119 lines
3.6 KiB
Markdown
119 lines
3.6 KiB
Markdown
# 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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| | | 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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## hex to decimal table
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hex | `0` | `1` | `2` | `3` | `4` | `5` | `6` | `7` | `8` | `9` | `A` | `B` | `C` | `D` | `E` | `F`
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-----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:
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`00` | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15
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`10` | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31
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`20` | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47
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`30` | 48 | 49 | 50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63
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`40` | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79
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`50` | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95
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`60` | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111
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`70` | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 122 | 123 | 124 | 125 | 126 | 127
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`80` | 128 | 129 | 130 | 131 | 132 | 133 | 134 | 135 | 136 | 137 | 138 | 139 | 140 | 141 | 142 | 143
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`90` | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 | 153 | 154 | 155 | 156 | 157 | 158 | 159
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`A0` | 160 | 161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 | 170 | 171 | 172 | 173 | 174 | 175
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`B0` | 176 | 177 | 178 | 179 | 180 | 181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 190 | 191
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`C0` | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 | 200 | 201 | 202 | 203 | 204 | 205 | 206 | 207
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`D0` | 208 | 209 | 210 | 211 | 212 | 213 | 214 | 215 | 216 | 217 | 218 | 219 | 220 | 221 | 222 | 223
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`E0` | 224 | 225 | 226 | 227 | 228 | 229 | 230 | 231 | 232 | 233 | 234 | 235 | 236 | 237 | 238 | 239
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`F0` | 240 | 241 | 242 | 243 | 244 | 245 | 246 | 247 | 248 | 249 | 250 | 251 | 252 | 253 | 254 | 255
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