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Main points of this past exam are: Coding Process, Numerical Answers, Partial Credit, Minimum Distance, Hamming Distance, Coding Process, Linear Code, Memory Systems, Even Parity, Parity Code
Typology: Exams
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Read all of the instructions and all of the questions before beginning the exam.
There are 6 problems in this exam. The total score is 250 points. Points are given next to each problem to help you allocate time. Do not spend all your time on one problem.
Unless otherwise noted on a particular problem, you must show your work in the space provided, on the back of the exam pages or in the extra pages provided at the back of the exam. Simply providing numerical answers will only result in partial credit , even if the answers are correct.
Draw a BOX or a CIRCLE around your answers to each problem.
Be sure to provide units where necessary.
“ Think of your happy place........” -Happy Gilmore Problem 1 Grab bag I 45 points
The error correction coding process can be viewed as a transformation from one space of bits (the unencoded data) to another (the coded data).
“ Sometimes I wish I had done more with my life than hanging out in front of places sellin' weed ... Like maybe be an animal doctor, I like seals... -Clerks 2
Problem 2 Grab bag II 25 points
a) Given a word-addressable memory arranged as a stack of 256 words, what is the minimum datapath hardware required to calculate the average value of all of the words in the stack? Draw your datapath circuit below. Make sure to label any control bits an external controller would need. (10 points)
b) Provide RTL code that accomplishes the averaging function with the hardware you drew above. (7.5 points)
c) Draw in the output waveform for the asynchronous SR latch. (7.5 points)
“Fight now, cry later.” -From Dusk Till Dawn Problem 3 Controller for a custom datapath 70 points A complex point c=x+jy is in the Mandelbrot set if the magnitude of the following sequence is bounded, as n goes to infinity: z 0 = c z (^) n+1 = z (^) n^2 +c
We can estimate whether a point belongs to the Mandelbrot set by evaluating the sequence for a bounded number of iterations, and checking whether the magnitude of each element of the sequence remains below 4.0. Your task: design hardware to carry out one iteration of this computation.
Above is the data-flow graph for the computation of one iteration of the Mandelbrot set calculation.
Inputs: znx, the real part of zn ; zny, the imaginary part of zn ; cx, the real part of c; cy, the imaginary part of c; n, the current iteration count
Outputs: znp1x, the real part of zn+1; znp1y, the imaginary part of z (^) n+1 ; bounded, which is a single bit which is true when zn+1 is still smaller than the threshold of 4.0; and np1, the resulting iteration count.
Component Latency
Multiply (*) 4 cycles
Add/Subtract (+/‐) 3 cycles
Double (*2) 1 cycle
Compare (<) 1 cycle
Complete your design by showing: d) An FSM that outputs control signals to any multiplexers you need at the inputs of your FP operators (20 points)
e) A schematic of the new design, complete with all necessary pipeline registers and multiplexers. You don’t need to implement or draw circuits for the FSM, just denote outputs of the FSM as labeled wires in your schematic. (20 points)
c) Using only inverters and passgates, or modules constructed of inverters and passgates, construct a full adder circuit. Hint: consider Carry as a function of (A xor B) and Cin. How many transistors did you use? (15 points)
d) Using your full adder circuit and your xor gate, construct a 4-bit wide ripple carry, twos- complement ALU that can compute either A+B or A-B for 4-bit inputs A, B. Use a 1 bit Subtract signal to choose the operation (0 = Add, 1 = Subtract). Produce a 4 bit Sum and a 1 bit Carry Out. (15 points)
“ Kansas City Shuffle is when everybody looks right and you go left.” -Lucky Number Slevin Problem 5 CMOS 40 points
Suppose I am interested in looking at the power consumption in a tiny wireless sensor mote. I am designing a tiny device (say <1 cm^3 ) which we’ll call a mote that has: a) a simple digital microcontroller, b) a radio, c) a MEMS sensor, d) a battery.
Since I am an evil scientist, I am going to make hundreds of these motes and throw them into people’s rooms to measure and report back on stuff (call me Prof. Big Brother). I need to know how long these motes will last before they run out of battery.
Given:
a) What must the equivalent resistance of a single MOSFET be in order for the microcontroller to operate at 200 MHz? (8 points)
“As the sun sets slowly in the West, we bid you a fine farewell. “ -True Romance Problem 6 FSMs and controllers 30 points
We want to design a smarter controller for our Evil Spy Mote© in Problem 4. This will sit outside the mote’s microcontroller and be responsible for cycling power (and killing James Bond).
a) Draw a Moore machine implementation of the controller. Please label all transitions and states neatly (15 points)
b) Draw a Mealy machine implementation of the controller. Please label all transitions and states neatly (15 points)