mirror of https://github.com/zeldaret/mm.git
276 lines
8.5 KiB
Markdown
276 lines
8.5 KiB
Markdown
# Useful conversions
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This article contains some useful conversion tables. Beware that we will omit the `0x` prefix on hex numbers: it will be evident from context which base is intended.
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- [Degrees and hex/binary angles](#degrees-and-hex-binary-angles)
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* [Small angles](#small-angles)
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* [Larger angles](#larger-angles)
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- [Round decimal numbers in hex](#round-decimal-numbers-in-hex)
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* [Small](#small)
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* [Medium](#medium)
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* [Large](#large)
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- [Extra large](#extra-large)
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- [Shifts/powers of 2 in dec and hex](#shifts-powers-of-2-in-dec-and-hex)
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## Degrees and hex/binary angles
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Conversion of degrees to binary angles in the two common ways, that give different answers. Table is produced using this script:
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```bash
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$ printf "%s\t%s\t%s\n" "d" "d * 2^16/360" "2^16/360 * d" ; for i in {0..360..5} ; do printf "%d\t%X\t\t%X\n" "$i" $(( "$i" * 0x10000 / 360 )) $(( 0x10000 / 360 * "$i" )) ; done
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```
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### Small angles
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| `d` | `d * 2^16/360` | `2^16/360 * d` |
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| ----: | -------------: | -------------: |
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| 0 | 0 | 0 |
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| 1 | B6 | B6 |
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| 2 | 16C | 16C |
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| 3 | 222 | 222 |
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| 4 | 2D8 | 2D8 |
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| 5 | 38E | 38E |
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| 6 | 444 | 444 |
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| 7 | 4FA | 4FA |
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| 8 | 5B0 | 5B0 |
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| 9 | 666 | 666 |
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| 10 | 71C | 71C |
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| 11 | 7D2 | 7D2 |
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| 12 | 888 | 888 |
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| 13 | 93E | 93E |
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| 14 | 9F4 | 9F4 |
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| 15 | AAA | AAA |
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| 16 | B60 | B60 |
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| 17 | C16 | C16 |
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| 18 | CCC | CCC |
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| 19 | D82 | D82 |
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| 20 | E38 | E38 |
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| 21 | EEE | EEE |
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| 22 | FA4 | FA4 |
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| 23 | 105B | 105A |
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| 24 | 1111 | 1110 |
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| 25 | 11C7 | 11C6 |
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| 26 | 127D | 127C |
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| 27 | 1333 | 1332 |
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| 28 | 13E9 | 13E8 |
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| 29 | 149F | 149E |
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| 30 | 1555 | 1554 |
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### Larger angles
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| `d` | `d * 2^16/360` | `2^16/360 * d` |
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| -----: | -------------: | -------------: |
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| 0 | 0 | 0 |
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| 5 | 38E | 38E |
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| 10 | 71C | 71C |
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| 15 | AAA | AAA |
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| 20 | E38 | E38 |
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| 25 | 11C7 | 11C6 |
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| 30 | 1555 | 1554 |
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| 35 | 18E3 | 18E2 |
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| 40 | 1C71 | 1C70 |
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| 45 | 2000 | 1FFE |
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| 50 | 238E | 238C |
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| 55 | 271C | 271A |
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| 60 | 2AAA | 2AA8 |
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| 65 | 2E38 | 2E36 |
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| 70 | 31C7 | 31C4 |
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| 75 | 3555 | 3552 |
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| 80 | 38E3 | 38E0 |
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| 85 | 3C71 | 3C6E |
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| 90 | 4000 | 3FFC |
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| 95 | 438E | 438A |
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| 100 | 471C | 4718 |
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| 105 | 4AAA | 4AA6 |
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| 110 | 4E38 | 4E34 |
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| 115 | 51C7 | 51C2 |
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| 120 | 5555 | 5550 |
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| 125 | 58E3 | 58DE |
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| 130 | 5C71 | 5C6C |
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| 135 | 6000 | 5FFA |
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| 140 | 638E | 6388 |
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| 145 | 671C | 6716 |
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| 150 | 6AAA | 6AA4 |
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| 155 | 6E38 | 6E32 |
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| 160 | 71C7 | 71C0 |
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| 165 | 7555 | 754E |
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| 170 | 78E3 | 78DC |
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| 175 | 7C71 | 7C6A |
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| 180 | 8000 | 7FF8 |
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| 185 | 838E | 8386 |
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| 190 | 871C | 8714 |
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| 195 | 8AAA | 8AA2 |
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| 200 | 8E38 | 8E30 |
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| 205 | 91C7 | 91BE |
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| 210 | 9555 | 954C |
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| 215 | 98E3 | 98DA |
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| 220 | 9C71 | 9C68 |
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| 225 | A000 | 9FF6 |
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| 230 | A38E | A384 |
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| 235 | A71C | A712 |
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| 240 | AAAA | AAA0 |
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| 245 | AE38 | AE2E |
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| 250 | B1C7 | B1BC |
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| 255 | B555 | B54A |
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| 260 | B8E3 | B8D8 |
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| 265 | BC71 | BC66 |
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| 270 | C000 | BFF4 |
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| 275 | C38E | C382 |
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| 280 | C71C | C710 |
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| 285 | CAAA | CA9E |
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| 290 | CE38 | CE2C |
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| 295 | D1C7 | D1BA |
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| 300 | D555 | D548 |
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| 305 | D8E3 | D8D6 |
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| 310 | DC71 | DC64 |
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| 315 | E000 | DFF2 |
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| 320 | E38E | E380 |
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| 325 | E71C | E70E |
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| 330 | EAAA | EA9C |
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| 335 | EE38 | EE2A |
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| 340 | F1C7 | F1B8 |
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| 345 | F555 | F546 |
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| 350 | F8E3 | F8D4 |
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| 355 | FC71 | FC62 |
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| 360 | 10000 | FFF0 |
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Similarly for small angles with a smaller increment:
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## Round decimal numbers in hex
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```bash
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printf "%s\t%s\n" "dec" "hex" ; for i in {0..100..5} ; do printf "%d\t%X\n" "$i" "$i" ; done
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```
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### Small
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| dec | hex |
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| -----: | --: |
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| 0 | 0 |
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| 5 | 5 |
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| 10 | A |
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| 15 | F |
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| 20 | 14 |
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| 25 | 19 |
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| 30 | 1E |
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| 35 | 23 |
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| 40 | 28 |
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| 45 | 2D |
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| 50 | 32 |
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| 55 | 37 |
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| 60 | 3C |
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| 65 | 41 |
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| 70 | 46 |
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| 75 | 4B |
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| 80 | 50 |
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| 85 | 55 |
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| 90 | 5A |
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| 95 | 5F |
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| 100 | 64 |
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### Medium
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| dec | hex |
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| -----: | ---: |
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| 100 | 64 |
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| 150 | 96 |
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| 200 | C8 |
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| 250 | FA |
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| 300 | 12C |
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| 350 | 15E |
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| 400 | 190 |
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| 450 | 1C2 |
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| 500 | 1F4 |
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| 550 | 226 |
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| 600 | 258 |
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| 650 | 28A |
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| 700 | 2BC |
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| 750 | 2EE |
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| 800 | 320 |
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| 850 | 352 |
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| 900 | 384 |
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| 950 | 3B6 |
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| 1000 | 3E8 |
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### Large
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| dec | hex |
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| -----: | ----: |
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| 1000 | 3E8 |
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| 1500 | 5DC |
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| 2000 | 7D0 |
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| 2500 | 9C4 |
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| 3000 | BB8 |
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| 3500 | DAC |
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| 4000 | FA0 |
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| 4500 | 1194 |
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| 5000 | 1388 |
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| 5500 | 157C |
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| 6000 | 1770 |
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| 6500 | 1964 |
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| 7000 | 1B58 |
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| 7500 | 1D4C |
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| 8000 | 1F40 |
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| 8500 | 2134 |
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| 9000 | 2328 |
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| 9500 | 251C |
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| 10000 | 2710 |
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## Extra large
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| dec | hex |
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| -----: | ----: |
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| 10000 | 2710 |
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| 11000 | 2AF8 |
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| 12000 | 2EE0 |
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| 13000 | 32C8 |
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| 14000 | 36B0 |
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| 15000 | 3A98 |
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| 16000 | 3E80 |
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| 17000 | 4268 |
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| 18000 | 4650 |
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| 19000 | 4A38 |
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| 20000 | 4E20 |
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| 21000 | 5208 |
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| 22000 | 55F0 |
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| 23000 | 59D8 |
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| 24000 | 5DC0 |
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| 25000 | 61A8 |
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| 26000 | 6590 |
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| 27000 | 6978 |
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| 28000 | 6D60 |
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| 29000 | 7148 |
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| 30000 | 7530 |
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## Shifts/powers of 2 in dec and hex
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```bash
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$ printf "%s\t%s\t%s\n" "n" "1 << n (hex)" "1 << n (dec)" ; for i in {0..15..1} ; do printf "%d\t%X\t\t%d\n" "$i" $(( 1 << "$i" )) $(( 1 << "$i" )) ; done
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```
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`1 << n` is the same as `2^n`.
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| `n` | `1 << n` (hex) | `1 << n` (dec) |
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| -----: | -------------: | -------------: |
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| 0 | 1 | 1 |
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| 1 | 2 | 2 |
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| 2 | 4 | 4 |
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| 3 | 8 | 8 |
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| 4 | 10 | 16 |
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| 5 | 20 | 32 |
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| 6 | 40 | 64 |
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| 7 | 80 | 128 |
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| 8 | 100 | 256 |
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| 9 | 200 | 512 |
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| 10 | 400 | 1024 |
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| 11 | 800 | 2048 |
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| 12 | 1000 | 4096 |
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| 13 | 2000 | 8192 |
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| 14 | 4000 | 16384 |
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| 15 | 8000 | 32768 |
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