Answer:
10000011111000
= 2 13 + 2 7 + 2 6 + 2 5 + 2 4 + 2 3
= 2 13 + 2 8 - 2 3
11111
= 2 5 - 2 0
(actually let's just write 2 0 as "1")
so 10000011111000 * 11111
= (2 13 + 2 8 - 2 3) * (2 5 - 1)
= (2 18 + 2 13 - 2 8) - (2 13 + 2 8 - 2 3)
= 2 18 - 28 - 28 + 2 3
= 2 18 - 29 + 2 3
= 111111111000001000
A minor grading note:
In general I tried not to penalize arithmetic errors,
but if you got one of the minus signs wrong for the 28 term and
ended up with 218 + 23, then you didn't have to do the
conversion from
2 18 - 29 + 2 3
back to binary (that is, there was no subtraction), so you couldn't get the
one point for that. So you would get 9 out of 10 if all else was well.
I thought this was an acceptable penalty despite the fact that I would prefer
not to penalize an arithmetic error at all.
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