mm/docs/useful_conversions.md

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
  • Small angles
  • Larger angles
• Round decimal numbers in hex
  • Small
  • Medium
  • Large
• Extra large
• Shifts/powers of 2 in dec and hex

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