The number usually is defined by the knots seperated by double knot.  This may seem forced.  However as a mnemonic it works fine. 

The word Tzitzit  is : 400 10 90 10 90 which adds to 600
to this we add the 5 seperating knots and the 8 strings that hand we get 613

That you should remember all the commandments of the Lord Bamidbar (Numbers) 15:40 - Since the numerical value of the word Tzitzit is 600, and together with the eight stands and five [double] knots, the total is 613 [the number of commandments in the Torah].

Rashi on Bamidbar (Numbers) 15:39        

Rashi, a prominent Jewish commentator, bases the number of knots on a gematria: the word tzitzit (in its Mishnaic spelling) has the value 600. Each tassel has eight threads (when doubled over) and five sets of knots, totalling 13. The sum of all numbers is 613, traditionally the number of mitzvot (commandments) in the Torah. This reflects the concept that donning a garment with tzitzit reminds its wearer of all Torah commandments.

Nachmanides disagrees with Rashi, pointing out that the Biblical spelling of the word tzitzit has only one Yod rather than two, thus adding up to the total number of 603 rather than 613. He points out that in the Biblical quote "you shall see it and remember them", the singular form "it" can refer only to the "p'til" (thread) of tekhelet, and that the reason for remembering the mitzvot is the color of the tekhelet, which resembles the ocean, which in its turn resembles the sky or heaven.

In the same way the unutterable word for God

adds to 26.  In the fringes the first two sets of windings (seven plus eight) equal fifteen. The third set of windings is eleven. Together they come to twenty-six representing YHVH

The value of the word Ekhad,  meaning "one in unity" works out to be 13.  

Thus “the Lord is one” can be spelled out numerically on each Tzitzit with four sets of windings (7+8+11 and 13), each separated by a double knot, for a total of 39 windings. Thus we are reminded of unity of God by looking at these knots

The number value for the Hebrew letters of the word for fringes  In gematria, the Hebrew   (Taryag mitzvot). TaRYaG in the gematria gives the number "613".  So it will read 613 Commandments.

What we have presented is the simplest system.  There are many other systems in existence used widely by the Jewish mystics especially the Cabbalists.  Dozens of other far more complicated methods are found  in Kabbalistic literature.  But it should be remembered that the system itself has no intrinsic sacredness.  It is only a method of coding used in the mnemonic system of how we can remember.  If you know the code, you can know the meaning.  This is why we have several knotting techniques, each sect using their own coding.

Many researchers connect the "Number of the Beast", referred to in the Book of Revelation of the New Testament, with either Greek or Hebrew Gematria as used by the early Christians.

These numerological interpretation are evidently forced and developed into a somewhat magical charms. It is like using spoken words, bibles and prayers as charms.   Avoiding these pitfalls, these do serve as a powerful means of communication and reminder which is what is intended in the use of the Prayer Shawls and its Tzitzits with its knots and colors. In fact the very fact that the interpretations are complex will themselves act as good mnemonic system of associational strength.   After all even our words and actions are expressions of the content that is intended to be transferred.

Here are a few other associations:

Mispar Gadol Method

Mispar Katan Method

The mispar katan method calculates the value of each letter as its standard value but simply truncates all of the trailing zeros.

 Ordinal Value Method

At Bash Method

Mispar HaKadmi Method

Mispar HaPerati Method

Mispar Shemi Method

 We will illustrate the method in two most popular gematria interpretations.

1. The Ashenazic method
2.  Sephardic method

If there is a blue thread, it is used as the binder bringing the whites together into a unity.  Remember blue is the extension of God which enters the earth among men.

The Ashenazic method of 7, 8, 11 and 13 has a total value of 39 which numerically represents the Shama, or Yahweh is one.   Again 39 is the healing number as the Messia received 39 lashes.  “By his stripes, we are healed”.

Again 39 is the healing number as the Messia received 39 lashes

Isaiah 53:5
"But He was wounded for our transgressions,
He was bruised for our iniquities;
The chastisement for our peace was upon Him,
And by His stripes we are healed."

The Sephardic method of tying represents a letter in the Name Yahweh. 10 = YUD, 5 = HEY, 6 = VAV  and 5 = HEY.