Radix, Roman, Spreadsheet

I was troubled by this problem that described a numeral system that had no zero. There existed two symbols: '4' and '7' in the system, but neither of them represented null, which means that if I wrote down a side-by-side comparison of it with the binary system, it would result in the following (for the sake of readability, I replaced '4' and '7' with '1' and '2' respectively):

Base 10		Base 2		Base 2 (w/o 0)
0			0			undefined
1			1			1
2			10			2
3			11			11
4			100			12
5			101			21
6			110			22
7			111			111
and so on

Since I was unfamiliar with base systems without zero (seriously, what?), I went down the rabbit hole. The first result I got from my search engine was "Roman Numerals", which made sense since it didn't have zero. Then I read more into it, and I found another result that, at first glance, looked completely unrelated - How to convert a column number (e.g. 127) into an Excel column (e.g. AA). Then it occurred to me that Excel columns did not have the concept of nothing. A-Z represent 1 to 26. In other words, the question is asking to convert Base 26 to Base 26 w/o 0. Let's check... yep someone has responded with a checked answer, hopefully. The code is as simple as the following:

while(from > 0)
{
	int modu = (from - 1) % MODULO;
	buffer += char_set[modu];
	if(modu == MODULO - 1)
	{
		from -= modu;
	}
	from /= MODULO;
}
reverse(buffer);

However, I didn't quite understand the fifth line. It turned out to be easier than met the eye. During each iteration, we are checking a specific digit of the number in base MODULO since division acts as a single right shift operation if the denominator is the same as the $n$ of base-$n$. In that digit, it is evident we are converting from $0 \sim n-1$ to $1 \sim n$; however, notice $0$ should become $n$ (index in the character set is $n-1$), hence line 3. After that, the if statement only applies to digit $0$. Notice if we hadn't applied this operation, we'd be left with one less offset each time we come across $0$. Remember how $100_2$ becomes $12_{wo0}$, so we'd count one more digit if we didn't subtract it with MODULO - 1.

Anyway, that's enough yapping and I almost forget what I'm writing about. See you in the next post.