Yes, I'm actually going to ask a question about two's complement
arithmetic! I feel quite stupid for mailing this, but I just can't figure
it out. And believe it or not, it really does have something to do with
classic computing. All right, here goes...
While I was in class Thursday, I got bored and decided to pass the time by
verifying that A-B=A+(-B) in two's complement binary arithmetic, using an
imaginary machine with a word size of 2 bits. I created the following
table:
Subtraction Equivalent Addition
AA-BB=CC CZSV AA+BB=CC CZSV
01 01 00 .x.. 01 11 00 xx..
01 00 01 .... 01 00 01 ....
01 11 10 x.xx 01 01 10 ..xx
01 10 11 x.xx 01 10 11 ..x.
00 01 11 x.x. 00 11 11 ..x.
00 00 00 .x.. 00 00 00 .x..
00 11 01 x... 00 01 01 ....
00 10 10 x.xx 00 10 10 ..x.
11 01 10 ..x. 11 11 10 x.x.
11 00 11 ..x. 11 00 11 ..x.
11 11 00 .x.. 11 01 00 xx..
11 10 01 .... 11 10 01 x..x
10 01 01 ...x 10 11 01 x..x
10 00 10 ..x. 10 00 10 ..x.
10 11 11 x.x. 10 01 11 ..x.
10 10 00 .x.. 10 10 00 xx.x
The left half iterates through all possible subtractions, which were each
performed by hand by binary subtraction. The results and the states of
the machine's flags (Carry/borrow, Zero, Sign, oVerflow), are shown.
The right half contains the same subtractions, this time done by adding by
hand the minuend and the two's complement of the subtrahend.
Note that the C and V flags behave differently in each half. This is very
disturbing, since I'm fairly certain that subtraction is implemented in
many processors as adding a negated subtrahend (ergo, I should see no
difference in the flags). What have I done wrong in my table?
--
Jeffrey S. Sharp
jss_at_subatomix.com
Received on Sat Sep 29 2001 - 23:32:15 BST