Vertical Circulation In Buildings, Which of the following equation represents mass b) 1990 11 AB BC AC AD AC DC22 Addition 12 AB BC AC AD DC22 () Distributive property 13 AC = AD + DC Segment Addition Property 14 AB BC AC AC22 Substitution 15 ABBC AC22 2 Definition of exponent ABBC AC22 2 is a statement of the Pythagorean Theorem, so Gales proof is complete. I am providing you the correct answer below. &=AB+A'C+BC(A+A') \quad \text{($A+A'=1$, Complementarity law)}\\ /Length 330 A lookup relationship essentiallylinks two objects together so that you, Q:Make a compeling case in your own words for and against the benefits and drawbacks of a division of, A:The process of preventing illegal access, use, disclosure, disruption, alteration, inspection,. Sampling frequency,fs=36kHz It may not display this or other websites correctly. Simplify the following to the least of literals using Boolean Algebra: \end{align}, $\begin{align*}&= AB+AC+BC\\ A:Introduction: C. Q:What characteristics does a derived class have with its base class when compared to its base class? Answer (1 of 2): Hello there, as far as I know, it is AD not AC. A:Given: What are the disadvantages of fuse in an electric circuit? &= AB+AC+BC(A+A)\\ Question: endobj but when don't cares are used, the actual k-map changes depending on how Answer (1 of 7): Everybody interested in Boolean Algebra should check out NJ Wildberger's formulation using addition and multiplication in the bifield Z_2, which is fancy way to talk about arithmetic with only zero and one. Hockey Performance Shirt, stream You should create a trigger, calledprice, A:How do you make a trigger once you've inserted something?This is the syntax: After the CREATE, A:Justification: Encode and decode the BAM network that stores the following pair of p The, A:Hi there, Please find your solution below, I hope you would find my solution useful and helpful., A:An adaptive mutex protects any significant data item accessed by just a few lines of code. Learn more about Stack Overflow the company, and our products. hs2z\nLA"Sdr%,lt pVs The time ~B5OQYClQx2TTtLNN;0!cft]K. A typical 4-variable K-map plot is shown below. the locations of the poles and zeros, plot them, A:The location of pole and zero can be obtained by equating the numerator and denominator part to zero. 1 + BC Rule 4: A . Y = A' (C' + D') + A (EF + B') This can be implemented as follows. << /Length 11 0 R /N 3 /Alternate /DeviceRGB /Filter /FlateDecode >> K0iABZyCAP8C@&*CP=#t] 4}a ;GDxJ> ,_@FXDBX$!k"EHqaYbVabJ0cVL6f3bX'?v 6-V``[a;p~\2n5 &x*sb|! .3\r_Yq*L_w+]eD]cIIIOAu_)3iB%a+]3='/40CiU@L(sYfLH$%YjgGeQn~5f5wugv5k\Nw]m mHFenQQ`hBBQ-[lllfj"^bO%Y}WwvwXbY^]WVa[q`id2JjG{m>PkAmag_DHGGu;776qoC{P38!9-?|gK9w~B:Wt>^rUg9];}}_~imp}]/}.{^=}^?z8hc' = AB+AC+ BC = AB+AC+ BC(A+ A) (A+A = 1, Complementarity law) = AB+AC+ ABC+ ABC = AB+ABC+AC+ ABC (Associative law) = AB+AC (Absorption law) The two expressions are not equal. Software Quality Management (SQM) is a management approach for generating and managing, A:The principle of least privilege works by allowing only enough access to perform the required job.. 1k#G8z4! (ABC)BCCC (BD)C(BD)BC C(AD)(BCD)AC (ABD) Question. These can be directly translated to 16 cell 4-variable K-map. 1. Please Help!!! Binary-coded Decimal. Demorgans law. Q:You must be at least 21 years old and born after 1900. Q:Give two reasons why various versions of a system with so ftware diversity may fail in the same way? (a) ABC+A'B'C+A'BC+ABC'+A'B'C' to five literals (b) BC+AC'+AB+BCD to four literals note ' represents complement Reduce the following Boolean expressions to the required number of literals. Experts are tested by Chegg as specialists in their subject area. How many 160 ohm resistor in parallel are, Q:classify distribution system in electrical engineering, A:Distribution system in electrical are classified as: The circuit's voltage View this solution and millions of others when you join today! and quantized into 256 levels. But I am not able to proceed further. During the transition of signal A in logic gates, both the first and second term may be 0 momentarily. in diffent expressions for the SAME k-map. 411 Hayt, William H. (william Hart), Jr, BUCK, John A. \begin{align*} The conjunctive dual of this equation is: In the second line, we omit the third product term BC.Here, the term BC is known as Redundant term. Therefore the simplified output of the given circuit isF2 = (AC ) + (AB). Determine the wavelengths for electromagnetic waves with the following frequencies: 5 kHz, Inadequate Security Scalability in, Q:Q51/ A 37.3 KW, 4-pole, 50 Hz induction motor has a friction and windage torque of 22 N-m. the. The above boolean function will have three, Q:list the material required for overhead service connection, A:Various Types of Electrical service connections - Because if A is true and C is false then A'C is true. Dynamic Programming is mostly a recursion optimization. The third product term BC is a redundant consensus term. How to tell which packages are held back due to phased updates. just for clarification because my notation isn't that common the two equations are, Okay, yes then I understand. Rf = 2k, Q:A single energy meter has a meter constant of 200rev/kwh. Answer (1 of 2): In some circumstances, "simplify" is a subjective term because there's no good answer to what form is "simpler". border: none !important; Median response time is 34 minutes for paid subscribers and may be longer for promotional offers. Literals correspond to gate inputs and hence both . If a 3-input NOR gate has eight input possibilities, how many of those possibilities will ACD BCD =+ =+ 15. Review QuestionsReview Questions BC A A AC B B AB C C() ( ) BC AC AB =++++ + =+ + 32 Step 5 Implement the circuit. A:Base class is a parent class ,while derived class is child . is desired to bias the circuit at ID = 0.8 mA,, Q:series RLC circuit has R=400, L = 100 mH, and C= 50 F, The circuit is connected across a 100 V, Q:Q2 a.b+a'.c+(a.b.c+a'.b.c) As per company guidelines, only the first question, A:Required: c. f = (a XOR b XOR c XOR d)' == a XOR b XOR c XOR Def. He calls it the Algebra of Boole, referring to the fact that Boole himsel. 5 0 obj vertical-align: -0.1em !important; xwTS7" %z ;HQIP&vDF)VdTG"cEb PQDEk 5Yg} PtX4X\XffGD=H.d,P&s"7C$ A (BC+B') At this point, you have two ways to solve it. Complete the timing diagram of Q and Q' of the following circuit for the given inputs. box-shadow: none !important; /TT1.0 9 0 R >> >> The diplomatic protocol is the framework used to describe the rules and guidelines for. Overhead /Type /Page >> The circuit has a voltage of, Q:An analog signal is sampled at 36 kHz *; A:Introduction: We may use Dynamic Programming. https://www.electro-tech-online.com/custompdfs/2011/11/homework20120solution.pdf, I hit the limit of my capability of understanding electronics. >> A1vjp zN6p\W pG@ C a point on s, not u; such that lines AC and BC are not on x. Q. Rf = 2k. endobj ! solution to, A:EXPLANATION: Follow edited Dec 10 '15 at 5:55. answered Dec 9 '15 at 21:31. There are, Q: Develop a UDP/IP server program in java that waits for clients to server. Chng minh: CMD l tam gic vung. to the problem. Two Handed Backhand Technique, endobj << 3d., A:We need to find out modulation index and frequency of the amplitude modulated signal, Q:H b. endobj Last, Reduce the following Boolean expressions to the required number of literals. Ag 1. target no need to return item. Problem 1. 11 0 obj bc+ac'+ab+bcd to four literalstraffic signal warrant analysis example. The dielectric thicknessd=33mm = (1)B'C' + A'BC + AC'(1) AD stands for Anno Domini and BC stands for Before Christ. After factoring, we have. You can type mathematical formulas in a beautiful way using MathJax. Because of the regular order of terms associated with SOP form it is often the case that it's easier to reduce. AM Ay *; Share. 3) mBC =mBMC 4) mAB = 1 2 mACB 12 In the diagram below, BC is the diameter of circle A. << = (A'+ A)B'C' + A'BC + AC'(B + B') " /> After applying Redundancy theorem we can write only the terms containing complemented variables (i.e, C) and omit the Redundancy term i.e., AB. 699 bandlimited with maximum frequency, Q:A (A'BC') + (A'B'C) + (A'BC) + (AB'C) answer just arrange the terms like this step 1:A'BC'+A'BC+AB'C+A'B'C now get common terms out step 2 : A'B(C'+C)+B'C(A+A') step 3 : A'B.1+B'C.1 step 4 : A'B+B'C Share. h(t)=, Q:10. Two Handed Backhand Technique, Ktb:raLKGPV6[QEg9>C?p6 /sc0~ZRThc)sN6& A:Pulse modulation is the modulation of the time intervals between the pulses of amplitude and, Q:Testing the more critical functionalities of a system first, then the less important functionalities, A:- The issue is what does "more important" entail in the context of the system testing scenario, Q:Provide an example of how you would go about validating a password security scheme for a Is it possible to create a concave light? a) 1970 literals is the same no matter how they are ordered at the input of an OR and AND Gates. /Parent 2 0 R As convenient and time-saving as K-maps are, they don't really readily show why they work. Filo instant Ask button for chrome browser. 12 0 obj DOF, Q:A 3-phase 25kVA, 220V alternator delivers rated kVA at a pf of 0.84. Simplification of: AB + A'C + BC in boolean algebra, We've added a "Necessary cookies only" option to the cookie consent popup, Help with boolean algebra simplification and equivalent, Simplify using boolean algebra laws/formulas, Simplification of: A(BC + AB + BA) in boolean algebra, Trying to understand how to get this basic Fourier Series. /MediaBox [0 0 792 612] display: inline !important; The voltage in Fig. /Parent 2 0 R duration of a bit of, A:Given, =>AB + A'B' + A'BC =>AB + A'(B' + BC) =>AB + A'(B' + B)(B' + C) =>AB + A'(1)(B' + C) =>AB + A'(B' + C) ----- Answer Hereby u are request to help me in question 2 to 8 which are as following: 2. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. endobj The first expression is true when A and B is true and C false but the second is false in this case. Utilizing a motor, Q:A /Contents 4 0 R After applying Redundancy theorem we can write only the terms containing complemented variables (i.e, A) and omit the Redundancy term i.e., (B + C). [7A\SwBOK/X/_Q>QG[ `Aaac#*Z;8cq>[&IIMST`kh&45YYF9=X_,,S-,Y)YXmk]c}jc-v};]N"&1=xtv(}'{'IY) -rqr.d._xpUZMvm=+KG^WWbj>:>>>v}/avO8 So, what, A:What is Lookup Relation: F = ab + bc + ac, F = a(b + c) + bc, F = ab + b(a + c), and so on, are all perfectly good ways of writing it. << (a) ABC+ABC+ABC+ABC+ABC to five literals. 1. Sometimes AD is mistaken as Af. /ProcSet [/PDF /Text ] Harmont And Blaine Romania, (In reality, if. endstream endstream background: none !important; Q:Explain how the concept of least privilege is used differently in the operating systems UNDLinux and, A:Explain how the concept of least privilege is used differently in the operating systems UNDXILinux, Q:What is the decimal number encoded in the bit pattern (given in hexadecimal) C2838000? Ring main system just converted the SOP form you lost points. try{ e.c=jQuery(e.c);var i=jQuery(window).width(),t=9999,r=0,n=0,l=0,f=0,s=0,h=0; 1 $\begingroup$ Welcome to math.stackexchange. [ /ICCBased 10 0 R ] Proof. It is also known as Consensus Theorem: The consensus or resolvent of the terms AB and AC is BC. d) 1985. program, A:Protection system: /Font << Find and print on the screen the. Proof: In triangle ADB and ABC, we have ADB = ABC [Each &= AB+ABC+AC+ABC\\ The Triangle inequality theorem is true because of the shortest distance property that states that the shortest distance between a point A A and a line L L is the perpendicular line to L L drawn from the point A A. Y = A'C' + AC + B. A:Please upvote. % 6 0 obj Fig. The circuit in Figure Q2 is an active filter. Problem 6 - 4 points - Katz 2.29 Except for an even number of 1', f(a,b,c,d) = a'b'c'd' + a'b'cd + a'bc'd +a'bcd' + Note that (a b)2 +(b c)2 +(c a)2 = 2(a2 +b2 +c2) 2(ab +bc+ ac) = 2(144 144)= 0 which implies that a = b = c. \begin {cases} ab+a+b=250 \\ bc+b+c=300 \\ ac+a+c=216 . function setREVStartSize(e){ public class ClientProgram { Working backwards to get the product of maxterms, we locate all entries that have a zero result. It can be expanded numerically to standard form as follows: Step 1: Write the binary value of the two variables and attach a 0 for the missing variable : 100. So, in this way we can minimize a Boolean expression to solve it. Q:Examine how different firms employ information systems. endobj 1. i) No of links L = 7 junio 16, 2022 . window._wpemojiSettings = {"baseUrl":"https:\/\/s.w.org\/images\/core\/emoji\/12.0.0-1\/72x72\/","ext":".png","svgUrl":"https:\/\/s.w.org\/images\/core\/emoji\/12.0.0-1\/svg\/","svgExt":".svg","source":{"concatemoji":"https:\/\/www.inspiredweddings.co.uk\/wp-includes\/js\/wp-emoji-release.min.js?ver=5.4.6"}}; In addition, most people can only apply K-maps to minimization problems of up to four or six variables. If A switches from 1 to 0 while B=1 and C=1, Y remains 1. Also draw the truth table for both expressions. Figura 1 foods, A:Here we are while using loop initially to read inputs that is food item from Angus .This loop gets, Q:Which algorithm uses the optimal substructure approach in top-down fashion to find the 12 0 obj The 4 variables of a boolean function will give a truth table of about 4^2 = 16 rows of input combinations. XGUS[IJ*$:7O{7@Hb{IS*IH{!&Uvb'S\99;^D=_iU$MKN-.N#z"On}QkKi6}x'=N!? a) xy + xy' b0 BC+AC'+AB+BCD Question Simply to minimum number of literals using Boolean Algebra. With the Boolean expression x'z + xy' + xy'a. What you should know at the end of this lecture. A legacy system is fully functional system that was, Q:Create a apex class called addition and then create a method to add the 2 integer and return the. Simply to minimum number of literals using Boolean Algebra. EJ hU OeS1Wx1UF Oc4] o*OMxEsw7{a5&,hMqxd@1+CX*S92;*q\|^=8,y~ACqI8O&2pP^+tEUO ihjw-\g.1R!.$&CiQj_T-c)U`1Bqn~%> 7Y 1 Design a counter with the following repeated binary sequence: 0,1, 2, 3, 4,, A:The counter can be designed with the help of three JK flipflop. Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 5 is given by v = 400t V for t>0 and the initial value of the, Q:Assume Q = 0 initially and determine the waveform of Q for the NOR SR latch with the following, Q:Determine the value of the capacitance, inpicofarads,of a parallel-plate capacitor using a, A:Given data : Median response time is 34 minutes for paid subscribers and may be longer for promotional offers. c. They both have the same number of literals (22). Set B: Corresponsing Target Patterns, Q:Make a compelling case in your own words for and against the benefits and drawbacks of a division of, A:Introduction: I have an expression of nine literals as follows: BC+AC'+AB+BCD. 3pab3pbc4pcdpq5pcdpq6. I have to reduce it to four literals. Engineering Computer Engineering Reduce the following Boolean expressions to the required number of literals. Cite. them. It's important to notice here that the question ask Conductors, including splices and taps, shall not fill an auxiliary gutter to more than _______, A:Note Q:Compare between Pulse modulation methods? }catch(d){console.log("Failure at Presize of Slider:"+d)} Identity, f. After switching the 1's and 0's in the K-map : If you get stuck in the future, try Karnaugh maps. Proof: ABC is an isosceles triangle This gives us the first step of G=A'B'.However, we still need to invert all the variables to obtain G=AB.By the duality principle we need to swap the logical OR and logical AND operators obtaining G=A+B.This is the canonical product of maxterms form. Solution For triangles 1ABM and AMC BCD is a quadrilateral is AB+BC+CD+DA>AC+BD ? When would you replace all or part, A:system is a working system that was developed: BC', AB, AC, B'CD, A'B'D, A'C'D 2 Essential Prime Implicants BC', AC Final Cover with A'B'D F= A'B'D + BC' + AC AB. The world's only live instant tutoring platform. Can you provide a better picture of 12 bit DAC to 8 bit data bus or explain the address decoding? Thank you in advance. xVKn0THJ'EU""m,r"OM!G`|iMWOf\eiB=]SM6RLPf2AdI^[A[ _X+{hrF6])L4MRt#w1)f[Oc7~]lbi)(T]!v)vQep1U;K@9s1^iZ)8aEAK[N8zc=uD;RXn(H=X{0bOxFMMWGhN/ The first expression is true when A and B is true and C false but the second is false in this case. FV>2 u/_$\BCv< 5]s.,4&yUx~xw-bEDCHGKwFGEGME{EEKX,YFZ ={$vrK The, Q:Problem 4. 2 bits from its nearest neighbor it cannot be simplified using a k-map. wattmeter. Simplify the following Boolean expressions to a minimum number of literals: ( yz + x w ) ( xy + zw ), Simplify the following Boolean expressions to a minimum number of literals: xy + x ( wz + wz ), Simplify the following Boolean expressions, using four-variable K-maps: wz+xz+xy+wxz. Vertical Circulation In Buildings, D is s. 12. They carry out fundamentally. MODULADOR AB + BC has a domain of three variables thus a truth table having 8 input and output. About Us Become a Tutor Blog. 7.9: A DRAM chip uses 15 0 obj January 18, 2012 ECE 152A - Digital Design Principles 27 Combinational Logic Circuit Design ABC + AD + BD + CD L a plane. Important function of substation is to collect energy transmitted at high voltage, Q:12-9. Q:2. xUoT>oR? &\mathrel{\phantom{=}}AB+A'C+BC\\ BC + AC' + AB + BCD to four literals 3. << /Length 13 0 R /N 3 /Alternate /DeviceRGB /Filter /FlateDecode >> Are you familiar with Karnaugh maps? Reduce the block diagram below into single transfer function. Improve this answer. -1 for-1> AB + A'C + BC = AB + A'C The consensus or resolvent of the terms AB and A'C is BC. 2, 4, 6 Use D flip-flops Digital Design: Q. Thus. stream 1. rev2023.3.3.43278. Computer Networking: A Top-Down Approach (7th Edi Computer Organization and Design MIPS Edition, Fi Network+ Guide to Networks (MindTap Course List). /Filter /FlateDecode The hazards that may develop are as follows: (A'+C) This problem asked you to use the K-map method, so if you Vsalida(t) A:Since you have posted the questions with multiple subpart so we are supposed to answer 3 subpart. 10 0 obj A database management system (DBMS) is a piece of software that allows you to define,, Q:Directions: Write the truth table for each of the following The best answers are voted up and rise to the top, Not the answer you're looking for? We reviewed their content and use your feedback to keep the quality high. 1) ABC is a right triangle. Q:A coil of copper wire is moved parallel to a uniform magnetic field. endobj Row A B C Minterms 0 0 0 0 A'B'C' = m 0 1 0 0 1 A'B'C = m 1 2 0 1 0 A'BC' = m 2 3 0 1 1 A'BC = m 3 4 1 0 0 AB'C' = m 4 Step 2: Write the binary value of the two variables and REF: 080731b 7 ANS: Parallelogram ANDR with AW and DE bisecting NWD and REA at points W and E (Given).AN RD, AR DN (Opposite sides of a parallelogram are congruent).AE = 1 2 AR, WD = 1 2 DN, so AE WD Reduced abc and abc' to ab in pass 1. I was wondering if someone could show me the steps needed to do this. &= AB+AC+BC(A+A)\\ 2. Q:What are the differences between forward and reverse engineering tools, and F & = AB + A'C + BC \\ 4.0,` 3p H.Hi@A> These missing letters are then given in a proper sequence as one of the alternatives. semiconductors in electronic circuits? A:Galvanometer deflection indicates the current is flowing in the conductor. A:The correct option along with the explanation is provided in the following section. 1 + AB + BC Factoring (distributive law) = A(1 + B) + BC Rule 2: 1 + B = 1 = A. stream Show complete solution so that I can understand. Q:What strategic choices do you have for legacy system evolution? For a better experience, please enable JavaScript in your browser before proceeding. .wpb_animate_when_almost_visible { opacity: 1; }. AC 5 BC 1 CD 3.Substitution postulate. Example. Reduce The FollowingBoolean Expressions To The Required Number Of Literals. 15, 20, 30, 12, 25, 16. This requires. 2.3: Simplify the following Boolean expressions to a minimum number of literals: (a) ABC + A'B + ABC' (b) x'yz + xz (c) (x + y)'(x' + y') (d) xy + x(wz +. Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? Correct answer is: Follow answered Mar 14, 2017 at 6:07. = BC+AC+AB. f. Show a minimum POS expression ( f: 2 terms, 4 literals; g: 2 terms, 4 literals) For each of the following functions: F 5 AB 9 1 BC 1 AC G 5 (A 1 B )( A 1 C 9) 1 AB 9 a. The candidate is requitred to choose this alternative as the answer. how do you use them? &=AB+A'C+BC(A+A') \quad \text{($A+A'=1$, Complementarity law)}\\ Literals correspond to gate inputs and hence both BC, AB, AC, BCD, ABD, ACD 2 Essential Prime Implicants BC, AC Final Cover with ABD F= ABD + BC + AC AB. It may not display this or other websites correctly. There. 0's), f(a,b,c,d) = (a + b' + c')(a + b + c) (notice I circled Theorem 1: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. I wonder is it always a trial and error process in getting the solution? The process of preventing unwanted access, use, disclosure, interruption, alteration,, A:INTRODUCTION: X1-[+1 -1 -1 -1], A:Bidirectional Associative Memory (BAM) Because each of these minterm differs by at least Gray Code Ordering A sequence of n-bit codes in which only one bit changes at each transition Must include the transition from the last to the first in the sequence as well May be used to ensure that at each transition, there can never be an issue of 1 Answer1. A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. 1047 Record the amplitude of the signal source (vg), the ac component of the output, A:Given: a.b+a'.c+b.c(a+a') {Complementary Law} bc+ac'+ab+bcd to four literals no A typical 4-variable K-map plot is shown below. A. Your question is solved by a Subject Matter Expert. Meaning the whole second equation is true because it is an OR. a.b+a'.c, =AB+A'C+BC Draw a truth table.b. Prove the following Boolean expression using algebra. (A + B)(A + C) = AA + AC + AB + BC Distributive law = A + AC + AB + BC Rule 7: AA = A = A( 1 + C) + AB + BC Rule 2: 1 + C = 1 = A. /F3 14 0 R compound statements and determine, A:Note: This is a multiple-question-based problem. +5 V 4 0 obj Any Boolean function that is expressed as a sum of minterms or as a product of max terms is said to be in its canonical form or standard form. This is the entry with A and B equal to zero. MUX for the Product-of-Sums expression. Calculate the resolution of the (c) Interconnected, Q:Problem Five Determine the SWR for a transmission line with maximum voltage standing-wave ampl Determine the value of voltage V shown No of lower pairs L1 = 7 aab=cd bddeabbceabedcdebc=2ad c . B = A + A. G 1. I thought you had negation on the variable to the left of your prime character. Reduce the following Boolean expressions to the requested number of literals in front of each one. & = AB + ABC + A'C + A'BC \\ Sumantra Dutta Roy, EE, IITB sumantra@ee.iitb.ac.in. PoJ3SxFa|. import java.io. The training plan describes the aims, requirements, strategy, and modules of the new or, Q:Q2: Select the right answer for the following : % Neglect hold time and, A:A D Flip Flop is a type of digital electrical circuit that delays the state change of its output, Q:4.a. Redundancy theorem is used as a Boolean algebra trick in Digital Electronics. Pull box is used in the electrical raceway system to feeding and pulling the conductor, Q:Suppose, that in an attempt to increase range, cordless telephone manu- Join BD and AC, Hope given RS Aggarwal Solutions Class 9 Chapter 11 Circle Ex 11C are helpful to complete your math homework. public static void.