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.