Name (1%):Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer ScienceDepartment of Mechanical Engineering6.050J/2.110J Information and Entropy Spring 2003Issued: May 23, 2003, 1:30 PM Final Exam Due: May 23, 2003, 4:30 PMNote: Please write your name at the top of each page in the space provided. The last page may be removedand used as a reference table for the calculation of logarithms.Problem 1: Knowin’ the Nomenclature (9%)From the list of terms below, select the one which best fits each of the following statements. Make sure youranswers to each part are different.a. can have units of Joules/Kelvin.b. is a fixed length code.c. The part of the heat-engine cycle without change in entropy is .d. is a reversible image compression technique.e. The is calculated by taking the number of ones in the XOR of twobinary strings.f. The energy values of an electron wavefunction in a square well are , not.g. A thermodynamic quantity that is the same for two systems in contact is .h. The maximum efficiency of a heat engine is named after .i. was the most interesting aspect of this course.adiabatic continuous extensive Jaynes poweranalog CRC Finlayson JPEG reversibleASCII DCT GIF Karnaugh TCPAvogadro digital Hamming distance Maxwell universalbit discontinuous heat macroscopic workBoltzmann’s constant discrete Huffman code microscopeCarnot energy intensive Morse codechannel capacity entropy irreversible MP-3compression Euler isothermal parityTable F–1: List of Terms1Final Exam; Name: 2Problem 2: Behaving Badly (10%)The new NANNY gate has been designed to tell whether a child has been misbehaving. In its intendedapplication, input A of the gate is set to 1 if and only if the nanny has reminded the child of an importantthing to do, like “sit up straight.” Input B is set to 1 if and only if the child has actually done that thing,whether or not reminded. The gate calculates whether scolding is called for, i.e., it returns 1 if the nannyhas made such a request and the child has not complied.a. Give the truth table and transition diagram for this gate.AB00011011Out------AB00011011Out01Figure F–1: NANNY Gate Truth Table and Transition Diagramb. Marketing research revealed that the nanny always reminds the child, and the child does theright thing 50% of the time. In this case, what are the probabilities of the four input events andtwo output events?.AB=00: AB=01: AB=10: AB=11:Out=0: Out=1:c. Nobody bought the product that used this gate, so the manufacturer is s tuck with excess inven-tory. He wants to find other uses for the gate, and has asked you a number of questions aboutthe gate.Is it reversible? Is it universal? Is it deterministic?d. How many NANNY gates would you need to make a NOT gate? How wouldyou do it?Final Exam; Name: 3Problem 3: Parity, Code-rates, and Framing Errors (10%)A particular application requires error detection. You have a long string of bits to transmit, and you decideto implement a parity scheme, where you insert an extra parity bit after each eight bits of data. If thenumber of bits is not a multiple of 8, the left over bits at the end get their own parity bit.a. What is the code rate of your scheme?code rate:b. Sometimes, for some unfortunate reason, some of the bits are completely lost. This causes a lossof the bit, with no indication of its existence at all. For example, if the fourth bit in the string‘00100’ was erased completely, this would produce the string ‘0010’, i.e., one bit shorter. Withyour error checking scheme is it always possible to detect this sort of error? Explain.Final Exam; Name: 4Problem 4: Architecture – Building Of Major Buildings (15%)MIT has a history of erecting unusual buildings. Some of its buildings are innovative in a successful way,some are what the architect Frank Gehry calls “square boxes,” and the rest are just plain ugly. Call theprobability that any building selected at random is in one of these three categories I, B, and U .a. MIT used to have a committee devoted to campus renovations and new campus buildings, calledthe Central Committee for Campus Planning. If you are told that a building was selected bythe CCCP for replacement, but do not know which one, and have no knowledge of how manybuildings on campus are in each of the three categories, what is your uncertainty Icatin bits ofwhich category the building is in, and what the three probabilities I, B, and U?I = B = U = Icat=b. The Union of Social Architects (the USA) rates buildings according to aesthetic criteria. It assignsa numerical score of 0 to an ugly building, 1 to a square box, and 5 to an innovative building. In1950 it reported that the “aesthetic index,” the average aesthetic measure of MIT buildings, was1.2. With this additional knowledge, you are able to estimate what the probabilities I, B, andU were in 1950 more accurately. First, you observe that I, B, and U cannot all range between 0and 1, but instead are bounded by minimum and maximum values.IminImaxBminBmaxUminUmaxc. The USA and the CCCP had an ideological disagreement, since the CCCP did not agree withwhat the USA considered good or bad architecture: the CCCP always marked a “square box”building for replacement, and always re placed it with an ugly building. In response to pressurefrom the Cambridge City Council, students, and passers-by alike, (all of whom agreed with theUSA) the CCCP and the USA entered into an agreement, called Mutual Architecture Deter-mination, such that every time the CCCP chose one building to be replaced, the USA got tochoose the next building that would b e replaced. Since the USA always decided to replace anugly building with an successfully innovative building, MIT’s aesthetic index rose from 1.2 in1950 to 1.6 in 1990. Was the maximum uncertainty about the category of a building selected atrandom in 1990 larger or smaller than in 1950?Larger/smaller than in 1950?:Reasoning:d. This period, which came to be known as the Campus Overall Layout Determination With Archi-tecture Replacement, lasted until the CCCP was disbanded in 1990. It was then replaced withseveral committees, each re sponsible for different areas of campus. Since then, the USA has notselected any buildings, and the new committees select buildings at random and replace themwith square boxes. On average, over a long time, will the aesthetic index go up or down?Aesthetic index up/down?:Final Exam; Name: 5Problem 5: Green Eggs and Hamming (15%)The new