Binary Numbers: What and Why
INNOVATION OF BINARY NUMBER
SYSTEM:-
The application of binary numbers is
quite recent, however the system itself was invented way back. Mathematician
Gottfried Leibniz invented the modern binary system in 1679 and published it in
1703.He was far sighted and successfully predicted its usefulness in primitive
machines.He mentioned how easy to work with the system was since there was no
need to go for trial and error in divisions unlike the ordinary decimal
process.[This by no means demeans the traditional number system, since that
also serves its purpose.But that’s a topic for another blog].
The world of Binary
THE STORY BEHIND BINARY NUMBERS:-
Religious philosophical view of creation
greatly contributed to Leibniz’s innovation.He was fascinated by the idea of
“creation out of nothing”.The initial idea was to create a system that would
translate logic into pure mathematical numbers.After his theory was
unacknowledged he came across an old chinese classic text of divination “I
Ching”, which used hexagon bits of visual binary code. Leibniz was more than
delighted to find a supporting block and finally completed his work in creating
a wholesome system of zeroes and ones.[Chinese or any kind of deviation is yet
to be proved scientifically and therefore this blog entertains no idea of
putting down or upholding this ideology].
 |
MATHEMATICIAN GOTTFRIED LEIBNIZ |
THE REVOLUTION OF BINARY:-
It's not that the binary number system
never existed before that but he was the one to actually give the system a
mathematical representation. These numbers made of 0 and 1 didn't contribute
much in the field of technology or science in the time of Gottfried. It was
only after a graduate student Claude Shannon, from Massachusetts Institute of
Technology; noticed how binary numbers closely relate to electric
circuits,amused by Boolean Algebra developed by George Boole's published paper
'The Mathematical Analysis of Logic' that describes an algebraic system of
logic. Shannon's thesis gave rise to the field information theory and played a
crucial part in the use of the binary code in practical applications such as
computers, electric circuits and many more.
DEFINITION OF BINARY NUMBER:- Now that you got a fair idea about why Binary came in the picture let's explore this interesting system.As the term itself suggests (bi = 2) a binary number is a number represented with 2 symbols only. Respectively, 0 and 1. For example, 110 (a binary number) is equivalent to 6 in the decimal system.
EXPLAINING THE BINARY WAY OF REPRESENTING NUMBERS:-
To understand how a system works it's
for the best if we understand it from the necessity of the system rather than
converting it into another. let's say a person has different numbers of # in
some boxes assigned to him to take care of.like, (# # # # # # #), (# # #)
[Consider '#' as some kind of product] Now he needs to keep count of these. He
wants a very simple process considering he is dumb. He can try putting in
tallies which will be hardworking as the numbers of these # increases.
What he can do is write down a system,
| | | | | |%|=#
| | | | |%| |=##
| | | |%| | |= ####
| | | |%| |%|=####+# = #####
and so on…..
Just like that all this hypothetical dumb
and lazy person has to do is, draw these | | | | | lines on a paper and put the
'%' sign in places according to the number of the products in each box.
Clear about this?Congrats, You are
extremely close to completely understanding binary!
In real life calculations we can't just
make a page full of lines and that's why we need a placeholder. Otherwise we
would probably be having a singular number system with the base 2! Cool right?
This placeholder is nothing but zero.
So 0 = # 10 = ## as for why it's 0 and
not %? We will get to that too.
Starting from the right side/0's place
each place responds to a power of 2 and the digit in that place is the number
to be multiplied with the 2 raised to the power of that place.
Since, 20 = 1, and (2x
+ 1) is always odd,(x = positive integer) we can represent both odd and even
numbers with this.
So, 1010 is nothing
But, 20*0 + 21*1 +
22*0 + 23*1 = 10.
Or, 11 is nothing
But, 20*1 + 21*1 =
2.
CONVERTING BINARY NUMBERS TO DECIMAL NUMBERS:-
The
process of converting them vice versa is fairly simple too. We simply need to
break down the decimal number in minimum terms of 2's powers. (20,21,22,23,24
e.t.c.)
18 = 24 + 21
Binary Number for 18 = 10010
Similarly, Binary Number for 29 = 11101
(24+23+22+20)
THE BINARY BITS:- A
bit is a binary digit. Quite obviously A bit can only hold one of the two
values, 0 or 1 corresponding to the electrical values off or on. This simple
and fundamental trick does most of the work in electrical devices like
computers, laptops,cell phones and so on. Electric flow determines whether a
task will be done or not. If the switch is on electrons would flow and if not
then it won't. The 0 and 1 tells the computer whether to turn on the switch or
not. Definitely it's not just this that makes a computer do so much but this is
the underlying principle of storing datas and performing endless functions.
Numbers are everywhere, you just nee
Check out our website to know more about us :
www.edixite.com
- Adrija panda, Team Edixite
Comments
Post a Comment