Look at the diagram on slide 3d-35. You could use it to add two 16-bit numbers X and Y. If you did that, C0 would always be 0 because there is no carry into the right-most position (units bit). Since you dont need a carry into the right-most bit, another option would be to replace the rightmost full adder by a half adder.

1a-1c. Complete the following statement: To add two 32-bit numbers, you could use 1a full adders, or 1b full adders along with 1c half adders.

1d. Why is the carryout from the rightmost adder (C1) used as input to the next adder to the left? (One sentence or equivalent will be enough for all why questions and explanations in this course.)

1e. The design of the ripple-carry adder depends on the fact that the carryout value always fits in one bit. Explain why you never need more than one bit for the carryout value. Consider the following binary addition: 0101 1001 1110

1f. In a ripple-carry adder, what would the value of C1 be? 1g. In the problem above, what would the value of C2 be?

- The right-most full adder does not need a carry-in. - However, from the point of view of manufacturing efficiency, it does not hurt to use the same circuit with the carry-in set to 0 . - You can do that by having no input to that item