# We use them all the time.

## By Annelise Graebner Anderson

If you do a standard branching diagram of your ancestors with the
men (fathers) on the upper line and women on the lower, as is
conventional, then number the positions of the diagram starting
with 1 (yourself) and proceeding from the top of each column (each
column being a generation) to the bottom, the numbers will be
Ahnentafel numbers (A-numbers). Most print-outs, e.g., PAF print-
outs, number the positions in the diagram in this way. Each position
is numbered, whether you know the person's name or not.
```	          4
2
1         5
6
3
7
```

Generation 1 has one member, #1.
Generation 2 has two members, #2 and #3; 2=father, 3=mother.
Generation 3 has four members, #4 to #7.
Generation 4 has eight members, #8 to #15.
The number of member in generation n is 2 raised to the (n-1) power.

Note that the number of members is the same as the number of the
first member of the generation.

For any person, say #7, that person's father's number is times 2
the person's number (thus 14) and the mother's number is times 2
plus 1, i.e., 15. A man's wife (or the mother of the child in
question) is always one number higher than he is, i.e., 14 is
married to 15, 148 is married to 149.

Each number identifies a person with a unique relationship to #1 on
the chart. E.g., #4 is always #1's father's father, #5 is always
#1's father's mother, #6 is always #1's mother's father, and #7 is
always #1's mother's mother. It's not terribly awkward to talk
about "my grandmother on my father's side", but when we get to
great grandparents and beyond, it's a mess. The A-number gives
more precise information; here, after all, we have four great
grandfathers:

#8 fff, father's father's father (000)
#9 ffm, father's father's mother (001)
#10 fmf, father's mother's father (010)
#11 fmm, father's mother's mother (011)
#12 mff, mother's father's father (100)
#13 mfm, mother's father's mother (101)
#14 mmf, mother's mother's father (110)
#15 mmm, mother's mother's mother (111).

If you substitute 0 for the f's (representing fathers) and 1 for
the m's, you notice that the eight people in the third generation
are numbered in three-digit binary numbers from 000 to 111, in
order. The next generation, which has sixteen members, takes four
places to represent the members (e.g., #16 is ffff, #1's father's
father's father's father, and #31 is mmmm). Again changing the f's
to zeros and the m's to ones produces the four-place binary numbers
from 0000 to 1111; 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111,
1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111.

An Ahnentafel chart (Ahnen=ancestors, Tafel=chart or table) lists
ancestors by number. Unlike a branching diagram, it gives the same
amount of space (one or two lines) to each person; the diagram gets
too crowded to list date and place of birth, death, marriage just
when we get to care, out there in the fifth and sixth generations,
where we're hunting for people we have not identified. This
numbered list contains just as much information as a diagram. PAF
will do Ahnentafel charts; see the "Charts and Forms" option.

You can convert A-numbers to their binary equivalents and thus
identify the precise relationship the person who is #1. For
example, I'm missing my #47. This is in the group starting with
#32, the sixth generation, which has 32 members. This generation
takes five binary places to represent each person, 2 to the fifth
power (2x2x2x2x2) is 32. The first one will be 00000. The 47th
will be 47-32, or 15, translated into its binary equivalent. You
can calculate the binary number in various ways; the easiest is to
use an electronic calculator (like Windows applet) to do it. 15 in
binary is 1111; using five digits, that's 01111. So ancestor #47
is fmmmm, or my father's mother's mother's mother's mother. Her
husband is #46; he is the father of #23 and #47 is the mother of #23.

So these A-numbers give the same information depicted in a diagram.
And of course everyone's #47 is his or her fmmmm. #23 ought to be
fmmmm, or 0111. 23-16=7; 7 in binary is 111, or 0111 given the
four places required to express fifth-generation relationships. So
that checks.

Given the precision of these numbered relationships, we can take
charts for two people (each #1 on his or her own chart) and
determine their relationship. For example, cousins will have one
set of grandparents in common (maybe, but maybe not, ones with the
same A-numbers).

This is probably how some computer programs calculate relationships.

The property of A-numbers, that any individual's father has an A-
number double his or hers and the mother has an A-number double
plus one, has often been stated. The material on binary
equivalents I worked out on my own, and I found it surprisingly
useful.

Finally, the A-number system is a tool, the use of which does not
imply any diminution of our concern with people.

Editors note: The author and I are aware of systems in which
siblings are shown with decimal numbers. Say, Jane is the ancestor
with A-number 11, and is the third of four children in her family.
Jane and her siblings could be shown with numbers 11.1, 11.2,
11(Jane), and 11.4. That leads to males with odd A-numbers.
Further, a two-dimensional chart becomes crowded and complex if
siblings' descendants are shown. Two such systems are discussed by
Dollarhide, William. Managing a Genealogical Project, Genealogical
Publishing Co., 1991.

Source: Anderson, Annelise Graebner. Missouri State Genealogical
Association Journal
XV:1, Winter 1995, pp. 52-53.
Copyright 1995 Missouri State Genealogical Assocation.
Posted by permission. 