Suanpan - Beads

Beads

There are two types of beads on the suanpan, those in the lower deck, below the separator beam, and those in the upper deck above it. The ones in the lower deck are sometimes called earth beads or water beads, and carry a value of 1 in their column. The ones in the upper deck are sometimes called heaven beads and carry a value of 5 in their column. The columns are much like the places in Arabic numerals: one of the columns, usually the rightmost, represents the ones place; to the left of it are the tens, hundreds, thousands place, and so on, and if there are any columns to the right of it, they are the tenths place, hundredths place, and so on.

The suanpan is a 2:5 abacus: two heaven beads and five earth beads. If one compares the suanpan to the soroban which is a 1:4 abacus, one might think there are two "extra" beads in each column. In fact, to represent decimal numbers and add or subtract such numbers, one strictly needs only one upper bead and four lower beads on each column. So these extra beads might be used to represent hexadecimal numbers on the suanpan and add or subtract them. Also, some "old" methods to multiply or divide decimal numbers use those extra beads like the "Extra Bead technique" or "Suspended Bead technique".

At the end of a decimal calculation on a suanpan, it is never the case that all five beads in the lower deck are moved up; in this case, the five beads are pushed back down and one carry bead in the top deck takes their place. Similarly, if two beads in the top deck are pushed down, they are pushed back up, and one carry bead in the lower deck of the next column to the left is moved up. In hexadecimal calculation, all seven beads on each column are used. The result of the computation is read off from the beads clustered near the separator beam between the upper and lower deck.

There exist different methods to perform division on the suanpan. Some of them require the use of the so-called "Chinese division table".

The two most extreme beads, the bottommost earth bead and the topmost heaven bead, are usually not used in addition and subtraction. They are essential (compulsory) in some of the multiplication methods (two of three methods require them) and division method (special division table, Qiuchu 九歸, one amongst three methods). When the intermediate result (in multiplication and division) is larger than 15 (fifteen), the lowest of the upper beads is moved halfway to represent ten (xuanchu, suspended). Thus the same rod can represent up to 19 (compulsory as intermediate steps in tradition suanpan multiplication and division).

The mnemonics/readings of the Chinese division method has its origin in the use of bamboo sticks, which is one of the reasons that many believe the evolution of suanpan is independent of the Roman abacus.

This Chinese division method (i.e. with division table) was not in use when the Japanese changed their abacus to one upper bead and four lower beads in about the 1920s.

The beads and rods are often lubricated to ensure quick, smooth motion.