There is an advantageous method of assigning ID numbers to your pedigree ancestors using binary numbers. Some of you right now are thinking that Dollarhide has gone ballistic (again), but please read on — there are some real rewards you should know about.

• Ahnentafel Numbers
• Convert to Binary Numbers
• Doubling Binary Numbers
• Counting Generations

Ahnentafel Numbers
If you need a review of ahnentafel numbers, see my earlier article, “An Awful Ahnentafel,” which explains how pedigree numbers can be assigned to ancestors in a very logical way. Here is an example of an ahnentafel:

			8. William Smith, Sr.
		4. William Smith, Jr.
			9. Polly Anderson
	2. Franklin Smith
			10. ---- Brown
		5. Elizabeth Brown
			11. ---- ----
1. James Smith
			12. ---- Johnson
		6. Martin Johnson
			13. ---- ----
	3. Martha Johnson
			14. ---- Brown
		7. Elizabeth Brown
			15. ---- ----

On the above chart of four generations there are some simple rules that can be seen for each of the numbered positions of ancestors:

1. Except for the first person, all husbands/males in the diagram are shown above their wives/females.

2. Except for the first person, who can be male or female, all males/husbands have an ID number which is an even number.

3. All females/wives have an ID number which is an odd number, a number one higher than their husband’s number.

4. The ID number of the father of any person is double that person’s number. (e.g., the father of number 1 is number 2. The father of number 3 is number 6. The father of number 6 is number 12, and so forth)

5. The ID number of the mother of any person is double that person’s number plus one. (e.g., the mother of number 5 is 10 + 1, or number 11)


Convert to Binary Numbers
Let’s see if it is possible to convert the ID numbers from digital numbers to binary numbers and see what happens. First, binary numbers use base two rather than base ten, as in decimal numbers. That means that only two characters are used, the one and the zero. Thus, the numbers 1, 2, 3, 4, 5 converted to binary numbers would read as 1, 10, 11, 100, 101.

Confused already? Don’t worry, you won't have to learn how to count in binary numbers to make this numbering scheme work for you. You just have to know some simple rules.

The same ahnentafel using binary numbers would appear as shown below:

			1000. William Smith, Sr.
		100. William Smith, Jr.
			1001. Polly Anderson
	10. Franklin Smith
			1010. ---- Brown
		101. Elizabeth Brown
			1011. ---- ----
1. James Smith
			1100. ---- Johnson
		110. Martin Johnson
			1101. ---- ----
	11. Martha Johnson
			1110. ---- Brown
		111. Elizabeth Brown
			1111. ---- ----

The exact same rules apply here as with the ahnentafel numbers in base ten. The binary numbers, as ID numbers, are unique, one for each ancestor. Except for number 1, the person (male or female) who starts the pedigree, all males have an even number, while all females have an odd number. In the case of binary numbers, that means that all males have a number that ends in “0," and all females have a number that ends in “1.”

And, it is still true that to find the father of any person on the chart, double that person’s ID number. In the case of James Smith, No. 1, his father is 10. And it is still true that to find a person’s mother, you must double the person’s number and add 1. (Using binary numbers, you would refer to “10" as “one zero,” rather than “ten.” Thus the number 1011 would be described as “one-zero-one-one.”


Doubling Binary Numbers
Now comes the good part. What may not be evident is that the binary numbers have something going for them that the decimal numbers don’t have. A rule in binary numbers is that any number can be doubled by adding a “0" to it. Thus, to double 1, just add a zero, making it “10,” and that is a number that is double of number 1. The same is true for number 10. Add a zero, 100, and that is a number that is double of number 10.

Look at numbers on the chart and check it out. Every number for a person’s father on the chart can be predicted by just adding zero to a person’s number. The father of 11 is 110. The father of 100 is 1000. The unknown father of 1101, although not shown on the chart, can therefore be predicted to be 11010, and the mother of 1101 would be 11011.

To identify a person’s mother, who always has a number which is one higher than her husband, you just add 1 to the father’s number. But, as it turns out, this is the same as adding one to the child’s number. So, the mother of 1 is 11. The mother of 10 is 101. The mother of 101 is 1011, and so on.

So, you really don’t have to know how to count in binary numbers to see and understand what is happening. All you need to know is the father of any person is double that person’s number. To double a number in binary code, you just need to add a zero to the number. And, to find a mother of any person, you just need to add “1" to the person’s number.

1 you
	10 your father
		100 your paternal grandfather
		101 your paternal grandmother
	11 your mother
		110 your maternal grandfather
		111 your maternal grandmother

Counting Generations
Now look at something else that is unique to the binary numbering system. Note that a person in the first generation has one digit (1). A person in the second generation has two digits (10 and 11). A person in the third generation has three digits (100, 101, 110, and 111). This continues for every generation removed from number 1. For example, a person in the 13th generation will have an ID number with 13 binary digits.

An example: 100001001 is a binary ID number for a female in the 9th generation. Her child (10000100) was a male, who had a male (1000010), who had a female (100001), who had a male (10000), who had a male (1000), who had a male (100), who had a male (10), who was the father of number 1.

Finally, a binary number gives you something you can’t get from decimals. Used as ID numbers for an ahnentafel, a binary number will tell you:

1. Whether the person is male or female
2. What generation the person is in
3. The exact lineage back to number 1

As you can see, the binary system is really quite simple. Give it a try!

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