## A Conversation for Complementary Arithmetic

### Tens Complement (and cars)

Dark Master - The end is now (2005/03/01) Officially Left Started conversation Feb 26, 2004

Why not think of it like a car's odometer. (distance measure)

If it was at 00 miles before you start then your drive 2 miles it will read 02. Whereas if you drove backwards 2 miles it would read 98 (coresponding to -2). Driveing 2 miles forward then 2 miles backward would mean that you effectively add 98 and 02 arriveing at 100, ignoring the carry leaveing 00. which is the overall displacement (distance from start to finish) you have covered.

In practice this might not happen because distance driven backwards is still considered distance driven in the car and hence is added positively to the total. But, try and ignore that and this example makes perfect sense.

### Tens Complement (and cars)

Old Hairy Posted Feb 26, 2004

This was indeed thought of, and specifically rejected, in the peer review thread for the original entry, see F151730?thread=326870&post=4201333#p4226425 (posting 33 and the next few).

The odometer analogy is perfect, but only gets one to representations of negative numbers. It does not really help to explain addition and subtraction, still less multiplication and division. It also does not help much in the case of binary numbers, which are these days the main application of complementary arithmetic.

Thank you for your comment all the same. Did you like the entry?

### Tens Complement (and cars)

Dark Master - The end is now (2005/03/01) Officially Left Posted Feb 26, 2004

The entry was fine, Sorry to have sugested things already rejected. I should spend more time researching before I post things.

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