Instructions:
You are encouraged to work on the problem set in groups and turn
in one problem set for the entire group. Remember to put all
your names on the solution sheet. Also, remember to put the name
of the TA and the time for the discussion section you would like
the problem set turned back to you. Show your work.
For example, in part a, the missing item is X. That is 0 OR 0 = 0 and 0 OR 1 = 1.
We wish to design a controller for an elevator such that if you push a button for a desired floor, the controller will output the floor number that the elevator should go to. However, to deter lazy people from going up or down one floor, if you push the button for the next floor (up or down), the elevator will stay on its current floor. If you push the button for the same floor that you're currently on, the controller will output the current floor number. There are four floors in the building.
Your job: construct a complete truth table for the elevator controller. It is not necessary to draw the logic here; the truth table is sufficient.
Hint: What information does the controller need in order to output the floor to go to?Hint: How many input bits will that require.
Hint: How many output bits will the controller have to supply.
Draw the transistor level circuit of a 2 input XOR gate
(Adapted from 3.30)
A comparator circuit has two 1-bit inputs, A and B, and three 1-bit outputs, G
(greater), E (equal), and L (less than). Refer to figures 3.40 and 3.41 on page
92 in the book for this problem.
One of Professor Patt's students is always late to meetings, so Professor Patt wants you to design an alarm clock to help his student be on time. Your job is to design a logic circuit whose output Z is equal to 1 when the alarm clock should go off. The circuit will receive four input variables (A, B, C, D) that answer four different yes/no question (1=yes, 0=no):
A <= Is it going to be sunny today?
B <= Is it the weekend?
C <= Is it 7:00am?
D <= Is it 9:00am?
Professor Patt wants the alarm clock to go off if it's sunny and it's either 7:00am or 9:00am. The alarm clock should go off if it's the weekend and it's 9:00am. The alarm clock should also go off if it's not the weekend and it's 7:00am. Write the truth table and draw a gate-level diagram that performs this logic.
In class, we showed that NOT((NOT A) AND (NOT B)) == A OR B using their truth tables. This equivalence is known as DeMorgan's law. Similarly, show that NOT((NOT A) OR (NOT B)) == A AND B.
Draw the transistor level circuit of a 3 input majority gate.