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314 EECS Fall 2007 HW 10 Problem 1 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ The big picture As you know from lecture notes, music on CD is recorded with 16- or 20-bit resolution, at the sampling rate of ~ 44 kHz. As you know from reading the labels, a blank CD has the capacity of 700 MB (megabytes; 1 Byte = 8 bits; 1 MB ~ 106 Bytes) and is rated for 80 minutes of music recording. In this Problem, you will put 2 and 2 together in order to see whether all of the above numbers make sense. Problem Part 1 (10 points) Assume that the music is recorded in two channels (stereo = left and right) that have the same resolution of 16 bits and the same sampling rate of 44 kHz. Calculate the amount of memory in MB required to record 1 minute of music. Your answer: _______________________ MB per minute of music Assume that a blank CD has the capacity of 700 MB. Calculate how many minutes of music can be stored on the CD. Your View Full Document

= _______________________ minutes on CD If your answer above is less than 80 minutes, it means that a data compression algorithm is used to record the data on music CDs. The compression can be easily quantified: for example, if you estimate the needed memory as 1 MB and the actual record requires only 0.8 MB, then the compression ratio equals 1/.8 = 1.25, which is very modest compared to that used in MP3 technology. Discuss your answer: if you found T > 80 minutes, no compression is needed. If, however, you found T < 80 minutes, compression is needed, and you are asked to calculate the compression ratio. Your answer on compression: _______________________________________________ Part 2 (5 points) Repeat Part 1 for 20-bit music recording. Your answer: _______________________ MB per minute of music Your = _______________________ minutes on CD Your answer on compression: _______________________________________________ 2007 Alexander Ganago Page 1 of 2 EECS 314 Fall 2007 HW 10 Problem 1 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ Part 3 (10 points) An important characteristics of sampling is the bit rate, usually expressed in kilobits/second, or kbit/sec, which is calculated for stereo recording as the product bits/sample number of samples/second 2 channels / 1000 bits/kilobit Calculate the bit rate for CD recording with 16-bit resolution. Your answer: _______________________ kbit/sec for 16-bit CD recording Compare your result with the popular MP3 standard 128 kbit/sec: calculate the ratio of bit rates in CD and MP3 recordings. Your answer: the ratio of bit rates (CD/MP3) equals _______________________ Assume a blank disk capacity of 700 MB, calculate the duration of music recordings in MP3 format that can fit on that disk. Express your result in seconds, as well as in hours and minutes (rounded to a single minute). Your 700 MB disk can hold the MP3 recordings of music that plays for _______________________ seconds, or _______________ hours and _______ minutes. Show your work for all parts on a separate page. 2007 Alexander Ganago Page 2 of 2 EECS 314 Fall 2007 HW 10 Problem 2 Student's name ___________________________ (Last name, first name, IN INK) For The big picture, refer to the lecture notes file named 2007 Analog and Digital. Assume that the analog signal sketched here is fed into the AD converter shown on the diagram below, with VREF = 8 V. Discussion section # __________ The problem contains 5 parts, 5 points each. 1. On the sketch above, draw horizontal lines that correspond to sampleand-hold circuit output, assuming that the sampling is done at the beginning of each time interval T1, T2, etc. 2. Analyze how the AD circuit works: show detailed calculations of the binary outputs D0, D1, D2 for the unlabeled time interval prior to T1 Continued on the next page 2007 Alexander Ganago Page 1 of 2 EECS 314 Fall 2007 HW 10 Problem 2 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ 3. Based on your circuit analysis in #2 above, calculate the binary outputs D0, D1, D2 obtained during time intervals T1 through T8 and draw the digital waveforms on the grid provided here: 4. Assume that the binary outputs D0, D1, D2 obtained during time intervals T1 through T8 are fed into a DA converter in order to restore the input signal. On the sketch of the input analog signal, which is repeated here for your convenience, draw DA converters outputs during time intervals T1 through T8 (use your results of #3 above). Assume that the DA converter circuit restores the positive sign of the input signal. 5. Briefly comment on the accuracy of the analog input signal restoration: do you consider it adequate? Explain how the accuracy can be improved: a. By sampling more often, for example, by dividing the time window into 16 or 32 time intervals b. By using more bits for AD conversion c. By both a and b above. 2007 Alexander Ganago Page 2 of 2 EECS 314 Fall 2007 HW 10 Problem 3 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ Assume that the binary waveforms D0, Part 1 (10 points) Show sample calculation of the output voltage VOUT(T) for the time interval D1, D2, D3 obtained during time intervals T1 through T8 are fed into the DA converter circuit with R = 40 k and RF = 5 k. T4 Part 2 (15 points) On the grid below, sketch the output voltage VOUT(T) for the time intervals T1 through T8 Carefully label the vertical axis in volts. 2007 Alexander Ganago EECS 314 Fall 2007 HW 10 Problem 4 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ Analog-to-digital conversion The big picture Analog signals (for example, voltages from sensors) are converted into binary numbers for transmission and processing in digital circuits. Problems from EECS 314 exams On the exams, only answers are required, but in the HW paper, show your work! Part 1 (Contributed by James Kim) (5 points) Voltage that varies between -12 V and 12 V is converted into binary numbers using an 8-bit A/D converter. Whats the LSB (least significant bit) of this converter? A. 93.75 mV B. 46.875 mV C. 187.5 mV D. 375 mV E. None of the above Part 2 (5 points) At the output of a 5-bit analog-to-digital converter, the least significant bit (LSB) corresponds to 1 mV. Therefore, the most significant bit (MSB) corresponds to A. 5 mV B. C. D. E. 24 mV = 16 mV 25 mV = 32 mV 104 mV = 10 V 105 mV = 100 V Part 3 (5 points) Voltage that varies between -5 V and +5 V is converted into binary numbers using an 8bit A/D converter. The maximal error of this digital representation is about A. B. C. D. E. 40 mV 20 mV 10 mV 5 mV Can be any of the above, on depending the magnitude of voltage at the particular moment of time. Comment: assume that the error equals LSB (the worst-case scenario) 2007 Alexander Ganago Page 1 of 2 EECS 314 Fall 2007 HW 10 Problem 4 Student's name ___________________________ (Last name, first name, IN INK) Part 4 (5 points) You have to measure the amount of liquid in a cylindrical tank that has 10,000 gal capacity, by monitoring the height H with a sensor. Given that the maximal error should not exceed 10 gal, you will choose an A/D converter with at least A. 10 bits B. 20 bits C. 16 bits D. 12 bits E. 8 bits Choose the minimal number of bits that satisfies the requirement. Discussion section # __________ Binary-to-decimal and decimal-to-binary conversion The big picture Numbers can be easily converted from decimal (base 10) to binary (base 2) and from binary to decimal. The rules are especially simple for natural numbers. Problems from EECS 314 exams On the exams, only answers are required, but in the HW paper, show your work! Part 4 (2.5 points) Convert the decimal number to binary: 9710 = Show your work. Your answer: __________________ Part 5 (2.5 points) Convert the binary number to decimal 10111002 = Show your work. Your answer: __________________ 2007 Alexander Ganago Page 2 of 2 EECS 314 Winter 2007 HW 10 Problem 5 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ The truth tables and logic gates The big picture Logic gates are the circuits that perform logic operations on signals (input voltages). The output signal (output voltage) of a logic gate is determined by the inputs and the type of the gate. Problem The two input signals of unknown logic gates are shown on the sketch. The output signals of three logic gates A, B, and C are sketched below. From the voltages determine the truth table of each gate; from the truth table determine the type of the logic gate: choose from 1. AND 2. OR 3. NAND 4. NOR 5. None of the above. Logic gate A is _______________ Logic gate B is _______________ Logic gate C is _______________ Write your answers above. Show your work on additional pages. 2007 Alexander Ganago EECS 314 Fall 2007 HW 10 Problem 6 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ Logic gates: Diode circuits The Big Picture When we analyze the logic function of a circuit, we have to solve 2 distinct questions: 1. What output voltage does the circuit produce for each of the possible combinations of input voltages? 2. What logic function corresponds to this combination of input and output voltages? To solve question 1, we have to perform the circuit analysis. Note that in the circuits below the sources are not shown explicitly. For example, the first circuit can be redrawn with the sources shown as follows: In the circuit analysis, we assume that the input voltages A and B and the output voltage C can be either LOW ~ 0 V or HIGH ~ 5 V. To determine whether each of the diodes conducts, use the ideal diode model. To answer question 2, we have to compare the obtained combination of HIGH and LOW voltages with the known truth tables. Note that two possibilities exist: in the so-called positive logic, which we use in this problem HIGH voltage ~ 5 V means 1 and LOW voltage ~ 0 V means 0, while in the so-called negative logic, the meanings of voltages are opposite: HIGH voltage ~ 5 V means 0 and LOW voltage ~ 0 V means 1. Thus the same combination of input and output voltages, derived from the circuit analysis, produces different truth tables depending on the type of the logic. The problem is continued on the next page. 2007 Alexander Ganago Page 1 of 2 EECS 314 Fall 2007 HW 10 Problem 6 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ Problem For each of the circuits, determine the combination of voltages (neglect the voltage drop across a forward-biased diode; if needed, assume R = 1k): Circuit 1 Circuit 2 A HIGH LOW HIGH LOW B HIGH HIGH LOW LOW C A HIGH LOW HIGH LOW B HIGH HIGH LOW LOW C Then, determine the type of logic gate, depending on the chosen type of logic: Type of gate Positive logic Write your answers in the tables above. Show your work below and/or on additional pages. Type of gate Positive logic 2007 Alexander Ganago Page 2 of 2 EECS 314 Fall 2007 HW 10 Problem 7 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ Logic gates: MOSFET circuits The Big Picture When we analyze the logic function of a circuit, we have to solve 2 distinct questions: 1. What output voltage does the circuit produce for each of the possible combinations of input voltages? 2. What logic function corresponds to this combination of input and output voltages? To solve question 1, we have to perform the circuit analysis. Note that in the circuits below the sources are not shown explicitly. For example, the first circuit can be redrawn with the sources shown as follows: In the circuit analysis, we assume that the input voltages A and B and the output voltage C can be either LOW ~ 0 V or HIGH ~ 5 V. Assume that a MOSFETs conducts (acts as a short circuit between the source S and the drain D) if the gate (G) voltage VGS exceeds 2 V; otherwise there is no current flowing between the source and the drain; always neglect the current through the gate terminal. To answer question 2, we have to compare the obtained combination of HIGH and LOW voltages with the known truth tables. Note that two possibilities exist: in the so-called positive logic, which we use in this problem HIGH voltage ~ 5 V means 1 and LOW voltage ~ 0 V means 0, while in the so-called negative logic, the meanings of voltages are opposite: HIGH voltage ~ 5 V means 0 and LOW voltage ~ 0 V means 1. Thus the same combination of input and output voltages, derived from the circuit analysis, produces different truth tables depending on the type of the logic. The problem is continued on the next page. 2007 Alexander Ganago Page 1 of 2 EECS 314 Fall 2007 HW 10 Problem 7 Student's name ___________________________ (Last name, first name, IN INK) Discussion section # __________ Problem (30 points) For each of the circuits, determine the combination of voltages. Neglect the voltage drop between the source and the drain of the MOSFET that conducts (when VGS > 2 V); if needed, assume R = 1k): Circuit 1 Circuit 2 A HIGH LOW HIGH LOW B HIGH HIGH LOW LOW C A HIGH LOW HIGH LOW B HIGH HIGH LOW LOW C Then, determine the type of logic gate, depending on the chosen type of logic: Type of gate Positive logic Write your answers in the tables above. Show your work on additional pages. Type of gate Positive logic 2007 Alexander Ganago Page 2 of 2 ...