The advantage of the binary system is that it can be used to represent numbers in systems mechanisms which are capable of being in two mutually exclusive states. This is the reason that the binary system is used internally by all modern computers.
However the first prototype binary computer was built by John Atanasoff, a physics professor at Iowa State College, in In his paper [7] he advocated the usage of the binary system in a calculating apparatus in comparison to the decimal system, for instance that the computation of a square root is especially simple in this system.
In Alan Turing designed an electromechanical multiplier. In , the American George Stibitz built an binary adder using electromechanical relays.
In A. Burks, H. Goldstine 1 and J. One way to transfer decimal numbers to binary system is by a process of successive division the so-called division by 2 using radix 10 arithmetic. For instance, to transform the integer from decimal to binary, the number is iteratively divided by 2 and the remainders of the successive divisions are stored. The iterative process ends when the quotient 0 is reached. Thus the representation of the decimal number in binary numeral system is The division is by 64 and the remainders are converted from radix 10 representation to binary ones.
To convert more positive integers from decimal to binary visit. To convert from binary to decimal is the reverse algorithm. For instance, to convert to decimal form we can use the template. A more efficient way of calculation is to proceed as follows. The idea behind the graphical representation is to always alternate horizontal and vertical moves, and adding on vertical moves and doubling on horizontal moves.
To convert more positive integers from binary to decimal form visit. The mentioned division by 2 using radix 10 arithmetic method can be also interpreted in form of the snake method as an algorithm to convert a number from its decimal representation to its binary representation. We now proceed from the left to the right. The concept of positional notation which is used in decimal numbers to determine the number using positional data is also applied in binary.
However, in binary, the base number or radix is always 2. The modern binary number system was first researched in Europe in the 16th and 17th centuries by Gottfried Leibniz, and a few other mathematicians. However, systems similar to the binary system appeared in the antiquity of various cultures and civilizations.
In this text, the concept of Yin-Yang describes the interconnection between forces in the world. In I Ching, yin-yang is represented by using trigrams and later renditions of the text utilise hexagrams. This is one of the very first versions of binary notations which, at the time, was used to interpret the quaternary divination technique, based on the duality of yin and yang.
Later on, the Song Dynasty scholar, Shao Young, repositioned the hexagrams in such a format that strongly resembled modern-day binary numbers. Even before these developments in China, the ancient scribes found in Egypt used something known as the Horus-Eye fractions, which was one of the two methods the Egyptians used to represent fractions.
The Horus-Eye fractions are actually a binary numbering system that was used for representing fractional quantities of grains, liquids and other measures at the time. Closer to home, the Indian scholar Pingala, the author of Chhandahshastra, was also known to be one of the earliest inventors of the binary system in the 2nd century BCE. According to researchers, his work described the binary numeral system using fixed patterns of short and long syllables when describing prosody the basic rhythmic structure of a verse in poetry.
This is also similar to Morse code. The short syllables were termed laghu while the long ones were called guru. The numerical value simply adds one to the sum of all the place values. Much further into the future, Thomas Harriot, an English mathematician and astronomer in the s delved into multiple positional numbering systems, which also included binary, however, he did not publish his results and they were found posthumously in his papers. In , Francis Bacon, an English philosopher researched a system where letters of the alphabet were converted to sequences of binary digits.
Possibly one of the most renowned names in the history of not just binary numbers, but also mathematics, Gottfried Wilhelm Leibniz wore many hats. He invented mechanical calculators, incepted the Leibniz wheel which was used in calculators up until the invention of electronic calculators in the 70s.
The use of binary numbers date back to ancient Egypt, but it was 17th-century philosopher and mathematician, Gottfried Wilhelm Leibniz, who created the current binary number system used today. Google celebrated his nd birthday on Sunday with a Google Doodle showing binary numbers.
Born on July 1, , Leibniz made great strides in the fields of philosophy and math. He developed a form of calculus around the same time as Sir Isaac Newton and was considered one of the greatest 17th-century philosophers of rationalism.
He was also an inventor, coming up with variations of the mechanical calculator.
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