The Knot System, applied
 The list of individuals in Ascent List N is calculated by successively dividing n by 2 and discarding all fractions until 1 is reached. The list includes both the person (called Person A in this example) and the ancestor (n). Thus, Person A's Ascent List 13 is composed of the following: Ancestor 13 (whose number is halved to create 6.5; the fraction is then dropped)Ancestor 6 (whose number is halved to create 3)Ancestor 3 (whose number is halved to create 1.5; the fraction is then dropped)Ancestor 1 This means that A's Ascent List 13 consists of four individuals: A himself or herself (n=l), A's mother (n=3), the mother's father (n=6), and the mother's father's mother (n=13). A's gender is unspecified. For the remaining individuals on the list, the gender is defined by the ancestor's position number as previously stated: even numbers represent males, odd, females. Therefore, A's Ascent List N is an exact description of A's kinship to the ancestor at position n.The most complex of the three basic relationships - i.e., the relationship between A and B, who have common ancestor C - can now be simply defined. One ascent list is compiled for A, beginning with him or her and ending with C. A second ascent list is compiled for B, beginning with him or her and ending with C. The resulting list number for A is linked to the resulting list number for B, by use of a decimal point - a.b being the manner of expressing this basic relationship.To illustrate, consider the relationship that is verbally identified as second cousins, once removed. It is typically depicted on a drop chart in the following manner:
 Cover pageKnot System definedKnot System applied--> Complex relationship--> Additive relationship--> Kin register--> ApplicationsNotations
 Since there can be only one individual at each ancestor position, the ancestor numbers has traditionally been used for both ancestor identification and for documentation of the ancestors relationship to the proband.In the Knot System however only the relationship property of these numbers is used.The Knot System is therefore not a solution to the ongoing genealogical quest for a numbering system for descendants.
 By comparison, separate ancestor charts for Martha and John IV would express the above lines as follows:
 Martha and John IV are obviously related through Matilda, who is the knot individual because she ties a "knot" of relationship between Martha and John IV. Under the Knot System, Martha's direct line that is depicted above would be identified as her Ascent List 13. John IV's line would be his Ascent List 17.These two ascent lists are combined, with a decimal point as separation, to form the KinCode element 13.17 - a combination that looks like an ordinary number (an integer + fraction) but is not. Recalling that the form for expressing the KinCode element is a.b, one could verbally read this KinCode element 13.17 as: "The ancestor of the proband, Martha, at position a (13) is the same individual as the ancestor of her relative, John IV, at position b (17)."It is obvious that all ancestors to C are also common ancestors to A and B. However, only C needs to be considered when numerically describing the basic relationship between A and B, because C is the common ancestor closest to the proband A and the related individual B.For all practical purposes, the KinCode elements can be treated as real numbers capable of being compared and sorted - as long as one precaution is observed. For all KinCode elements that have identical numbers to the left of the decimal point, the expressions to the right of the decimal point should all have the same number of digits. (Zeroes can be added to the right hand number to achieve this, but any added zero must appear immediately after the decimal point. Table 1 illustrates the point, to use KinCode elements 46.068 and 46.092 as examples: zeroes were added to each so that 68 and 92 would have the same number of digits as the fraction part of element 46.116). Experience has proved it practical, always, to have at least two digits to the right of the decimal point. This permits the ascent list to span more than five generations and accommodate most known descendant relations.