نظام عد رباعي
أنظمة ترقيم حسب الثقافة | |
---|---|
ترقيم هندي عربي | |
نظام ترقيم غربي عربي شرقي Khmer |
عائلة هندية براهمني تايلندي |
ترقيم غربي آسيا | |
صيني Suzhou |
Counting rods منغولي |
ترقيم أبجدي | |
أبجدي أرمني سريالي Ge'ez |
عبري اغريق (Ionian) |
أنظمة أخرى | |
Attic بابلي مصري |
Etruscan مايا Roman Urnfield |
List of numeral system topics | |
Positional systems by base | |
نظام عشري (10) | |
2, 4, 8, 16, 32, 64 | |
1, 3, 6, 9, 12, 20, 24, 30, 36, 60, more… | |
نظام العد الرباعي (بالإنجليزية: Quaternary numeral system) هونظام عد ذورقم أساس 4، ويسمى هذا النظام عد رباعي وهي تستخدم غالباً تحت عنوان "أنظمة خاصة" أي أنها ليست شائعة في استخدامها كثيراً في تحويلها إلى نظام عد آخر.
Relation to other positional number systems
Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Quaternary | 0 | 1 | 2 | 3 | 10 | 11 | 12 | 13 | 20 | 21 | 22 | 23 | 30 | 31 | 32 | 33 | |
Octal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | |
Hexadecimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | |
Binary | 0 | 1 | 10 | 11 | 100 | 101 | 110 | 111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 | |
Decimal | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | |
Quaternary | 100 | 101 | 102 | 103 | 110 | 111 | 112 | 113 | 120 | 121 | 122 | 123 | 130 | 131 | 132 | 133 | |
Octal | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | |
Hexadecimal | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1A | 1B | 1C | 1D | 1E | 1F | |
Binary | 10000 | 10001 | 10010 | 10011 | 10100 | 10101 | 10110 | 10111 | 11000 | 11001 | 11010 | 11011 | 11100 | 11101 | 11110 | 11111 | |
Decimal | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | |
Quaternary | 200 | 201 | 202 | 203 | 210 | 211 | 212 | 213 | 220 | 221 | 222 | 223 | 230 | 231 | 232 | 233 | |
Octal | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | |
Hexadecimal | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 2A | 2B | 2C | 2D | 2E | 2F | |
Binary | 100000 | 100001 | 100010 | 100011 | 100100 | 100101 | 100110 | 100111 | 101000 | 101001 | 101010 | 101011 | 101100 | 101101 | 101110 | 101111 | |
Decimal | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 |
Quaternary | 300 | 301 | 302 | 303 | 310 | 311 | 312 | 313 | 320 | 321 | 322 | 323 | 330 | 331 | 332 | 333 | 1000 |
Octal | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 100 |
Hexadecimal | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 3A | 3B | 3C | 3D | 3E | 3F | 40 |
Binary | 110000 | 110001 | 110010 | 110011 | 110100 | 110101 | 110110 | 110111 | 111000 | 111001 | 111010 | 111011 | 111100 | 111101 | 111110 | 111111 | 1000000 |
Relation to binary and hexadecimal
+ | 1 | 2 | 3 |
1 | 2 | 3 | 10 |
2 | 3 | 10 | 11 |
3 | 10 | 11 | 12 |
As with the octal and hexadecimal numeral systems, quaternary has a special relation to the binary numeral system. Each radix 4,ثمانية and 16 is a power of 2, so the conversion to and from binary is implemented by matching each digit with 2, ثلاثة or أربعة binary digits, or bits. For example, in base 4,
- 2302104 =عشرة 11 00عشرة 01 002.
Since 16 is a power of 4, conversion between these bases can be implemented by matching each hexadecimal digit with 2 quaternary digits. In the above example,
- 23 02 104 = B2416
× | 1 | 2 | 3 |
1 | 1 | 2 | 3 |
2 | 2 | 10 | 12 |
3 | 3 | 12 | 21 |
Although octal and hexadecimal are widely used in computing and computer programming in the discussion and analysis of binary arithmetic and logic, quaternary does not enjoy the same status.
Although quaternary has limited practical use, it can be helpful if it is ever necessary to perform hexadecimal arithmetic without a calculator. Each hexadecimal digit can be turned into a pair of quaternary digits, and then arithmetic can be performed relatively easily before converting the end result back to hexadecimal. Quaternary is convenient for this purpose, since numbers have only half the digit length compared to binary, while still having very simple multiplication and addition tables with only three unique non-trivial elements.
By analogy with byte and nybble, a quaternary digit is sometimes called a crumb.
Fractions
Due to having only factors of two, many quaternary fractions have repeating digits, although these tend to be fairly simple:
Decimal base Prime factors of the base: 2, 5 Prime factors of one below the base: 3 Prime factors of one above the base: 11 Other Prime factors: 7 13 |
Quaternary base Prime factors of the base: 2 Prime factors of one below the base: 3 Prime factors of one above the base: 11 Other Prime factors: 13 23 31 |
||||
Fraction |
Prime factors of the denominator |
Positional representation | Positional representation |
Prime factors of the denominator |
Fraction |
1/2 | 2 | 0.5 | 0.2 | 2 | 1/2 |
1/3 | 3 | 0.3333... = 0.3 | 0.1111... = 0.1 | 3 | 1/3 |
1/4 | 2 | 0.25 | 0.1 | 2 | 1/10 |
1/5 | 5 | 0.2 | 0.03 | 11 | 1/11 |
1/6 | 2, 3 | 0.16 | 0.02 | 2, 3 | 1/12 |
1/7 | 7 | 0.142857 | 0.021 | 13 | 1/13 |
1/8 | 2 | 0.125 | 0.02 | 2 | 1/20 |
1/9 | 3 | 0.1 | 0.013 | 3 | 1/21 |
1/10 | 2, 5 | 0.1 | 0.012 | 2, 11 | 1/22 |
1/11 | 11 | 0.09 | 0.01131 | 23 | 1/23 |
1/12 | 2, 3 | 0.083 | 0.01 | 2, 3 | 1/30 |
1/13 | 13 | 0.076923 | 0.010323 | 31 | 1/31 |
1/14 | 2, 7 | 0.0714285 | 0.0102 | 2, 13 | 1/32 |
1/15 | 3, 5 | 0.06 | 0.01 | 3, 11 | 1/33 |
1/16 | 2 | 0.0625 | 0.01 | 2 | 1/100 |
انظر أيضاً
- نظام عد ثنائي
- نظام عد ثماني
- نظام عد خماسي
- نظام عد سداسي
- نظام عد ثماني
- Conversion between bases
- Moser–de Bruijn sequence, the numbers that have only 0 or 1 as their base-4 digits
الهامش
- ^ "Archived copy" (PDF). Archived from the original (PDF) on December 14, 2010. Retrieved November 27, 2010. CS1 maint: archived copy as title (link)
External links
مشاع الفهم فيه ميديا متعلقة بموضوع [[commons:خطأ لوا في وحدة:WikidataIB على السطر 496: attempt to index field 'wikibase' (a nil value).|خطأ لوا في وحدة:WikidataIB على السطر 496: attempt to index field 'wikibase' (a nil value).]]. |
- Quaternary Base Conversion, includes fractional part, from Math Is Fun
- Base42 Proposes unique symbols for Quaternary and Hexadecimal digits
- Visualization of nucleotide sequence, Visualization of numeral systems