After learning that I got my checksums terribly wrong , I need to ask this question. I am having trouble understanding the 2's compliment. Wikipedia says

the N's are in superscript so does that mean 2 to the N power

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JMP $FFD2

In this case, it is 2 to the Nth power (2^N).

For an 8 bit value, 2^N is 256. So, the two's compliment of number x is 256 - x. The one's compliment is 255 - x. That is why they say the two's compliment is the same as the one's compliment plus 1 (256 = 255 + 1).

Daryl

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To negate a number, you flip all the bits and add one. So, in binary, 00000001 becomes 11111110 and then 11111111. Which is to say, minus 1 is all-ones. This is nicely consistent, because adding 1 to all-ones is obviously going to give you all zeros. And a carry, which you can use or ignore as you see fit.

The neat thing about two's complement is that for addition and subtraction you can ignore it: you go through exactly the same moves for a signed number as you do for an unsigned number. Which is to say, a number isn't signed or unsigned until you treat it as such. Another nice thing is that the top bit is a 1 for a negative number and 0 for a positive one, so the sign of a number is very easy to determine.

Ed

it's the complement in 2 * n
in decimal the 2's complement of 8 is 20 - 8
it's like you've pre subtracted 8 and take a result
via addition mod 20 and interpret 10..19 as negative
numbers
20 - 8 = 12
9 - 8 = 1 = (9 + 12) % 20
5 - 8 = -3 = 5 + 12 = 20 - 3
it's just easy to get the 2's complement
in binary by inverting and adding 1

?? The appropriate example for decimal is 10's complement, which is the 9's complement plus 1. The 9's complement is just each digit's difference from 9.

For example, the 10's complement of 42 is 57+1, which is 58. To subtract 42 from a number, say 78, you can instead add 58. If you add 58 to 78 you get 36 and a carry. Indeed, 36 is 78-42.

You could also think of 58 as being the difference of 42 from 100, but if you could do multi-digit subtraction you wouldn't need the 10's complement in the first place!

Hope this helps!
Ed