By pragyansharma polavarapu
AN
INTRODUCTION
(1)
Earlier
to 1950s computers were only giant size mathematical calculators . A
single machine occupied a big hall with its 10-15 cabinets of
electrical /electronic equipment and connecting wires.
However they
could do a million calculations like 2+3 in just a millionth of second! They
had awe inspiring calculating power and were mysterious machines.
After
discovery of sand-grain sized transistor triodes there was a sea change in
computer production technology. The tiny sturdy high performance transistors replaced the 15,000 big electric bulb sized glass diodes in
computer’s logic circuits !
Computers
became small like radio sets (old tube
radios of 60 years back) requiring only a small office table in a small room.
During the period of about
three decades, roughly 1960s to 1980s , small
computers(electronic calculating machines based on minute transistor
circuits) called MINIs became important in the field of computer
technology.
The
MINI had computing power equal to that of the
respected ENIAC( the giant size hall-size calculator) . It was not only most
elegant to look at but performed equal to or better than old giant
computer-calculators .
With
the appearance of MINIs the entire idea of computer utilization changed and scientists were immediately
engaged in checking its great potentialities .Now in present
era we know what a computer can do and
know that there is almost nothing which cannot be done by a computer.
Modern
computer can write/print/publish a
book. It can play music, take photos , play live audio and video and play the old
audio/ video records(like ,say ,old classic Hindi film songs). It can create well-organized databases for years-- long records of banks/big businesses/government
offices. It can establish
error-free digital international telephone network etc.
When
the computer reached the size of MINI ( the size of a
radio/TV table type) scientists and engineers realized
that a new world that will be filled with computers would dawn. The world of table computer proved more powerful than the world of books and
newspapers to which the
world is accustomed for last 500/600 years.
The
small tabletop computer is a great new facility given to man to gather and organize all knowledge for welfare and
progress of society.
The
development of MINI was not accidental. Its development resulted
from the important discovery of transistor triodes . A single transistor triode is a rigid
crystal of less than one millimeter level dimensions and even far smaller ! In comparison, the
glass diodes /triodes made with thermionic tubes
were of the size of big electric bulbs each having a hot filament
inside.
The
thermionic valves were
frequently damaged due to heat generated in the miles long electric
circuits(all requiring 10-15 cabinets in
a big a/c hall) .The discovery of
transistor proved to be one of the greatest boons to mankind. The transistors were not only sturdy and
solid but also performed even better
than the thermionic valves. Within a few years the thinking about use of computer (by then a small table
top machine ) changed .
(2)
THE
FUNDAMENTALS
Now
let us go to the very fundamentals. Ever
since the new form of energy called
electricity was discovered
scientists were absolutely fascinated by the speed of flow of
electricity in wires ( a little less than 300,000 kilometers per
second )
The scientists and mathematicians
examined whether this speed property of
electricity can be utilized in solving mathematical problems . If this is possible the toughest mathematical problems
in all science and engineering can be solved in seconds.
Scientists
noticed that there are two very definite states “switch on” and
“switch off” in the electric currents. Can a two symbol mathematics be invented
so that “switch on”/”switch off” states can be utilized to represent numbers
big and small?
Can
an electric measuring unit like volt be utilized to denote numbers? Volt
is like depth of water in a perfectly built canal like a cement canal or
a glass made canal. Two voltages like (2volts,5volts),(3volts/8volts) etc
can be used to denote the two binary digits (0,1) the only two digits of
Boolean mathematics.
George
boole( 1815-1864 ) the British mathematician could represent all
numbers small and big of ordinary mathematics by different combinations of 0 and 1 symbols . examples are given below.
0000
0001=1
0000
0110=6
0000
1000=8
Such
ideas were forerunners for creating a mathematical theory for use of the two- states of electrical energy to create an electronic
mathematical machine .
These
(0,1) binary digits do not belong to mathematics but are just two
electrical symbols like
(p,q) or (x,y).
George
boole invented methods to perform addition, subtraction, multiplication,
division and also other mathematical operations like square,square root
etc in the Boolean 01010101
notation.
(3)
But
this was not enough –to make numbers “flow” in electrical wires!
Scientists of Electrical science invented a method . Numbers cannot be
denoted in electric currents by a single “0” type notation or single “1”
type notation . They should be represented as a group of 0s and 1s . They selected a group of eight 0s and
1s both 0s and 1s taken together. A
number can be represented by a group of eight parallel un-mixing electric currents
like a group of eight very long concentric or parallel cement canals. Each
canal is separate with water flowing in it at one of the two levels—level
represented either by binary electric symbol
“1” or by the other binary electric symbol “0”.
Let
us imagine eight perfectly parallel glass or cement canals,
all of perfectly similar rectangular cross section. The canals never meet
and are of infinite length and parallel. Or they can be circular and parallel
like wide concentric circles .In some of these canals water of 2cm height flows
. In the remaining canals water of 5cm height flows. This entire
group of eight parallel canals as a group represents a single number—just
one single number. To represent very large numbers scientists use strings of 0s
and 1s of longer length.
Electrical
current is similar to a fast flowing stream of billions of electrical particles
called electrons. Voltage of electric current is just like depth of water in
the glass/cement water canals.
Thus
scientists created a group of eight parallel currents ---(independent unmixing
endless straight currents or very wide concentric parallel current circuits)---
using only two voltages. The two voltages ,say (2volts,5volts) , represent the binary
digits (0 and 1) are taken. By taking an
eight group of parallel unmixing currents
a single number is created in Boolean
algebra.
The
Boolean number system formed only by the two electrical voltage symbols 0 and 1
is accepted by the IEEE the international controlling authority of Electrical
and Electronic Engineers .
The
manufacturer of computers should specify at time of manufacture which two
voltages are used in all his company’s computers to represent the electric
voltage symbols “0” and “1”.
Ordinary
numbers are denoted as below.
0000
0001=1
0000
0010=2
0000
0011=3
0000
0100=4
0000
0101=5
0000
0110=6
0000
0111=7
0000
1000=8 ….etc.
After
further improvements in computer technology , like WORD PROCESSING programs and
WINDOWS programs in modern times , and under specific approval of IEEE, not only numbers but also alphabets and
symbols like =,+,?,@ etc are represented by 0,1 notation. An extra two digit
code like 01,11, 10 is added as prefix to the number code to represent
alphabets like A,B,C,D,E or special symbols like @,$,%,+,= etc. These codes are
called ASCII codes (American Standard Code for Information Interchange)
This
0,1 notation is standardized for entire world . Without such standardization
computer networks of different countries cannot communicate in a reliable way and
cannot do scientific work .
@@@@
Let
us take for example addition of three large numbers 6259, 9486 and 61165 by using the 01010101 notation i.e. by using a computer .here
we should note that though outwardly the nembers in normal way as shown above
are added by computer’s “calculator” software in fraction of a second , deep
inside the computer’s digital processors like ALU and CPU they are dealt only in the binary code
of 01010101.
This involves mixing of voltages and is
a most complicated work. For doing this work most
accurately, scientists invented small standatd electronic unit circuits called
“logic gates” . Only when numbers are processed
inside computer using only the digital “logic gate” circuits , then only the answers to the most
complicated mathematical problems would come out of computer
in millionth of second.
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