The most significant and outstanding counting system in the Chinese Calendar is the Heavenly Stem and Earthly Branch. There are 10 Stems and 12 Branches. Stem and Branch are used together. The Stem is used in the front of (on the top of) the Branch. Chinese call them Heavenly Stem and Earthly Branch and use a specific sequence as the counting system for the calendar.
10 Stems and 12 Branches are combined into a cycle of 60 counting systems which begin fromWooden Rat and end with Water Pig. You can see the entire sequence from the Chinese New Year's page. From Year 1924 to Year 1983 is a complete cycle. Year 1999 is the Brown Rabbit which is the 16th of the Stem-Branch system. Year 2000 is the White (Golden) Dragon.
Nobody knows who invented Stem-Branch. This means the Chinese knew about Stem-Branch before the invention of Chinese characters. Today we can see the Stem-Branch symbols in the ancient Chinese oracle bones. At the beginning, Stem-Branch was for counting the DAY only. Later, the Yin-Yang Five-Element scholars applied Stem-Branch into a MONTH, YEAR and HOUR system. Five-Element scholars also applied Stem-Branch to the Five Elements which are the foundation of Chinese Fortune-Telling systems.
When Yin-Yang applies to the numbers. The odd numbers (1,3,5...) are in the Yang group. The even numbers (2,4,6...) are in the Yin group. Yang implies male and Yin implies female. From the sequence order of Stem-Branch, we know the Rat, Tiger, Dragon, Horse, Monkey, and Dog are Yang or male and Cow, Rabbit, Snake, Sheep, Chicken (Hen) and Pig are Yin or female. Note: there is no Ox, Bull or Rooster in this animal list.