Wednesday, September 02, 2009 9:48 PM,

A student writes:



	Dr. Patt,

	My name is ********* and I had a question regarding problem 7c on the
	problem set. Since 10000000 is negative, I understand that I must 
	find the positive equivalent that when added to 10000000 the sum 
	is zero. 



Indeed, that is the process that usually works.



	But when you do this process, you come up with 10000000. 
	Clearly, 10000000 + 10000000 cannot equal 00000000 since 
	both these 2's complimentary numbers are negative. 



Clearly.  That is why I said usually.  You have found the ONE case where it 
doesn't.



	How should I go about solving this problem?

	Thanks,
	<<name withheld to protect the student who is troubled by 10000000>>



If you recall when we specified the negative numbers, we had 2^n 
representations (since we had n bits).  One of them is 0, 2^(n-1) -1 of them 
are positive, and by using the procedure you are referring to, we were able to 
determine the representations of the 2^(n-1) -1 negative numbers having the 
same magnitude as the corresponding
2^(n-1) -1 positive numbers.  This accounts for 1 + (2^(n-1) -1) +
(2^(n-1) -1) of the 2^n representations.  How many representations are left?  
What did we decide to do about that.  Ergo, the answer!

Good luck with the rest of the problem set.

Yale Patt