Stupid question that's been annoying me

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(a)subatomix.com