Question

Explain how an Abacus works doing addition and subtraction arithmetic.

Cylinders left to right, “100” then “20” then “5” then “1”. The “100” has a quantity of 5 tokens. The “20” has a quantity of 4 tokens. The “5” has a quantity of 3 tokens.   The “1” has a quantity of 4 tokens.

Answer 1

Addition:

The abacus is used for performing the addition operation at high speed. It consists of vertical rods and movable beads. The vertical rods are placed in a serial manner with movable beads on each vertical rod.

A horizontal bar called beam separates the lower portion and upper portion of the abacus. The upper portion of the abacus is called upper deck and the beads placed in the upper deck are called upper beads. The lower portion of the abacus is called lower deck and the beads placed in the lower deck are called lower beads.

In the upper portion or upper deck, each vertical rod has one bead whereas in the lower portion or lower deck, each vertical rod has four beads. In the upper deck, each bead has a value of five (in the ones column) whereas in the lower deck, each bead has a value of one (in the ones column).

When all the lower beads and upper beads are placed away from the horizontal bar, the beads value is counted as zero. When we push the upper beads down towards the horizontal bar or when we push the lower beads up towards the horizontal bar, the beads value is counted.

The right most column in the abacus is the one’s column. When we push one lower bead in the ones column up towards the horizontal bar, its value is counted as one. When we push one upper bead in the ones column down towards the horizontal bar, its value is counted as five.

To the left side of one’s column is the tens column. When we push one lower bead in the tens column up towards the horizontal bar, the bead value is counted as 10. When we push one upper bead in the tens column down towards the horizontal bar, the bead value is counted as 50.

To the left side of tens column is the hundreds column. When we push one lower bead in the hundreds column up towards the horizontal bar, the bead value is counted as 100. When we push one upper bead in the hundreds column down towards the horizontal bar, the bead value is counted as 500. The process is same for thousands, ten thousands, and so on.

Similarly, Subtraction is performed by first registering the minuend and then subtracting, starting from the left, by removing beads from either or both the lower or upper decks. The final bead-positions represent the answer.