Calculating with Ahnentafels

kw: family history, genealogy

A few days ago I wrote about Ahnentafel numbers, or "ancestry table" numbers. See the explanation there.

When I am confronted with an Ahnentafel number (AN) larger than about 32, I have to do some work to figure out where in the family tree this person fits. Converting the number base makes it simpler. I have a scientific calculator that can convert from base 10 to bases 2, 8 and 16. I use base 2 for smaller numbers, and an intermediate of base 8 for larger ones, for which I can pretty easily convert to base 2 (binary) for whatever next step I have in mind.

If you don't have a calculator that will do it for you, you can convert from base 10 to base 8 with pencil and paper, using successive division and keeping remainders. I'll do an example with the AN 10569:

10569/8 = 1321 with a remainder of 1; that is what the first two lines show. You keep dividing until you get a number smaller than 8, and that is your last remainder. Based on the calculation shown, the base 8 (octal) representation of 10569 is 24511.

For many needs, it is most convenient to know the binary representation. For example, if you have an AN of 19 for an ancestor, in binary it is 1011. The first 1 is always you, and after that zeroes represent males, and ones represent females, so this is your father's mother's mother. Your father's father's father has a binary representation of 1000, which is 16. Memorize the table that follows if you don't already know these:

These make it simple to turn 24511 (8) into binary: 010 100 101 001 001 or 10100101001001, discarding any leading zeroes. Now, you can read this off as "my father's mother's, etc." but it has a more practical use. I have for years kept family records according to which great-grandparent's line they were in (Great grandparents have AN's of 8-15, or in binary, 1000-1111). The first four binary digits in 10569 are 1010, which equals 10 in decimal. This works out to the line of my father's mother's father.

Also, the charts you can print from Ancestry.com have five generations. The root sheet thus has people with AN's from 1 (you) to 31. If, as I do, you print successive sheets starting with the people in the rightmost column (fifth generation, including you), you can figure out where 10569 is, such as which sheet she is on (odd AN's are for females). Take the number five bits at a time, but overlapping by one bit, and converting a leading zero to a one: 10100, (1)1010, (1)0100, (1)1. These four binary numbers represent 20, 26, 20, and 3.

I number sheets in the corner according to the AN of the root person for that sheet. The figuration here is a bit tricky:

• The root sheet is sheet 1.
• The second sheet with the line to 10569 is sheet 20.
• The third sheet is 20x16+10 = 330 (26 is 16+10).
  
• The fourth sheet is 330x16+4 = 5284.
• Person 10569 is in position 3 (mother of root person 5284).

I find these numerical tools for converting to octal and binary very useful. I have seen articles advocating the use of wholly octal AN's, and there are some benefits to doing so. With a bit of practice, you can just about read off the person's affiliation by scanning the AN. However, putting the AN's on the sheets, if you don't have software that does it for you, would be tricky: in octal, 200x2 = 400, but 217x2 = 436. It takes a lot of practice to do this comfortably.