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81
MIDI implementation
2. Supplementary material
●
Decimal and Hexadecimal table
(An “H” is appended to the end of numbers in hexadecimal notation.)
In MIDI documentation, data values and addresses/sizes of Exclusive messages,
etc. are expressed as hexadecimal values for each 7 bits.
The following table shows how these correspond to decimal numbers.
fig.11-22e
* The decimal expression of the MIDI channel, program change, etc., is one
greater than the decimal value shown in the table above.
* The hexadecimal expression for each 7 bits allows a maximum of 128 steps (0--
127) to be expressed by one byte of data. Multiple bytes are used if the data
requires greater resolution than this. For example, a value expressed by two 7-
bit bytes “aa” and “bbH” would be aa x 128 + bb.
* In the case of signed (+/-) data, 00H = -64, 40H = +/-0, and 7FH = +63; i.e., a
value 64 less than the decimal value shown in the above table is used. In the
case of a two-byte value, 00 00H = -8192, 40 00 = +/-0, and 7F 7F = +8191. For
example, a value of “aa” and “bbH” would have a decimal expression of aa
bbH - 40 00H = aa x 128 + bb - 64 x 128.
* In the case of data indicated as “use nibble data,” hexadecimal expression in 4-
bit units is used. A nibble-expressed value of the two bytes 0a and 0bH would
have a value of a x 16 + b.
<Example1>
What is the decimal expression of 5AH?
From the preceding table, 5AH = 90.
<Example2>
What is the decimal expression of the 7-bit hexadecimal value 12 34H?
From the preceding table, 12H = 18, and 34H = 52.
Thus, this is 18 x 128 + 52 = 2356
<Example3>
What is the decimal expression of the nibble-expressed value 0A 03 09 0D?
From the preceding table, 0AH = 10, 03H = 3, 09H = 9, and 0DH = 13.
Thus, this is ((10 x 16 + 3) x 16 + 9) x 16 + 13 = 41885
<Example4> What is the nibble-expressed value of decimal 1258?
1258 ÷ 16 = 78 (quotient) ... 10 (remainder)
78 ÷ 16 = 4 (quotient) ... 14 (remainder)
4 ÷ 16 = 0 (quotient) ... 4 (remainder)
From the preceding table, 0 = 00H, 4 = 04H, 14 = 0EH, 10 = 0HA.
Thus, the nibble-expressed value is 00 04 0E 0AH
Dec. Hex. Dec. Hex. Dec. Hex. Dec. Hex.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
00H
01H
02H
03H
04H
05H
06H
07H
08H
09H
0AH
0BH
0CH
0DH
0EH
0FH
10H
11H
12H
13H
14H
15H
16H
17H
18H
19H
1AH
1BH
1CH
1DH
1EH
1FH
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
20H
21H
22H
23H
24H
25H
26H
27H
28H
29H
2AH
2BH
2CH
2DH
2EH
2FH
30H
31H
32H
33H
34H
35H
36H
37H
38H
39H
3AH
3BH
3CH
3DH
3EH
3FH
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
40H
41H
42H
43H
44H
45H
46H
47H
48H
49H
4AH
4BH
4CH
4DH
4EH
4FH
50H
51H
52H
53H
54H
55H
56H
57H
58H
59H
5AH
5BH
5CH
5DH
5EH
5FH
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
60H
61H
62H
63H
64H
65H
66H
67H
68H
69H
6AH
6BH
6CH
6DH
6EH
6FH
70H
71H
72H
73H
74H
75H
76H
77H
78H
79H
7AH
7BH
7CH
7DH
7EH
7FH
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