Fundamentals of Computer > Introduction to Computer & Computer System > Evolution of Computer

1. The Abacus: First Counting Device

Abacus is a wooden frame with balls or beads strung on parallel rods fixed in the frame which is divided by a horizontal beam into two regions-

• Upper region of the beam is known as “heaven”.
• Lower region is termed as “earth”.

Origin: Between 5000 and 2000 B.C. in China and was used by Greek, Roman, Japanese and Chinese in pre-Christian times.

Figure-1 below shows the simplified diagram of an abacus.

Two fundamental concepts were associated with the abacus:

1. Numerical information can be represented in a physical form.
2. This information can be manipulated in the physical form to produce the required result.

Representing Numerical Values Using Abacus:

• In the Chinese Abacus, there are 2 beads on each wire in the heaven and 5 beads on each wire in the earth.
• A bead in heaven was considered to have a power (value) of 5 and the bead on earth a power (value) of 1.
• Calculations were performed by moving beads away from towards the beam; the rule being that a bead has a numerical value only when it is adjacent to the beam.

Figure-2 shows a Chinese abacus representing the number 001532786.

2. Soroban: Japanese version of the Abacus:

• In 1530, the two extra beads of the Chinese abacus were eliminated and adopted in the Japanese version of abacus called “Soroban”, i.e. one bead in the heaven and four beads in the earth.Figure-3 shows a Japanese abacus representing the number 02634190.

3. Napier’s Bones

Napier's bones, also called Napier's rods, is a manually-operated calculating device which was used to perform multiplication, division, square root etc. using logarithmic rules.

• It was invented by John Napier, a mathematician from Scotland.
• The rods used in the device were carved from bones of dead animals.
• These rods have numbers marked on them in such a way that by simply placing them side by side, products and quotients of large numbers can be obtained.

Note:

• Rules of logarithm was at first invented by John Napier.

Figure-4: The Napier’s Bones

• A set consists of 10 rods corresponding to digits 0 to 9, and a special eleventh rod that is used to represent the multiplier.
• Surface of each rod comprises 9 squares, and each square, except for the top one, comprises two halves divided by a diagonal line.
• The first square of each rod holds a single digit, and the other squares hold this number's double, triple, quadruple, quintuple, and so on.
• The digits of each product are written one to each side of the diagonal; numbers less than 10 occupy the lower triangle, with a zero in the top half.

Figure-5: Set of Rods

Illustrating Napier's Bones for multiplication:

Problem-1: Multiply 425 by 6 (425 x 6 = ?)

Solution:

• At first, place the bones (rods) corresponding to the leading number of the problem side by side. In this example, the bones 4, 2, and 5 are placed in the correct order as shown below. The rod that represents the multiplier is placed at the left-most of the other rods.
• Looking at the first column, choose the number wishing to multiply by. In this example, that number is 6. The row this number is located in is the only row needed to perform the remaining calculations and thus the rest of the board is cleared below to allow more clarity in the remaining steps.
• Starting at the right side of the row, evaluate the diagonal columns by adding the numbers that share the same diagonal column. Single numbers simply remain that number. Now read the results of the summations from left to right produces the final answer of 2550.

Problem-2: Multiply 6785 by 8 (6785 x 8 = ?)

Solution:

• In this example, the bones 6, 7, 8 and 5 are placed in the correct order as shown here. The rod that represents the multiplier is placed at the left-most of the other rods. Here, the multiplier is 8.
• Starting at the right side of the row, evaluate each diagonal column. If the sum of a diagonal column equals 10 or greater the tens, place of this sum must be carried over and added along with the numbers in the diagonal column to the immediate left as demonstrated below.

• After each diagonal column has been evaluated, the calculated numbers can be read from left to right to produce a final answer which is 54280.

Problem-2: Multiply 6785 by 8 (6785 x 8 = ?)

Solution:

• In this example, the bones 6, 7, 8 and 5 are placed in the correct order as shown here. The rod that represents the multiplier is placed at the left-most of the other rods. Here, the multiplier is 8.
• Starting at the right side of the row, evaluate each diagonal column. If the sum of a diagonal column equals 10 or greater the tens, place of this sum must be carried over and added along with the numbers in the diagonal column to the immediate left as demonstrated below.

• After each diagonal column has been evaluated, the calculated numbers can be read from left to right to produce a final answer which is 54280.

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