# Quaternary numeral system

Numeral systems by culture
Hindu-Arabic numerals
Western Arabic
Eastern Arabic
Khmer
Indian family
Brahmi
Thai
East Asian numerals
Chinese
Chinese counting rods
Korean
Japanese
Alphabetic numerals
Abjad
Armenian
Cyrillic
Ge'ez
Hebrew
Ionian/Greek
Sanskrit

Other systems
Attic
Etruscan
Urnfield
Roman
Babylonian
Egyptian
Mayan
List of numeral system topics
Positional systems by base
Decimal (10)
2, 4, 8, 16, 32, 64
3, 9, 12, 24, 30, 36, 60,
[ e]

Quaternary is the base-4 numeral system. It uses the digits 0, 1, 2 and 3 to represent any real number.

It shares with all fixed-radix numeral systems many properties, such as the ability to represent any real number with a canonical representation (almost unique) and the characteristics of the representations of rational numbers and irrational numbers. See decimal and binary for a discussion of these properties.

### Relation to binary

As with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4, 8 and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2, 3 or 4 binary digits, or bits. For example, in base 4,
302104 = 11 00 10 01 002
Although octal and hexadecimal are widely used in computing and programming in the discussion and analysis of binary arithmetic and logic, quaternary does not enjoy the same status.

### Hilbert Curves

Quaternary numbers are however used in the representation of 2D Hilbert-curves. Here a real number between 0 and 1 is converted into the quaternary system. Every single digit now indicates in which of the respective 4 sub-quadrants the number will be projected.

### Genetics

Parallels can be drawn between quaternary numerals and the way genetic code is represented by DNA. The four DNA nucleotides in alphabetical order, abbreviated A, C, G and T, can be taken to represent the quaternary digits in numerical order 0, 1, 2, and 3. With this encoding, the complementary digit pairs 0↔3, and 1↔2 (binary 00↔11 and 01↔10) match the complementation of the base pairs: A↔T and C↔G.

For example, the nucleotide sequence GATTACA can be represented by the quaternary number 2033010 (= decimal 9156).

## See Also

• Conversion between bases

## External links

numeral system (or system of numeration) is a framework where a set of numbers are represented by numerals in a consistent manner. It can be seen as the context that allows the numeral "11" to be interpreted as the binary numeral for three
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Hindu-Arabic numeral system (also called Algorism) is a positional decimal numeral system documented from the 9th century.

The symbols (glyphs) used to represent the system are in principle independent of the system itself.
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Arabic numerals, known formally as Hindu-Arabic numerals, and also as Indian numerals, Hindu numerals, Western Arabic numerals, European numerals, or Western numerals, are the most common symbolic representation of numbers around the world.
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The Eastern Arabic numerals (also called Arabic-Indic numerals, Arabic Eastern Numerals) are the symbols (glyphs) used to represent the Hindu-Arabic numeral system in conjunction with the Arabic alphabet in Egypt, Iran, Afghanistan, Pakistan and parts of India, and also in
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Khmer numerals are the numerals used in the Khmer language of Cambodia. In informal spoken language one can ignore the last "sep" (30 to 90) and it is still understood.
e.g.
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symbols used in various modern Indian scripts for the numbers from zero to nine:

Variant 0 1 2 3 4 5 6 7 8 9 Used in
Eastern Nagari numerals ০ ১ ২ ৩ ৪ ৫ ৬ ৭ ৮ ? Bengali language
Assamese language

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Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). They are the direct graphic ancestors of the modern Indic and Hindu-Arabic numerals.
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Thai numerals (ตัวเลขไทย) are traditionally used in Thailand, although the Arabic numerals (also known as Western numerals) are more common.
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This page contains Chinese text.
Without proper rendering support, you may see question marks, boxes, or other symbols instead of Chinese characters.

Numeral systems by culture
Hindu-Arabic numerals
Western Arabic
Eastern Arabic
Khmer Indian family
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Counting rods (Traditional Chinese: ; Simplified Chinese: ; Pinyin: chou2
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sset
• 여덟 권 yeodeolgwon (eight (books)) is pronounced like [여덜꿘] yeodeolkkwon
Several numerals have long vowels, namely 둘 (two), 셋 (three) and 넷 (four), but these become short when
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Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000.
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Abjad numerals are a decimal numeral system which was used in the Arabic-speaking world prior to the use of the Hindu-Arabic numerals from the 8th century, and in parallel with the latter until Modern times.
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Armenian numerals is a historic numeral system created using the majuscules (uppercase letters) of the Armenian alphabet.

There was no notation for zero in the old system, and the numeric values for individual letters were added together.
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Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. The system was used in Russia as late as the 1700s when Peter the Great replaced it with the Hindu-Arabic numeral system.
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Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet.

In this system, there is no notation for zero, and the numeric values for individual letters are added together. Each unit (1, 2, ...
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Greek numerals are a system of representing numbers using letters of the Greek alphabet. They are also known by the names Milesian numerals, Alexandrian numerals, or alphabetic numerals.
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Attic numerals were used by ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2nd century manuscript by Herodian.
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Etruscan numerals were used by the ancient Etruscans. The system was adapted from the Greek Attic numerals and formed the inspiration for the later Roman numerals.

Etruscan Decimal Symbol *
θu 1 I
ma? 5 ?
śar 10 X
muval? 50
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/» and the fifths place with a stroke from the top-left to the bottom-right «\». The numbers from 1 = / to 29 = ////\\\\\ have been found.

## Interpretation

These embossed marks, unique in objects from the Bronze Age, were introduced in cast-iron molds and were not
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Roman numerals is a numeral system originating in ancient Rome, adapted from Etruscan numerals. The system used in classical antiquity was slightly modified in the Middle Ages to produce the system we use today. It is based on certain letters which are given values as numerals.
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Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record.
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Egyptian numerals was a numeral system used in ancient Egypt. It was a decimal system, often rounded off to the higher power, written in hieroglyphs. The hieratic form of numerals stressed an exact finite series notation, being ciphered one:one onto the Egyptian alphabet.
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Maya numerals is very simple. [1]
Addition is performed by combining the numeric symbols at each level:

If five or more dots result from the combination, five dots are removed and replaced by a bar.
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This is a list of numeral system topics (and "numeric representations"), by Wikipedia page. It does not systematically list computer formats for storing numbers (computer numbering formats). See also number names.
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A positional notation or place-value notation system is a numeral system in which each position is related to the next by a constant multiplier, a common ratio, called the base or radix of that numeral system.
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base or radix is usually the number of various unique digits, including zero, that a positional numeral system uses to represent numbers. For example, the decimal system, the most common system in use today, uses base ten, hence the maximum number a single digit will ever
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decimal (base ten or occasionally denary) numeral system has ten as its base. It is the most widely used numeral system, perhaps because humans have four fingers and a thumb on each hand, giving a total of ten digits over both hands.
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binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2.
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octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7.

Octal numerals can be made from binary numerals by grouping consecutive digits into groups of three (starting from the right).
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