The Chinese calendar, dated back to 2697 B.C., comprises 60-year cycles called the Sexagenary Cycle.  Each year of the cycle is given a name and is made up of two characters.  The first character is from an ordered set of 10 characters, called celestial stems, and the second character is from another ordered set of 12 characters, called terrestrial branches.  The first set repeats 6 times and the second set repeats 5 times in a 60-year cycle. The ten celestial stems are related to the five elements - Wood, fire, soil, metal and water. These elements are associated to the movement of the sun through the day that described a certain kind of electromagnetic energy flow which called 'chi'. The twelve terrestrial branches are commonly known as the Chinese Zodiac, symbols representing 12 animals. Thus, the name of each year would reappear in every 60 years.

Decoding Chinese calendar sexagenary numbers system - The sexagenary number or the 2-character Chinese year name can be derived using the matrix table show below. The intersection point of the matrix would be the sexagenary number. For example:  = 1  or = 44

Since first Sexaganary Cycle began in 2697BC, then year 1984 would be the beginning of the 78th 60 year cycle. The year 2003 is thus the 20th year of the 78th 60 year cycle, and is the year named , { ([78 completed cycles] x 60) + 20 = 4700 years }.
Year AD BC      Year 24 of 78,  60 year cycle.   Lunar year 4704

Wood
+
1 51 41 31 21 11
Wood
--
2 52 42 32 22 12
Fire
+
13 3 53 43 33 23
Fire
--
14 4 54 44 34 24
Earth
+
25 15 5 55 45 35
Earth
--
26 16 6 56 46 36
Metal
+
37 27 17 7 57 46
Metal
--
38 28 18 8 58 48
Water
+
49 39 29 19 9 59
Water
--
50 40 30 20 10 60