9/15/04

A student, having started Problem Set 2, writes:

     On problem 10, part b, do we assume that A, B, and the output
     are in 2's complement representation or in unsigned binary
     representation?

Part b asks you to design a circuit that implements A+B and A-B using the diagram of Figure 3.39 as a building block. Figure 3.39 uses 0s and 1s as inputs to its circuits. A is one 4-bit binary value. B is another 4-bit binary value. The full adders do not care whether you are using 2's complement or unsigned or ASCII code representation, for that matter. The full adders will just perform their logic function, as specified by the truth table on page 62.

So, I guess your first job is to see what happens in the circuit of Figure 3.39 if A and B represent 2's complement numbers, or unsigned numbers, or 4-bit floating point numbers (if you care to invent some). Try a few examples. You might answer your own question.

     In the future, which representation should we assume binary
     numbers are in?

I understand exactly where you are coming from!

However, my job is to try to help you understand this stuff, so if I don't tell you explicitly which representation we are talking about, then I must think it is part of your learning experience to figure out for yourself which representation makes sense. Sometimes it will be 2's complement integers, sometimes ASCII, sometimes something else.

     Second, also on problem 10, part b, if A, B, and the output
     are in unsigned binary representation, are we allowed to design our
     own "subtractor" circuit?

You can assume A,B and the output are in whatever representation you wish, and you are to then design whatever circuit you wish to perform the subtraction. Depending on which representation you pick, you might find the circuit you have to design pretty simple, or very, very complicated. If you find it to be very complicated, you might re-examine whether you have selected an inappropriate representation.

     Is such a circuit needed or expected in the solution of the
     problem?

     << name withheld >>

The problem asks you to design whatever circuit you wish to do the job. It gives you a big-time hint that if you use the circuit of Figure 3.39 as a starting point, life will be easier.

Two questions for you:

     1. Have you asked any of the TAs about this? You really should.
     2. Are you working alone or in a study group?

Yale Patt