EE118 FALL 2012 SAN JOSE STATE UNIVERSITY Department of Electrical Engineering TEST 2 — Digital Design I October 24, 2012 10:30 a.m. – 11:45 a.m. — Closed Book & Closed Notes — — No Crib Sheet Allowed — STUDENT NAME: (Last) Claussen , (First) Matthew STUDENT ID NUMBER (LAST 4 DIGITS): No interpretation of test problems will be given during the test. If you are not sure of what is intended, make appropriate assumptions and continue. Do not unstaple !!! Problems 1-14(4 points each) TOTAL Problems 15 – 17 (15 pts each) 1203 2 For the next 14 problems, circle the correct answer. No partial credit will be given. PROBLEM 1 (4 points) Which statement is not true? A. Any combinational circuit may be designed using multiplexers only. B. Any combinational circuit may be designed using decoders only. C. All Sequential circuits are based on cross-coupled NAND or NOR gates. D. A hazard in a digital system is an undesirable effect caused by either a deficiency in the system or external influences. E. None of the above PROBLEM 2 (4 points) For a 2-bit comparator comparing 2-bit numbers A = (a1 a0) and B = (b1 b0), what is the proper function for the f(A>B) output through logical reasoning? A. a1 b1’ + (a1 b1 + a1’b1’ ) a0 b0’ B. a1 b1’ + (a1 b1’+ a1’b1 ) a0 b0 C. a1 a0’ + (a1 a0 + b1’b0’ ) b1 b0’ D. a1 a0 + (a1 a0’+ b1’b0 ) b1 b0 PROBLEM 3 (4 points) What is the priority scheme of this encoder? Inputs Outputs I3 I2 I1 I0 O1 O 0 d d 1 d 0 1 d d 0 1 0 0 d 1 0 0 1 0 1 0 0 0 1 1 A. I3 > I2 > I1 >I0 B. I0 > I1 > I2 >I3 C. I1 > I0 > I2 >I3 D. I2 > I1 > I3 >I0 3 PROBLEM 4 (4 points) Which is the correct binary representation of the decimal number 46.625? A. 101101.001 B. 101000.01 C. 111001.001 D. 101110.101 PROBLEM 5 (4 points) Which is the decimal equivalent number of the sum of the two 8-bit 2’s complement numbers FB16 and 3748? A. 3 B. 5 C. 7 D. 9 PROBLEM 6 (4 points) For the MUX-based circuit shown below, f(X,Y,Z) = ? X Y Z f A. X’Y’ + Y’Z’ B. X’Y’Z’ + YZ’ C. XYZ’ + Y’Z D. X’Y’Z’ + YZ 1 0 MUX 4 PROBLEM 7 (4 points) Which is the correct output F of this circuit? E C B D F A A. (A’E+AB)(C’D) B. (AE+A’B)(C’+D) C. (A’E+AB)(C’D’+CD’+CD) D. (A’E+AB)(CD’)’ PROBLEM 8 (5 points) In order to correctly perform 2910  14510, how many bits are required to represent the numbers? A 8 B 9 C 10 D 11 PROBLEM 9 (4 points) Which is the negative 2’s complement equivalent of the 8-bit number 01001101? A. 11001101 B. 10111100 C. 10110000 D. 10110011 0 2-1 1 MUX 0 0 1 1 2-4 decoder 2 EN 3 5 PROBLEM 10 (4 points) Which is the correct statement describing the behavior of the following Verilog code? module whatisthis(hmm, X, Y); output [3:0] hmm; input [3:0] X, Y; assign hmm = (X < Y) ? X : Y; endmodule A. If X>Y, hmm becomes 1111. B. hmm assumes min(X,Y). C. If X<Y, hmm becomes 1111. D. hmm assumes max(X,Y). PROBLEM 11 (4 points) Which Boolean expression corresponds to the function g(W,X,Y,Z) implemented by the following “non-priority” encoder-based circuit? Assume that one and only one input is high at any time. f W X g Y Z A. Y + Z B. W + Y C. X + Y D. X + Z PROBLEM 12 (4 points) Which Boolean expression corresponds to the output of the following logic diagram? (/B = B’) A. Z = ( A(B’ + C)’ )’ + ( (B’ + C)’ + D )’ B. Z= A(B C’) + (B C’ + D) C. Z = (A(B’ + C)(B’ + C + D) )’ D. Z = A(B’ + C)’ + (B’ + C + D)’ 0 0 1 1 2 3 Encoder 6 PROBLEM 13 (4 points) Which is the correct gate-level circuit in minimal SOP form for the following circuit? A F = Y’X’ + W’ZY’X B F = YX’ + W’Z’Y’X C F = YX’ + W’ZY’X D F = Y’X + W’ZY’X’ PROBLEM 14 (4 points) For the following flow map of a certain cross-coupled gate circuit, the circuit is currently in the underlined state. If the inputs YZ change to 11, the circuit becomes meta-stable. Between which two states (WX) does the circuit oscillate ? A 00  11 B 01  10 C 11  10 D 10  00 YZ WX 00 01 11 10 00 00 11 00 10 01 10 10 10 01 11 00 00 11 01 10 10 01 01 10 G1 Y0 G2A Y1 G2B Y2 Y3 A Y4 B Y5 C Y6 Y7 G1 Y0 G2A Y1 G2B Y2 Y3 A Y4 B Y5 C Y6 Y7 OR W X Y Z X Y Z F + 5 V 7 For each of the next 3 problems, show all your work. Partial credits will be given. PROBLEM 15 (15 points) 1) Which logic variable causes the hazard for the circuit given by the K-map below? 2) Using the timing diagram, clearly show how the hazard occurs. 3) Find the best hazard-free logic function. YZ WX 00 01 11 10 00 0 0 1 1 01 0 0 0 0 11 1 0 0 0 10 1 0 1 1 8 PROBLEM 16(15 points) Analyze the following cross-coupled NAND gates by showing: (a) flow map with stable states circled and with meta-stability condition shown by arrows, (b) state table, and (c) completed timing diagram below. Note that d is the propagation delay of each gate. XY G1(t)G2(t) 00 01 11 10 00 01 11 10 Inputs  XY=00 XY=01 XY=11 XY=10 Present States  X Y G1(t) G2(t) 0 d 2d 3d 4d 5d 6d 7d 8d 9d X Y G1 G2 9 PROBLEM 17 (15 points) Using Quine-McCluskey algorithm, find the minimal SOP for the following minterm list. f(A, B, C) = (1,2,3,4,6,7) w(j) j Match I Match II 0 1 2 3 PI Covering Table

## EE118 FALL 2012 SAN JOSE STATE UNIVERSITY Department of Electrical Engineering TEST 2 — Digital Design I October 24, 2012 10:30 a.m. – 11:45 a.m. — Closed Book & Closed Notes — — No Crib Sheet Allowed — STUDENT NAME: (Last) Claussen , (First) Matthew STUDENT ID NUMBER (LAST 4 DIGITS): No interpretation of test problems will be given during the test. If you are not sure of what is intended, make appropriate assumptions and continue. Do not unstaple !!! Problems 1-14(4 points each) TOTAL Problems 15 – 17 (15 pts each) 1203 2 For the next 14 problems, circle the correct answer. No partial credit will be given. PROBLEM 1 (4 points) Which statement is not true? A. Any combinational circuit may be designed using multiplexers only. B. Any combinational circuit may be designed using decoders only. C. All Sequential circuits are based on cross-coupled NAND or NOR gates. D. A hazard in a digital system is an undesirable effect caused by either a deficiency in the system or external influences. E. None of the above PROBLEM 2 (4 points) For a 2-bit comparator comparing 2-bit numbers A = (a1 a0) and B = (b1 b0), what is the proper function for the f(A>B) output through logical reasoning? A. a1 b1’ + (a1 b1 + a1’b1’ ) a0 b0’ B. a1 b1’ + (a1 b1’+ a1’b1 ) a0 b0 C. a1 a0’ + (a1 a0 + b1’b0’ ) b1 b0’ D. a1 a0 + (a1 a0’+ b1’b0 ) b1 b0 PROBLEM 3 (4 points) What is the priority scheme of this encoder? Inputs Outputs I3 I2 I1 I0 O1 O 0 d d 1 d 0 1 d d 0 1 0 0 d 1 0 0 1 0 1 0 0 0 1 1 A. I3 > I2 > I1 >I0 B. I0 > I1 > I2 >I3 C. I1 > I0 > I2 >I3 D. I2 > I1 > I3 >I0 3 PROBLEM 4 (4 points) Which is the correct binary representation of the decimal number 46.625? A. 101101.001 B. 101000.01 C. 111001.001 D. 101110.101 PROBLEM 5 (4 points) Which is the decimal equivalent number of the sum of the two 8-bit 2’s complement numbers FB16 and 3748? A. 3 B. 5 C. 7 D. 9 PROBLEM 6 (4 points) For the MUX-based circuit shown below, f(X,Y,Z) = ? X Y Z f A. X’Y’ + Y’Z’ B. X’Y’Z’ + YZ’ C. XYZ’ + Y’Z D. X’Y’Z’ + YZ 1 0 MUX 4 PROBLEM 7 (4 points) Which is the correct output F of this circuit? E C B D F A A. (A’E+AB)(C’D) B. (AE+A’B)(C’+D) C. (A’E+AB)(C’D’+CD’+CD) D. (A’E+AB)(CD’)’ PROBLEM 8 (5 points) In order to correctly perform 2910  14510, how many bits are required to represent the numbers? A 8 B 9 C 10 D 11 PROBLEM 9 (4 points) Which is the negative 2’s complement equivalent of the 8-bit number 01001101? A. 11001101 B. 10111100 C. 10110000 D. 10110011 0 2-1 1 MUX 0 0 1 1 2-4 decoder 2 EN 3 5 PROBLEM 10 (4 points) Which is the correct statement describing the behavior of the following Verilog code? module whatisthis(hmm, X, Y); output [3:0] hmm; input [3:0] X, Y; assign hmm = (X < Y) ? X : Y; endmodule A. If X>Y, hmm becomes 1111. B. hmm assumes min(X,Y). C. If X

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Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

## Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

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