Page 20 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 1: Number Systems

Notes

Convert the value 2AFCB = ? 2
16

The Indian Numeral System

lthough the Chinese were also using a decimal based counting system, the Chinese
lacked a formal notational system that had the abstraction and elegance of the Indian
Anotational system, and it was the Indian notational system that reached the Western
world through the Arabs and has now been accepted as universal. Several factors contributed to
this development whose significance is perhaps best stated by French mathematician Laplace:
“The ingenious method of expressing every possible number using a set of ten symbols (each
symbol having a place value and an absolute value) emerged in India. The idea seems so
simple nowadays that its significance and profound importance is no longer appreciated.
Its is simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst
useful inventions.”
Brilliant as it was, this invention was no accident. In the Western world, the cumbersome
Roman numeral system posed as a major obstacle, and in China the pictorial script posed as a
hindrance. But in India, almost everything was in place to favour such a development. There
was already a long and established history in the use of decimal numbers, and philosophical
and cosmological constructs encouraged a creative and expansive approach to number theory.
Panini’s studies in linguistic theory and formal language and the powerful role of symbolism
and representational abstraction in art and architecture may have also provided an impetus,
as might have the rationalist doctrines and the exacting epistemology of the Nyaya Sutras,
and the innovative abstractions of the Syadavada and Buddhist schools of learning.

Influence of Trade and Commerce, Importance of Astronomy
The growth of trade and commerce, particularly lending and borrowing demanded an
understanding of both simple and compound interest which probably stimulated the interest
in arithmetic and geometric series. Brahmagupta’s description of negative numbers as debts
and positive numbers as fortunes points to a link between trade and mathematical study.
Knowledge of astronomy—particularly knowledge of the tides and the stars—was of great
import to trading communities who crossed oceans or deserts at night. This is borne out
by numerous references in the Jataka tales and several other folk tales. The young person
who wished to embark on a commercial venture was inevitably required to first gain some
grounding in astronomy. This led to a proliferation of teachers of astronomy, who in turn
received training at universities such as at Kusumpura (Bihar) or Ujjain (Central India) or
at smaller local colleges or Gurukuls. This also led to the exchange of texts on astronomy
and mathematics amongst scholars and the transmission of knowledge from one part of
India to another. Virtually every Indian state produced great mathematicians who wrote
commentaries on the works of other mathematicians (who may have lived and worked in
a different part of India many centuries earlier). Sanskrit served as the common medium of
scientific communication.

The science of astronomy was also spurred by the need to have accurate calendars and a
better understanding of climate and rainfall patterns for timely sowing and choice of crops.
At the same time, religion and astrology also played a role in creating an interest in astronomy
Contd...

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