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mm/docs/useful_conversions.md

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Useful conversions

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.

Degrees and hex/binary angles

Conversion of degrees to binary angles in the two common ways, that give different answers. Table is produced using this script:

$ 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

Small angles

d d * 2^16/360 2^16/360 * d
0 0 0
1 B6 B6
2 16C 16C
3 222 222
4 2D8 2D8
5 38E 38E
6 444 444
7 4FA 4FA
8 5B0 5B0
9 666 666
10 71C 71C
11 7D2 7D2
12 888 888
13 93E 93E
14 9F4 9F4
15 AAA AAA
16 B60 B60
17 C16 C16
18 CCC CCC
19 D82 D82
20 E38 E38
21 EEE EEE
22 FA4 FA4
23 105B 105A
24 1111 1110
25 11C7 11C6
26 127D 127C
27 1333 1332
28 13E9 13E8
29 149F 149E
30 1555 1554

Larger angles

d d * 2^16/360 2^16/360 * d
0 0 0
5 38E 38E
10 71C 71C
15 AAA AAA
20 E38 E38
25 11C7 11C6
30 1555 1554
35 18E3 18E2
40 1C71 1C70
45 2000 1FFE
50 238E 238C
55 271C 271A
60 2AAA 2AA8
65 2E38 2E36
70 31C7 31C4
75 3555 3552
80 38E3 38E0
85 3C71 3C6E
90 4000 3FFC
95 438E 438A
100 471C 4718
105 4AAA 4AA6
110 4E38 4E34
115 51C7 51C2
120 5555 5550
125 58E3 58DE
130 5C71 5C6C
135 6000 5FFA
140 638E 6388
145 671C 6716
150 6AAA 6AA4
155 6E38 6E32
160 71C7 71C0
165 7555 754E
170 78E3 78DC
175 7C71 7C6A
180 8000 7FF8
185 838E 8386
190 871C 8714
195 8AAA 8AA2
200 8E38 8E30
205 91C7 91BE
210 9555 954C
215 98E3 98DA
220 9C71 9C68
225 A000 9FF6
230 A38E A384
235 A71C A712
240 AAAA AAA0
245 AE38 AE2E
250 B1C7 B1BC
255 B555 B54A
260 B8E3 B8D8
265 BC71 BC66
270 C000 BFF4
275 C38E C382
280 C71C C710
285 CAAA CA9E
290 CE38 CE2C
295 D1C7 D1BA
300 D555 D548
305 D8E3 D8D6
310 DC71 DC64
315 E000 DFF2
320 E38E E380
325 E71C E70E
330 EAAA EA9C
335 EE38 EE2A
340 F1C7 F1B8
345 F555 F546
350 F8E3 F8D4
355 FC71 FC62
360 10000 FFF0

Similarly for small angles with a smaller increment:

Round decimal numbers in hex

printf "%s\t%s\n" "dec" "hex" ; for i in {0..100..5} ; do printf "%d\t%X\n" "$i" "$i" ; done

Small

dec hex
0 0
5 5
10 A
15 F
20 14
25 19
30 1E
35 23
40 28
45 2D
50 32
55 37
60 3C
65 41
70 46
75 4B
80 50
85 55
90 5A
95 5F
100 64

Medium

dec hex
100 64
150 96
200 C8
250 FA
300 12C
350 15E
400 190
450 1C2
500 1F4
550 226
600 258
650 28A
700 2BC
750 2EE
800 320
850 352
900 384
950 3B6
1000 3E8

Large

dec hex
1000 3E8
1500 5DC
2000 7D0
2500 9C4
3000 BB8
3500 DAC
4000 FA0
4500 1194
5000 1388
5500 157C
6000 1770
6500 1964
7000 1B58
7500 1D4C
8000 1F40
8500 2134
9000 2328
9500 251C
10000 2710

Extra large

dec hex
10000 2710
11000 2AF8
12000 2EE0
13000 32C8
14000 36B0
15000 3A98
16000 3E80
17000 4268
18000 4650
19000 4A38
20000 4E20
21000 5208
22000 55F0
23000 59D8
24000 5DC0
25000 61A8
26000 6590
27000 6978
28000 6D60
29000 7148
30000 7530

Shifts/powers of 2 in dec and hex

$ 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

1 << n is the same as 2^n.

n 1 << n (hex) 1 << n (dec)
0 1 1
1 2 2
2 4 4
3 8 8
4 10 16
5 20 32
6 40 64
7 80 128
8 100 256
9 200 512
10 400 1024
11 800 2048
12 1000 4096
13 2000 8192
14 4000 16384
15 8000 32768