Abacus emerged around 5000 years ago in Asia Minor and it is still in use in some parts of the world. The word 'abacus' was derived from the Arabic word 'abaq', which means 'dust'. An abacus consists of sliding beads arranged on a rack, which has two parts: upper and lower (see Figure 1.2). The upper part contains two beads and the lower part contains five beads per wire. The numbers are represented by the position of the beads on the rack. For example, in the upper part of the rack, a raised bead denotes 0, whereas a lowered bead denotes digit 5. In the lower part, a raised bead stands for 1 and a lowered bead stands for 0. The arithmetic operations like addition and subtraction can be performed by positioning the beads appropriately.

In 1614, John Napier, a Scottish mathematician, made a more sophisticated computing machine called the Napier bones (see Figure 1.3). This was a small instrument made of 10 rods on which the multiplication table was engraved. It was made of the strips of ivory bones, and so the name Napier bones. This device enabled multiplication in a fast manner, if one of the numbers was of one digit only (for example, 6 × 6745). Incidentally, Napier also played a key role in the development of logarithms, which stimulated the invention of slide rule, which substituted the addition of logarithms for multiplication. This was a remarkable invention as it enabled to perform the multiplication and division operations by converting them into simple addition and subtraction operations.

1.3.4 Slide Rule

The invention of logarithms influenced the development of another famous invention known as slide rule (see Figure 1.4). In 1620 AD, the first slide rule came into existence. It was jointly devised by two British mathematicians, Edmund Gunter and William Oughtred. It was based on the principle that actual distances from the starting point of the rule is directly proportional to the logarithm of the numbers printed on the rule. The slide rule is embodied by two sets of scales that are joined together, with a marginal space between them. This space is enough for the free movement of the slide in the groove of the rule. The suitable alliance of two scales enabled the slide rule to perform multiplication and division by a method of addition and subtraction.

1.3.5 Pascaline

In 1623, Wilhelm Schickard invented the 'calculating clock', which could add and subtract, and indicated the overflow by ringing a bell. Subsequently, it helped in the evolution of Pascaline (see Figure 1.5). In 1642 AD, Blaise Pascal, a French mathematician, scientist and philosopher, invented the first functional automatic calculator. It had a complex arrangement of wheels, gears and windows for displaying numbers. It was operated by a series of dials attached to the wheels with each wheel having 10 segments (numbered from zero to nine) on its circumference. When a wheel made a complete turn, the wheel on its left advanced by one segment. Indicators above the dial displayed the correct answer. However, the usage of this device was limited to addition and subtraction only (Figure 1.5).

1.3.8 Difference Engine

In 1822, Charles Babbage, a professor of mathematics, devised a calculating machine known as difference engine, which could be used to mechanically generate mathematical tables. The difference engine can be viewed as a huge complex abacus. It was intended to solve differential equations as well. However, Babbage never made a fully functional difference engine and in 1833, he quit working on this machine to concentrate on the analytical engine.

1.3.9 Analytical Engine

Analytical engine is considered to be the first general-purpose programmable computer. Babbage's innovation in the design of the analytical engine made it possible to test the sign of a computed number and take one course of action if the sign was positive and another if the sign was negative. Babbage also designed this device to advance or reverse the flow of punched cards to permit branching to any desired instruction within a program. This was the fundamental difference between the analytical engine and the difference engine. Lady Ada Lovelace helped him in the development of the analytical engine. She not only helped Babbage with financial aid, but also, being a good mathematician, wrote articles and programs for the proposed machine. Due to her contributions, she is known as the 'first programmer'. However, Babbage never completed the analytical engine, but his proposal for this device reviewed the basic elements of modern computer such as input/output, storage, processor and control unit.