Tiangan and Dizhi

The Chinese calendar uses the terminology Tiangan (Heavenly Stems) and Dizhi (Earthly Branches). The 10 Tiangan are Jia, Yi, Bing, Ding, Wu, Ji, Geng, Xin, Ren and Gui, and in Chinese they are甲、乙、丙、丁、戊、己、庚、辛、壬、癸. The 12 Dizhi are Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu and Hai, and in Chinese they are子、丑、寅、卯、辰、巳、午、未、申、酉、戌、亥.
Initially the ten stems were invented to record days. Jia referred to the first day, Yi to the second day, Bing to the third day, etc. The twelve branches were invented to record the months. Zi referred to the first month, Chou to the second month, Yin to the third month, etc. Ancient people used the Heavenly Stems and the Twelve Earthly Branches t o formulate a sixty-year cycle. Beginning in the Han (206BC-220 AD), however, the sixty-year cycle began to be used in both official and unofficial ways. These sixty combinations have been applied widely—to days, months and any variety of other items that can be counted in a cycle. Before the 1911 revolution, years were always counted starting from the date a new emperor came to power.
So how does one count years? Within each 60 year cycle, each year is assigned a name consisting of two components. The first component is a Heavenly Stems, and the second component is an Earthly Branch. Each of the two components is used sequentially. For example, the first year of the 60-year cycle is called jiazi(甲子)，the second year yichou(乙丑)，the third year bingyin (丙寅), etc. When we arrive at gui (癸), the last one of the Heavenly Stems, we call the 100 year as gui-you(癸酉). Then we restart with jia, the first Heavenly Stem, and call the 11th year as Jia-xu (甲戌). After we arrive at hai (亥), the last of the Earthly Branches, we will restart with zi. Such a process goes on until we arrive at the 60th year that is called gui-hai(癸亥).