98 lines
1.8 KiB
Markdown
98 lines
1.8 KiB
Markdown
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# hexadecimal
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the hexadecimal numeral system differs from the decimal system by having 16 digits rather than 10:
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```
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hex| decimal
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---|---------
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`0`| 0
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`1`| 1
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`2`| 2
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`3`| 3
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`4`| 4
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`5`| 5
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`6`| 6
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`7`| 7
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`8`| 8
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`9`| 9
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`A`| 10
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`B`| 11
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`C`| 12
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`D`| 13
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`E`| 14
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`F`| 15
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```
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when there is more than one digit, these are multiplied by 16, 256, 4096 and so on rather than 10, 100, 1000:
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```
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hex | decimal
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----|---------
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`00`| 0
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`04`| 4
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`08`| 8
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`0F`| 15
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`10`| 16
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`11`| 17
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`12`| 18
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`13`| 19
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`20`| 32
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`30`| 48
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`40`| 64
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```
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# hex to decimal
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for example, take hexadecimal number `AA`:
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```
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2nd digit -\ /- 1st digit
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A A
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16^1*10 = 16*10 = 160 + 10 = 170
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```
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now for hexadecimal number `4C5F`:
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```
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3rd digit -\ /- 2nd digit
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4th digit -\ | | /- 1st digit
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4 C 5 F
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| | | |
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| | | 15 = 15 = 15 +
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| | \16^1*5 = 16 * 5 = 80
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| \--- 16^2*12 = 256 * 12 = 3072
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\--------- 16^3*4 = 4096 * 4 = 16384
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-------
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= 19551
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```
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# decimal to hex
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if it's less than 16, just memorize the table at the top of this document.
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otherwise find the power of 16 that is closest to the number you want to convert, but no larger than the number.
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then divide, and take the remainder.
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divide the remainder with the previous power of 16, until the divider is 1.
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for example, for the decimal number `220`:
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```
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220 ÷ 16 = 13 (r = 12) D
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12 ÷ 1 = 12 (stop here) C
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= DC
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```
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now for decimal number `69420`:
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```
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69420 ÷ 65536 = 1 (r = 3884) 1
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3884 ÷ 4096 = 0 (r = 3884) 0
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3884 ÷ 256 = 15 (r = 44) F
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44 ÷ 16 = 2 (r = 12) 2
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12 ÷ 1 = 12 (stop here) C
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= 10F2C
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```
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