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CS150 Fall 2009
Final
NAME:________________________ SID_____________________
Instructions
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.
GOOD LUCK!
PROBLEM POINTS MAX
“ 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).
a) In the (n,k) notation for an error correction code, k is the unencoded data width in bits and n
is the encoded width. Which is larger, n or k? Why must it be this way? (5 points)
b) Define the minimum Hamming distance, d min , of an error correction code: (5 points)
c) For a code with d min minimum distance, what is the formula for the maximum number of
errors, Edetect , that can be detected? (5 points)
d) For a code with d min minimum distance, what is the formula for the maximum number of
errors, Ecorrect , that can be corrected? (5 points)
“ 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:
- The battery has 1000 J worth of energy in it and can put out 2.5 V as the power supply voltage (V (^) DD ).
- I will make my digital microcontroller in CMOS.
- Every 10 minutes the mote computes something for 45 seconds.
- When not computing, all gates in the microcontroller remain connected to V (^) DD and GND.
- The IC module consists entirely of inverters (which is an awful assumption, btw)
- Each inverter sees a capacitance of 10fF at its output; this capacitance includes all contributions from wires, other inverters connected, etc.
- During the 45 seconds of activity, every inverter switches its output on each clock cycle with probability equal to 0.2.
- The clock speed is 200 MHz.
- The inverters have symmetrical rise and fall times (ie. they switch between GND and VDD as fast as they switch between V (^) DD and GND).
- An inverter must force its output greater than 2.2 V for the next gate to “see” a logical 1
- An inverter must force its output less than 0.2 V for the next gate to “see” a logical 0
- On any cycle that an inverter is not switching, it “leaks” 1 nA from VDD to GND.
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).
- Besides the standard system clock, assume there exists a clock, COMPCLOCK, which has a 50% duty cycle and a 1 minute period.
- The microcontroller, the radio and the audio sensor can be disconnected from the power supply independently via transistors. o The COMPON signal controls the state of the microcontroller power connection (connected or disconnected). o The SENSORON signal controls the state of the audio sensor power connection (connected or disconnected). o The RADIOON signal controls the state of the radio power connection (connected or disconnected).
- A separate temperature sensor cannot ever be turned off and reports on the ambient temperature to the power controller using two bits (TEMP): o 00 (unused) o 01 (normal office temperature) o 10 (night time office temperature) o 11 (body temperature)
- A normal computation is started when COMPCLOCK switches to high. This connects the mote block to the power rails (COMPON output) and powers up the sensor (SENSORON output).
- Once computation is finished, the microcontroller will set DONE to high.
- If TEMP = 01 when COMPCLOCK goes high, the radio must be turned on when the microcontroller issues the DONE signal and the microcontroller must be left on until the radio issues a TRANSDONE signal. Then everything must be turned off.
- If TEMP = 10 the radio should be left off and everything shut off once DONE is high.
- If TEMP = 11, follow the same procedure as TEMP = 01, except the EXPLODE_IN_BONDS_PANTS bit must be set to high once TRANSDONE is high.
- The BOND_BUTTON bit high disconnects power to all three blocks at any time.
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)
