the statements shown, but are not proofs thereofbecause they are only an example. Show an algebraic expression in product of maxterms form. Minterm vs Maxterm. 100% (1 rating) Transcribed image text: Discrete Mathematics home > 5. A*B = A and B. Write it as a product of maxterms. A. Previous question Next question. Check out a sample Q&A here. What is Minterm? Minterms are the product of various distinct literals in which each literal occurs exactly once. There are two types of canonical forms: SOP: Sum of products or sum of minterms Example of SOP: XY + X’Y’ POS: Product of sums or product of max terms Example of POS: (X+Y) (X’+Y’). (MK 2-20) Simplify the following Boolean functions by finding all prime implicants and essential prime implicants and applying the selection rule: Engineering Computer Science Example 3. 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. All logic functions can be described using sum of minterms where. Its De Morgan dual is a " Product of Sums " ( PoS or POS) for the canonical form that is a conjunction (AND) of maxterms. Maxterm of ‘n’ variables is a sum of ‘n’ variables which appear exactly once in True or Complemented form. Then take each term with a missing variable and AND it with . ) 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 ′. b) Find the minimal sum of products expression. Hence, we can say that it shows the PDNF. Obtain the function F as the sum of minterms from the simplified expression and show that it is the same as the one in part (a) e. Obtain the truth table of F and represent it as sum of minterms b. Groups must be a power of 2. The sum of minterms is called a Canonical Sum of Product. Question: Identify the Boolean function that is defined by the following input/output table. To understand better about SOP, we need to know about min term. Show 0 1 1 0 0 10001 10111 1 1 0 1 1 11110. As the sum of minterms b. It is used for finding the truth table and the nature of the expression. A maxterm, such as A ¯ + B + C ¯, from section 3. If the variable value is 0, take its complement. Simplify the following Boolean expressions to a minimum number of literals. g. . ) F (x,y,z)= x'y + x + xyz. Then make sure that every term contains each of a, b, and c by using the fact that x + x ′ = 1. Though, we do have a Sum-Of-Products result from the minterms. 9 find the displayed function expressed as a sum of minterms and also find the function as a product of maxterms. arrow_forward. Fig. 3. Question: 17. Derive the simplified expression in SOP. Th. And what is minterm. The membership of any minterm depends upon the membership of each generating set [Math Processing Error] A, B, C or [Math Processing Error] D, and the relationships between them. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. It is represented by m. CSE370, Lecture 51 Canonical forms! Last lecture " Logic gates and truth tables " Implementing logic functions " CMOS switches Today™s lecture " deMorgan™s theorem " NAND and NOR " Canonical forms #Sum-of-products (minterms) #Product-of-sums (maxterms) 2 de Morgan™s theoremObtain the truth table of the following functions and express each function in sum of minterms and product of maxterms: a) (xy + z) ( y + xz) b) (A’+ B) (B’+C) c) y’z + wxy’ + wxz’ + w’x’z 3. So, the canonical form of sum of products function is also known as “minterm canonical form” or Sum-of-minterms or standard canonical SOP form. (c). Sum of minterms is unique. Sum of Product is the abbreviated form of SOP. 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. ISBN: 9780133923605. Step 4. (e) Simplify E and F to expressions with a minimum of literals. Sum of product form is a form of expression in Boolean algebra in which different product terms of inputs are being summed together. 1-minterms = minterms for which the function F = 1. x’ and y’. . Show a minimum SOP expression (f. Question: 7. Suppose Limor Fried expands her business, Adafruit Industries, to make electric scooters. It is represented as the sum-of-minterms (expression 1), together with the don’t care conditions d (expression 2) as shown below:(a) Construct the truth table. 1. For the Boolean functions E and F, as given in the following truth table (a) List the minterms and maxterms of each function. b) The Boolean function G = F 1 F 2 containsonly the minterms that are common to F 1 andF 2. The complement of a canonical product becomes a sum. . an implicant with the fewest literals. Obviously, this requires a methodology. These output lines can provide the minterms of input variables. 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. [d] Write the short form Product of Sums (POS) expression (list. To expand wx into the sum-of-minterms using wxy+wxy', we need to find all the possible combinations. b) Find the minimal sum of products expression. Each is worth 3. • A function is in Sum of Products (SOP) form if it is written as product terms ORed together – Example: f(x y z) = xy’z + xz + y • A function is in Canonical SOP form if it is in SOP form and all terms are minterms – Example: g(x y z) = xy’z + x’yz + xyz. It also looks strange that (A+B+C) is mapped into the cell 000. e. 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. (b) List the minterms of E and F (e) List the minterms of E+ Fand F. " The term "Sum of Products" is widely used for the canonical form that is a disjunction (OR) of minterms. See examples, procedures, and diagrams for each type of term. 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. qx3zqy7 Jump to level 1 1 a b с у 2 0 0 0 0 3 0 0 1 1 0 1 0 0 0 1 1 0 5. Simplify the sum of minterms to a minimum number of literals. (d) Obtain the function F as the sum of. 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. Unlock. See the difference between the two expressions, the truth table, the K. Definition of minterm in the Definitions. List the. Question: Sum-of-minterms form is a canonical form of a Boolean equation where the right-side expression is a sum- of-products product term having exactly one literal for every function variable compact function notation that represents each literal by a number variable appearance in an expression in true or complemented form . Place ‘1’ in the minterms (cell) which are covered by each prime implicant. Sum of the Minterms = Sum-of. There are 2 steps to solve this one. E. Minterm. F (a,b,c,d)=b (ac+a′c′)+a′d D. (for example, after you have combined the first two terms to A′B′D′ A ′ B ′ D ′, you can do. Y 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Expert Solution. 3. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Chap 4 C-H6. Then for Z it's --1, where the values can be 001, 011, 101, 111. 4. Limor must decide on the best sales mix. Here’s the best way to solve it. 1 will be used to illustrate Petrick's method. Implement the sum of minterms of this function and connect a, b, c and d to clock. 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. Sum of Products (SOP) Product of Sums (POS) Sum of Products (SOP) A boolean expression consisting purely of Minterms (product terms) is said to be in canonical sum of products form. To expand wx into the sum-of-minterms using wxy+wxy', we need to find all the possible combinations. Select a next property from the right to apply wy wly:1) w (ly:1). 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. b. (b) List the minterms of E and F . 10, then from the table we get F = 1 for minterms m3, m4, m5, m6, and m7. F(x,y,z) = xy'z + xy + yz Is the given equation in the canonical sum of minterms form? If not, convert it into this form. Question: Expand wy to sum-of-minterms form wyz+wyz' 1. Using Boolean algebra, derive a simplified Sum of Products (SOP) expression for the function. 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. Groups must be a power of 2. b Show sum of minterms 0011 1 01000. B(A,D,W)=A′D′W′+A′D′W+AD′W′+AD′W+ADWB(A,D,W)=A′DW′+A′D′W+ADW′+AD′W+ADWB(A,D,W)=A′DW+A′D′W+ADW′+AD′W′+ADWB(A,D,W)=A′DW′+AD′W+ADW′+AD′W+A′DW Q7. [c] Write the short form Sum of Products (SOP) expression (list minterms). Expert Answer. 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. 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. Often sum-of-product expressions may be simplied, but any nontrivial simplication will produce an expression that is not in sum-of-product form. b. 1a, it is possible to represent only 14 minterms. It is used for finding the truth table and the nature of the expression. In this form of expression, the first canonical form, a set of minterms (minimum terms) that are AND logical operators are created (one for each line of the truth table where the output is a logic 1). Shows how to derive the sum of minterms for a 4 variable truth tableA Boolean function can be represented in the form of sum of minterms or the product of maxterms, which enable the designer to make a truth table more easily. 2: Convert to sum-of-minterms form. There are 2 steps to solve this one. Design a logic circuit using a minimum number of 3 -to-8 decoders (74LS138) and logic gates that does the following: a. I use Morgan and get this: ((¬b ∨ ¬d) ∧ ((b ∨ (¬c ∨ d)) ∧ (¬a ∨ (b ∨ d)))) which doesn't have an equivalent truth table. 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. View the full answer. We count the number of “successes” corresponding to each minterm by using the MATLAB function sum, which gives the sum of each column. Determine the Sum of Minterms expression for the function F (A,B,C). Express the following POS equations in SOP form. 1 . This is certainly a compact means of describing a list of minterms or cells in a K-map. Show the minterms of f' (complement of f) in numeric form. Final answer. Answered 2 years ago. Though, we do have a Sum-Of-Products result from the minterms. Show transcribed image text. For example, consider the truth table in Figure 3. (A*-B)+ (-A*B) = XOR. You got this!The switching function is specified with a sum of minterms and don’t cares. . What if instead of representing truth tables, we arranged in a grid format. Question: CHALLENGE ACTIVITY 1. Sum of product (SOP) Product of Sum (POS) According to the need of problem. (e) Using Boolean algebra, derive a simplified product of sums expression. See Answer. Also, draw the truth tables showing the minterms and maxterms. 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. 10. Question: Identify the Boolean function that is defined by the following input/output table. F=x'yz'+xy'z'+xy'Z+xyz'+xyz' d. Computer Science questions and answers. g. Exercise 5. 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. As the sum of minterms b. Support Simple Snippets by Donations -Google Pay UPI ID - tanmaysakpal11@okiciciPayPal - paypal. Question: 4. Try focusing on one step at a time. It is a product of all variables in a function and that function has the property that it is equal to 1 on exactly one row of the truth table. 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. (Digital_design-__morris_mano-fifth_edition) Boolean functions expressed as a sum of minterms or product of. 3. The following questions refer to the Truth Table below Q7. B Sum-of-Products (SOP) Equation The SOP equation can be represented by an expression that is a sum of minterms, where each mintermComputer Science questions and answers. If each product term is a minterm, the expression is called a canonical sum of products for the function. The grouping of 0’s result in Product of Sum expression & the grouping of 1’s result in Sum of Product expression. Therefore, F = m3 + m4 + m5 + m6 + m7, which is the same as above when we used term expansion. Therefore M i = m’ i. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. In this lesson, we will look at one of two "standard forms" of boolean functions. Q7. Sum of Product is the abbreviated form of SOP. Answered: Q2. 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 . 9: Sum and Product Notation is shared under a GNU. The answer should list the minterms as m0+m1+m2. View the full answer. 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. Question: Express the complement of the following functions in sum-of-minterms form: (a) F(w,x,y,z)=ÎŁ(1,5,7,11,12,14,15) (b) F(x,y,z)=Π(2,4,5) Show transcribed image text. A maxterm is any sum of n literals where each of the n variable appears once in the sum. As discussed in the “Representation of Boolean Functions” every boolean function can be expressed as a sum of minterms or a product of maxterms. 0-minterms = minterms for which the function F. It is represented as the sum-of-minterms (expression 1), together with the don’t care conditions d (expression 2) as shown below: Consider a logic function F, which has four inputs A, B, C and D. It generates the sum of minterms expression F = ÎŁ m (1, 5, 9). 2) Example of sum of products form. - (P* (-P+Q))+Q = Modus ponens. k. To grasp this concept fully, Table 1. The minterms with output values of false (-1) were eliminated, leaving only 6 minterms. (b) Determine the sum of minterms expression. For maxterms this is the location of 0 s, as shown below. . 4 Points. The boolean algebra calculator is an expression simplifier for simplifying algebraic expressions. Express the complement of the following functions in sum-of-minterms form: a) F(A, B, C, D) =E(2,4, 7, 10, 12, 14). a) extbf{a)} a) F. My method of finding them, however, is wrong, because the minterms are actually 0,3,5, and 7. Obtain the truth table of the following functions, and express each function in sum‐of‐minterms and product‐of‐maxterms form: (a) (b + cd)(c + bd)(a) Express X as a sum-of-minterms and product-of-maxterms (b) Express Y as a sum-of-minterms and product-of-maxterms 4. (10 points) 3. Sum-of-minterms 2. The Product of Sum (POS) form . What does minterm mean? Information and translations of minterm in the most comprehensive. The imp. Step1: Represent the minterms for a function by decimal 1 in column 4 of table below. Transcribed Image Text: Write down an expression for F(X,Y,Z) in (a) sum of minterms form and (b) product of maxterms form for the truth table below: 4. 0 0 0 0 0 0 0 0 0 0 Without Using truth table find sum-of. Electrical Engineering questions and answers. Jump to level 1 2 Consider a function with three variables: a, b, c. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. 10 of a logic function f of three variables. Who are the experts? Experts have been vetted by Chegg as specialists in this subject. 0000 0. Its De Morgan dual is a "Product of Sums" or "PoS" for the canonical form that is a conjunction (AND) of maxterms. Q: Express each of the following function as a sum of minterms and as a product of maxterms F = x′z +… A: As given, I need to express the given functions as a sum of minterms and product of maxterms. 5) Given the Boolean function F= xyz + x'y'z + w'xy + wx'y + wxy a) Obtain the truth table of the function. In the canonical sum of products, there could have been as many as 9 minterms, because there are two 3-valued inputs. Convert the Boolean function F = x + y z into a sum of minterms by using a truth table. b. Express f (x, y, z) = x ˉ + y ˉ z as a canonical SOM. A*B = A and B. (a) minterms of E: X Y Z , X Y Z, X YZ , XY Z 0,1,2,5 This video describes how to Express a boolean function in sum of minterms Sum-of-products AND gates to form product terms (minterms) OR gate to form sum Product-of-sums OR gates to form sum terms (maxterms) AND gates to form product EECS150 - Fall 2001 1-3 Two-level Logic using NAND Gates Replace minterm AND gates with NAND gates Place compensating inversion at inputs of OR gate EECS150 - Fall 2001 1-4 A sum term containing all the input variables of the function in either complemented or uncomplemented form is called a maxterm. Each variable in a Boolean expression can hold only one value out of two: 1 for all truthy values and 0 for all falsy values. You'll get a detailed solution from a subject matter expert that helps you learn core concepts.