Note:  Solo only -- you may not work in teams on this assignment.

Also note:  Because this assignment includes circuit drawings which are hard to email, you may submit your assignment on paper (so long as it is done very neatly).  In any case, it must be received by 8:15am on the due date.

Also note:  This assignment is due tomorrow (Friday) morning, even if you do not have class tomorrow due to rotation.

Also note:  Assignment 3 will be available tomorrow (Friday) by end of school, and will be due on Monday morning.
 

Date Assigned:	Thu Sep-7
Date Due:	Fri Sep-11 by 8:15am

0a.  Finish reading Brookshear 1.1.  Also note that the Solutions to Assignment 1 are available online now for your review.

0b.  (Only for Period 1 class):  Don't forget to show up with some interesting current event issues to discuss.

1.  Today in class, we reviewed the proof that Nor is a logical basis (the extra credit problem from last assignment).  We noted that And,Not is a logical basis, so we just needed to reduce And and Not to Nor.  To do that, we proved that  ~x  ==  x nor x.   We also stated, but did not prove, that x and y == (x nor x) nor (y nor y).  Your job here is to prove that statement.  Construct a truth table for (x nor x) nor (y nor y) and demonstrate that it has exactly the same values as x and y for all values of x and y.

2.  Draw a circuit for x xor y using only And, Or, and Not gates (hint:  we did this in class today, so if you took good notes, this one is a "gimme").  Be sure to put the label ("And" or "Or") inside your gates so I can tell what kind of gates they are.  Draw your circuit neatly, and try to minimize the number of times lines cross.

3.  Draw a circuit for x and y using only Or and Not gates.  Hint:  Recall DeMorgan's Law:  x and y = ~ (~x or ~y).

4.  Referring the the Chapter Review Problems in Brookshear on pp. 70-71:
4a.  Do problem 1a on p. 70.  Note that the rightmost gate is an Xor gate.
4b.  Do problem 2a. on p. 70.
4c.  Do problem 3a. on p. 71.

5.  Easier Extra Credit (Not Required):  In the lecture notes (available online) from the first lecture, I asked how many binary Boolean functions there are.  Well, how many are there?  How can you be certain of this answer?

6.  Harder Extra Credit (Not Required):  Here we build a "one-bit adder".  The job is to construct a circuit which takes two inputs (like we've been doing so far), but instead of only one bit of output, this circuit has two bits of output (two lines out).  Call them B1 and B2.  B1 should represent the sum of the two bits in:  if both are 0, B1 should be 0, if either is 1, B1 should be 1.  We run into a problem, though, when both bits are 1.  B1 can only be 0 or 1, and both are the wrong answer, since 1+1 is, of course, 2.  What to do?  That's where B2 comes in.  B2 is what we call the "overflow" bit, and it is normally set to 0 when everything is ok. But in the special case when both inputs are 1 and B1 overflows, then B2 is set to 1 (and B1 is set to 0), indicating that there was an overflow.  Your task:  draw the circuit for a one-bit adder.

See Course Home Page.