Reading the Appendix A (Binary numbers) of Structured Computer organization by Tanenbaum I've found this exercise:Signed decimal numbers consisting of $n$ digits can be represented in $n + 1$ digits without a sign. Positive numbers have $0$ as the leftmost digit. Negative numbers are formed by subtracting each digit from $9$. Thus the negative of $014725$ is $985274$. Such numbers are called nines complement numbers and are analogous to ones complement binary numbers. Express the following as three-digit nine's complement numbers: $6$. $-2$, $100$, $-14$, [etc].Ok, it all works fine with $6$ for instance: using the given rule it is $006 \mapsto 993$. That makes sense: as Tanenbaum says this system for negative-value representation is similar to one's complement: it has two different zero representation ($000$ and $999$) and it has negative possible value as much as the positive ones.What I don't understand is how can $100$ fit in this scenario. To me, with 3 digits I ca only represent value in range $[-900, 099]$; moreover $100$ is not considered a positive number --it shoudl have a $0$ as leftmost digit.Is there an error in Tanenbaum-exercise?, if not, where I'm wrong?
Can I express 100 as a three-digit 9's complement number?
binary arithmetic