Answer:
a)
| x | y | | c | s |
|---|
| 0 | 0 | | 0 | 0 |
| 0 | 1 | | 0 | 1 |
| 0 | 2 | | 0 | 2 |
| 1 | 0 | | 0 | 1 |
| 1 | 1 | | 0 | 2 |
| 1 | 2 | | 1 | 0 |
| 2 | 0 | | 0 | 2 |
| 2 | 1 | | 1 | 0 |
| 2 | 2 | | 1 | 1 |
b)
- The most obvious answer is the system of two's-complement arithmetic,
with the two's-complement algorithm for negation, adding the two's-complement
to subtract, etc.
- Most issues surrounding multiplication are unclear -- it depends upon
what the analogues of our familiar gates are under this trinary system.
However, one genuine new issue which is certainly raised regarding
multiplication is that a single-digit multiplication can have a carry-out.
In binary arithmetic, the maximal one-digit product is 1; in trinary
arithmetic, the maximal one-digit product is 4, which is a product of 1 with a
carry-out of 1.
This is a new wrinkle.
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