Hi folks,
After telling you a few things about the concept of zero then about numbers, today we tell just a few sentences on the binary numeration system.
Etymologically, the word « binary » has its origins in the Latin « bis » which means « double« , same as lots of other words starting with the « bi » prefix, such as « bicycle » (because of having two wheels), « binocular » (involving two eyes) and the list goes on and on.
Of course, not all words starting with « bi » expresses « two », so a ‘bishop’ isn’t a priest owning two shops nor is ‘bilirubin’ a substance made of two rubies.
The binary number system is a system of notation that uses base 2, instead of the base 10 (ten) largely used.
So apart from « 0 » and « 1 » which are the same in both base-2 and base-10 number notation systems, the « 2 » in base-10 is written as « 10 », the « 3 » is « 11 », the « 4 » is « 100 » and so forth.
Perhaps not very intuitive for us humans used to the base-10 but really convenient for computer technology, because it is much easier and more reliable from a physical point of view to handle elements associated with just 2 states (« 0 » and « 1 », « on » or « off », etc) than it would be handling 10 states.
So computer hardware uses the « 0 » and « 1 » which is called a bit (from ‘binary digit‘) and bits are usually grouped in « words » of 8, called a « byte« .
With 8 bits in a byte one can represent 256 values (ranging from 0 to 255).
In a sense, this is similar to the Morse code which is some kind of binary system too as it is based on just 2 symbols: the dot and the dash.
Another surprising binary system is the Braille tactile writing system invented by the French Louis Braille for the use of blind and visually impaired persons (Braille himself went blind after an accident in his childhood).
The Braille writing system was invented in the first half of the 1800’s and his inventor Louis Braille was merely aged fifteen years old when figuring it out.
As told you in our previous article, it was the German mathematician Leibniz who around 1679 realized that the simplest possible positional numbers system based on just 2 digits was actually all that was needed to be able to handle any arithmetics problem.
So he described the binary system and showed that binary arithmetic is just as good as decimal one.
There are claims that Leibniz’s source of inspiration was the ancient Chinese « I-Ching » (« The Book Of Changes ») one of the oldest Chinese texts.
The I-Ching depicts 64 hexagrams, one hexagram being a figure made out of 6 horizontal lines, stacked one upon the other and each horizontal line can have only 2 values.
The uninterrupted (un-broken) ones are the Yang and the broken (gapped in the middle) ones are the Yin.
In other words, hexagrams are « words » made up of 6 ‘letters’ and each ‘letter’ can have one of two possible values.
Debates on Leibniz’s inspiration by the I-Ching are still on but it seems clearer and clearer that he was not aware of the I-Ching at the time he dealt with the binary system (only much later did he become acquainted with it).
Finally, we have to mention the contribution of British mathematician, logician and philosopher George Boole, inventor of the Boolean logic which is an algebra subdomain based on the two notions of « true » and « false ».
Because it is one of the basis of digital computer sciences, Boole is considered one of the founders of modern computing.
All in all, we’ve thought about telling you these few things about the binary system in a separate article not only because it is the ‘engine’ of the digital era we currently live in but also because duality is in the nature of human thinking.
We think in terms of « true » or « false », « right » and « wrong », « good » and « bad », « presence » and « absence » and one of the most praised existential questions is a binary one: « to be or not to be »?
See you next week, folks!
Bogdan