Nepedia
Back to Discover
Advanced Reader
🔢

Binary number

math Maturity 7-9 Next article →

A binary number is a value expressed in the base-2 numeral system. Unlike the decimal system we use daily, binary relies on only two symbols: zero and one. Each individual digit in this system is known as a bit, which is short for binary digit. This system uses positional notation with a radix of 2. This means the position of each bit determines its specific value. Binary can also represent rational numbers. These are numbers formed by dividing an integer by a power of two.

Binary counter
Binary counter

Modern computing relies almost entirely on this system. Digital electronic circuitry implements binary through the use of logic gates. This method is preferred by nearly all modern computers and digital devices. The simplicity of the language provides high noise immunity in physical implementation. This means the system is very resistant to errors caused by electrical interference. Because electronic states are easily divided into two distinct levels, binary is the most efficient way for hardware to process information.

Half Adder
Half Adder

Binary concepts appeared in many ancient cultures long before modern computers. In Egypt, scribes used Horus-Eye fractions to measure grain and liquids. This system expressed fractions as sums of 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. Early documents from the Fifth Dynasty date to approximately 2400 BC. The fully developed hieroglyphic form appeared during the Nineteenth Dynasty around 1200 BC.

Oudjat
Oudjat

Ancient Egyptian multiplication also used a binary-related method. This process involved doubling values or adding a number back to itself. The order of these steps followed the binary representation of the multiplier. The Rhind Mathematical Papyrus from 1650 BC shows this method in use.

Other civilizations developed unique binary-style systems for different purposes. In China, the I Ching used binary notation for divination as early as the 9th century BC. It utilized eight trigrams and 64 hexagrams, which are analogous to three-bit and six-bit binary numerals. The Song dynasty scholar Shao Yong rearranged these hexagrams into a format resembling modern binary. In India, the scholar Pingala developed a binary system around the 2nd century BC. He used it to describe prosody, or the rhythm of poetry. He categorized syllables as laghu (light) or guru (heavy). His system in the Chandaḥśāstra increased values toward the right rather than the left.

Bagua-name-earlier
Bagua-name-earlier

West African traditions also feature sophisticated binary systems. The Yoruba people used the Ifá divination system, which originated in the 15th century. This system can produce up to 256 binary signs. This total comes from squaring 16, matching the possibilities of an 8-bit sequence. Divination is performed using an Ọpẹlẹ chain containing 8 seeds. Each seed can land in one of two positions: open or closed. This creates all possible combinations known as Odú. UNESCO added Ifá to its list of Masterpieces of the Oral and Intangible Heritage of Humanity in 2008.

European thinkers laid the groundwork for modern binary mathematics. In the 13th century, Ramon Llull used binary combinations to organize human knowledge. In 1605, Francis Bacon suggested encoding the alphabet into binary sequences. He noted this could be done with any object that has a twofold difference, such as bells or torches. In 1617, John Napier described location arithmetic for binary calculations. Thomas Harriot also investigated positional numbering systems, including binary, though he did not publish his findings. The first European publication of the system likely came from Juan Caramuel y Lobkowitz in 1700.

Gottfried Leibniz is a central figure in the history of binary. He wrote over a hundred manuscripts on the subject. In 1679, his work "On the Binary Progression" introduced methods to convert between decimal and binary. He also created algorithms for binary addition, subtraction, multiplication, and division. Leibniz even developed a binary algebra to calculate square roots.

Gottfried Wilhelm Leibniz, Bernhard Christoph Francke
Gottfried Wilhelm Leibniz, Bernhard Christoph Francke

He famously corresponded with the Jesuit priest Joachim Bouvet. Through Bouvet, Leibniz realized the I Ching used a binary notation. Leibniz saw this as evidence of the universality of mathematics.

Decimal to Binary Conversion
Decimal to Binary Conversion

The transition from theoretical math to digital hardware required further breakthroughs. In 1854, George Boole published his work on an algebraic system of logic. This became known as Boolean algebra.

George Boole color
George Boole color

This logical calculus was essential for designing digital electronic circuits. In 1937, Claude Shannon applied Boolean algebra to electronic relays and switches. This work bridged the gap between mathematical logic and physical computing. Today, binary remains the fundamental language of the digital age.

Binary clock
Binary clock
730 words

Where will your curiosity go next?

Keep exploring at your chosen reading level.

🖼️ Images & Media (9)
File:Oudjat.SVG
Oudjat.SVG
File:Bagua-name-earlier.svg
Bagua-name-earlier.svg
File:Gottfried Wilhelm Leibniz, Bernhard Christoph Francke.jpg
Gottfried Wilhelm Leibniz, Bernhard...
File:George Boole color.jpg
George Boole color.jpg
File:Binary clock.svg
Binary clock.svg
File:Binary counter.gif
Binary counter.gif
File:Binary_guess_number_trick_SMIL.svg
Binary_guess_number_trick_SMIL.svg
File:Half Adder.svg
Half Adder.svg
File:Decimal to Binary Conversion.gif
Decimal to Binary Conversion.gif
More to explore

🔬 Go deeper

More advanced topics to explore

🪜 Step back

Simpler topics to build understanding

What is Nepedia?

A free, ad-free encyclopedia for children. Every article is written at five reading levels, so the same page works for a five-year-old and a fifteen-year-old — use the level switcher above to see this one change. No account needed to read.