Exercises 3 (18 pts)

1.  (3 pts)  A logic family has the following ranges of voltages to represent the high and low values: HIGH = 3.5 V to 5.0 V, LOW = 0.0 to 1.5 V.
a.    For the following signal values, determine the corresponding logic values for the positive and for the negative logic.
i.    1.0 V
ii.    4.5 V
iii.    2.0 V
iv.    -1.0 V
b.    For a module with inputs x1 and x0 and output z you have performed the following set of voltage measures (all in volts). Determine the logic operation implement for positive and negative logic by completing the tables at right.
 
Voltages
x1    x0    |    z 
0.3   0.2   |    0.5
0.3   4.5   |    4.4
4.5   0.2   |    4.4
4.5   4.5   |    0.2		 Positive
x1    x0    |    z 
            |
            |
            |
            |		 Negative
x1    x0    |    z 
            |
            |
            |
            |
2. (2 pts)   Show a CMOS circuit that implements the following function for positive logic.
x1    x0    |    z
 0     0    |    0
 0     1    |    1
 1     0    |    0
 1     1    |    0
3.    (2 pts)    Given the voltage waveform for a gate with inputs x and y and output z below:

a.    What positive logic operation (i.e. LOW = 0, HIGH = 1) is implemented? What negative logic operation (i.e. LOW = 1, HIGH = 0) is implemented?
b.    What is the propagation delay for this gate (i.e. tpHL and tpLH)?
4. (1 pt)    What is the rise and fall times for the gate output z depicted in the waveform of Question 3?

5. (8 pts)
        A)    For the gate diagram below, compute the fan-in and fan-out of each CMOS gate using the text table on page 75.

i.      NOT
ii.     AND2
iii.    OR3
iv.    AND4
    B)   Given equal tpHL and tpLH gate propagation times for 4 input AND of 15 ns., 2 input AND of 10 ns., OR of 7.5 ns. and NOT of 5 ns. Then, assuming that A=False, B=False, C=False, D=True, and E=True, what is the shortest propagation time for the device given that input for A changes to True and E changes to False simultaneously?
     
    C)    Assuming that A=False, B=False, C=False, D=True, and E=True, what is the propagation time for the device given that the input for C changes to True?

    D)    In the following, assuming that A=True, B=False, C=True, D=False, S0=False, S1=True, S2=False, and S3=False, what is Z?

    E)    What are the necessary values of S0, S1, S2, and S3 for Z=C?