Hexadecimal notation
I assume 16 a bottom (てい), and hexadecimal notation (じゅうろくしんほう British: hexadecimal) is a method to express a number on the basis of bottom and 冪.
Table of contents
Numeration system
十六進記数法 is grading numeration system to assume 16 a bottom. According to the usage, the normal Arabic numeric assumes it 十進表記; the notation in 十六進記数法 (express it in 16) of with )16 (parenthesis and bottom. I may call a number expressed as custom in 十六進記数法 "hexadecimal number", but am not a meaning called "time of p = 16 in p 進数".
In general, I use 16 number 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. F expresses 15 from 10 in 十進 each from A.
- (50)16 expresses 5*161 + 0*160 = 80.
- I express (B4)16 = 11*161 + 4*160 = 180.
十六進表記 with the computer
With the computer, I often express a bit and an octet as a unit by data. I can express it with one column of the binary notation, eight columns each. 十六進表記 is used well, and the latter can express it in one which four columns can express with one column of the binary notation more briefly than binary notation. I can express 1 octet in two columns of 十六進表記 (0x00 - 0xff). I can regard this as 16-16 進表記, and it may be said that it is special expression of 256 進表記.
One column of 十六進表記 is called the nybble.
Notation method
Because 十六進表記 is used well, special notation is often prepared for by the programming language as re-TERAL. Generally, I do not distinguish a-f of the small letter from A-F of the capital letter. (1000)I give 16 examples written on the cover.
| Notation example | Language, processing system | Remarks |
|---|---|---|
0x1000 | When I describe integer re-TERAL. | |
\x1000 |
| When I describe a character code in letter re-TERAL and character string re-TERAL. |
#x1000 | The integer value outside expression. | |
&# x1000; | When I describe cf. letter substance とてし character code. | |
1,000h or 1000H |
| When I describe integer イミディエート. You may have to add 0 to the top to distinguish it from variable names when 十六進表記 begins in an English letter (A - F) in the case of this notation. An example: 0A000H |
& h1000 | When I describe integer re-TERAL. | |
$ 1,000 |
| When I describe integer re-TERAL. A document of an assembly language, microcomputers mainly affiliated with Motorola. |
I read the reading of with "0, X, いち, 0, 0, 0" as a letter row. Or "hexa, the と reading of that I said is performed 1,000" by the usage "hexaの 1,000".
I took h and x which the number mentioned above had out of hexadecimal which meant hexadecimal notation in English. I state that it is 十六進表記 clearly.
Early notation
The method to express numbers more than 9 using a letter of A - F was not yet common at the computer dawn.
- Implementation to attach macron ("¯") on the number of 0-5 until the 50s, and to express numerical value of 10-15 was liked.
- A letter of U - Z was used in Bendix G-15.
- A letter of F, G, J, K, Q, W was used in Librascope LGP-30 () [1].
- Bruce Alan Martin of Brookhaven Natl. Lab. showed discomfort for notation by A–F and I devised a totally new number based on bit sequence and suggested it to CACM () in 1968, but there were few assenters [2].
- Soviet program electronic calculator Б3-34 () and the copy product used "-", "L", "C", "Г", "E", "" (space mark).
Correspondence with 2.8, 十進表記
| 十六進表記 | 十進表記 | 八進表記 | Binary notation | |||
|---|---|---|---|---|---|---|
| (0)16 | (0)10 | (0)8 | 0 | 0 | 0 | 0 |
| (1)16 | (1)10 | (1)8 | 0 | 0 | 0 | 1 |
| (2)16 | (2)10 | (2)8 | 0 | 0 | 1 | 0 |
| (3)16 | (3)10 | (3)8 | 0 | 0 | 1 | 1 |
| (4)16 | (4)10 | (4)8 | 0 | 1 | 0 | 0 |
| (5)16 | (5)10 | (5)8 | 0 | 1 | 0 | 1 |
| (6)16 | (6)10 | (6)8 | 0 | 1 | 1 | 0 |
| (7)16 | (7)10 | (7)8 | 0 | 1 | 1 | 1 |
| (8)16 | (8)10 | (10)8 | 1 | 0 | 0 | 0 |
| (9)16 | (9)10 | (11)8 | 1 | 0 | 0 | 1 |
| (A)16 | (10)10 | (12)8 | 1 | 0 | 1 | 0 |
| (B)16 | (11)10 | (13)8 | 1 | 0 | 1 | 1 |
| (C)16 | (12)10 | (14)8 | 1 | 1 | 0 | 0 |
| (D)16 | (13)10 | (15)8 | 1 | 1 | 0 | 1 |
| (E)16 | (14)10 | (16)8 | 1 | 1 | 1 | 0 |
| (F)16 | (15)10 | (17)8 | 1 | 1 | 1 | 1 |
Conversion from binary notation to 十六進表記
I show below a method to convert into 十六進表記 from binary notation.
Integer part
- I divide binary notation by four columns sequentially from the right. When last (for the most left part) is less than four columns, all 0 not crowded partial (the left side) considers it that there is it.
- (111010)2 → (11, 1010) 2 → (0011, 1010) 2
- I convert each part into 十六進表記.
- (0011)2 = (3)16, (1010)2 = (A)16
- I display provided 十六進表記 (3A), and 16 is provided.
This method is good regardless of the number of the figures. For example, it becomes (4CBA)16 because (100110010111010)2 is 2 (0100, 1100, 1011, 1010).
Decimal part
The conversion methods of the decimal part are as follows.
- I divide binary notation by four columns sequentially from the left on the basis of a decimal point. When last (for the most right part) is less than four columns, all 0 not crowded partial (the right side) considers it that there is it.
- (0.110101)2 → (0., 1101, 0100) 2
- I convert each part into 十六進表記.
- (1101)2 = (D)16, (0100)2 = (4)16
- I display provided 十六進表記, and (0.D4)16 is provided.
Therefore, (111010.110101) it is 2 = (3A.D4)16. This method is good regardless of the number of the figures.
Multiplication table
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| 2 | 0 | 2 | 4 | 6 | 8 | A | C | E | 10 | 12 | 14 | 16 | 18 | 1A | 1C | 1E |
| 3 | 0 | 3 | 6 | 9 | C | F | 12 | 15 | 18 | 1B | 1E | 21 | 24 | 27 | 2A | 2D |
| 4 | 0 | 4 | 8 | C | 10 | 14 | 18 | 1C | 20 | 24 | 28 | 2C | 30 | 34 | 38 | 3C |
| 5 | 0 | 5 | A | F | 14 | 19 | 1E | 23 | 28 | 2D | 32 | 37 | 3C | 41 | 46 | 4B |
| 6 | 0 | 6 | C | 12 | 18 | 1E | 24 | 2A | 30 | 36 | 3C | 42 | 48 | 4E | 54 | 5A |
| 7 | 0 | 7 | E | 15 | 1C | 23 | 2A | 31 | 38 | 3F | 46 | 4D | 54 | 5B | 62 | 69 |
| 8 | 0 | 8 | 10 | 18 | 20 | 28 | 30 | 38 | 40 | 48 | 50 | 58 | 60 | 68 | 70 | 78 |
| 9 | 0 | 9 | 12 | 1B | 24 | 2D | 36 | 3F | 48 | 51 | 5A | 63 | 6C | 75 | 7E | 87 |
| A | 0 | A | 14 | 1E | 28 | 32 | 3C | 46 | 50 | 5A | 64 | 6E | 78 | 82 | 8C | 96 |
| B | 0 | B | 16 | 21 | 2C | 37 | 42 | 4D | 58 | 63 | 6E | 79 | 84 | 8F | 9A | A5 |
| C | 0 | C | 18 | 24 | 30 | 3C | 48 | 54 | 60 | 6C | 78 | 84 | 90 | 9C | A8 | B4 |
| D | 0 | D | 1A | 27 | 34 | 41 | 4E | 5B | 68 | 75 | 82 | 8F | 9C | A9 | B6 | C3 |
| E | 0 | E | 1C | 2A | 38 | 46 | 54 | 62 | 70 | 7E | 8C | 9A | A8 | B6 | C4 | D2 |
| F | 0 | F | 1E | 2D | 3C | 4B | 5A | 69 | 78 | 87 | 96 | A5 | B4 | C3 | D2 | E1 |
Unit system
I transcribe the number in the hexadecimal notation of the unit system using a decimal system and adopt a method to bring a unit forward when it leads to 16.
By the yard pound method, hexadecimal notation is used for a unit of mass.
Hexadecimal notation is used for a part of the unit of mass of Japanese traditional weights and measures.
- One loaf of = 16.
Footnote
- This ^ strange sequence comes from the turn of the 6 bits character cord in LGP-30. LGP-30 PROGRAMMING MANUAL
- ^ Letters to the editor: On binary notation, Bruce Alan Martin, Associated Universities Inc., Communications of the ACM, Volume 11, Issue 10 (October 1968) Page: 658 doi: 10.1145/364096.364107
Allied item
This article is taken from the Japanese Wikipedia Hexadecimal notation
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