We talked about an ALU that takes two 4-bit inputs, A and B, and then generates a 4-bit result, S, based on a 2-bit command, F1F0. (In the lecture slides, these are called C1C0, but I'm changing the name to avoid confusion with the carry signals that we often label as C0, C1, etc.) The meaning of the 2-bit command we discussed is:
- If F1F0 == 00, then the ALU computes the sum (S = A + B).
- If F1F0 == 01, then it computes the difference (S = A - B).
- If F1F0 == 11, then it generates a true/false indication of whether A < B (S = 0001 for true, 0000 for false).
We didn't use a command encoding of 10. So let's say we want to add that encoding and generate the "true" indication of 0001 if A > B, and the "false" indication of 0000 if A is not greater than B. In order to do this, we'll need to make some changes to what we discussed in the lecture:
(a) We have a control signal called Subtract that, when asserted, causes operand B to be inverted and causes a carry-in of 1 to be fed into the ripple carry adder. In the lecture, we said this signal was equivalent to C0, but that's not sufficient now. What does the logic for this Subtract signal need to be now?
(b) Assuming we have correctly controlled our ripple carry adder to perform a subtraction, the sign bit of the result plays a role in determining the comparison result. If we're trying to determine if A is greater than B, there are two reasons why we can't just look at the sign bit to see if it's 0. What are those two reasons?
