MIDI Implementation
12
3. Supplementary Material
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Decimal and Hexadecimal Table
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.
+------+------++------+------++------+------++------+------+
| D | H || D | H || D | H || D | H |
+------+------++------+------++------+------++------+------+
| 0 | 00H || 32 | 20H || 64 | 40H || 96 | 60H |
| 1 | 01H || 33 | 21H || 65 | 41H || 97 | 61H |
| 2 | 02H || 34 | 22H || 66 | 42H || 98 | 62H |
| 3 | 03H || 35 | 23H || 67 | 43H || 99 | 63H |
| 4 | 04H || 36 | 24H || 68 | 44H || 100 | 64H |
| 5 | 05H || 37 | 25H || 69 | 45H || 101 | 65H |
| 6 | 06H || 38 | 26H || 70 | 46H || 102 | 66H |
| 7 | 07H || 39 | 27H || 71 | 47H || 103 | 67H |
| 8 | 08H || 40 | 28H || 72 | 48H || 104 | 68H |
| 9 | 09H || 41 | 29H || 73 | 49H || 105 | 69H |
| 10 | 0AH || 42 | 2AH || 74 | 4AH || 106 | 6AH |
| 11 | 0BH || 43 | 2BH || 75 | 4BH || 107 | 6BH |
| 12 | 0CH || 44 | 2CH || 76 | 4CH || 108 | 6CH |
| 13 | 0DH || 45 | 2DH || 77 | 4DH || 109 | 6DH |
| 14 | 0EH || 46 | 2EH || 78 | 4EH || 110 | 6EH |
| 15 | 0FH || 47 | 2FH || 79 | 4FH || 111 | 6FH |
| 16 | 10H || 48 | 30H || 80 | 50H || 112 | 70H |
| 17 | 11H || 49 | 31H || 81 | 51H || 113 | 71H |
| 18 | 12H || 50 | 32H || 82 | 52H || 114 | 72H |
| 19 | 13H || 51 | 33H || 83 | 53H || 115 | 73H |
| 20 | 14H || 52 | 34H || 84 | 54H || 116 | 74H |
| 21 | 15H || 53 | 35H || 85 | 55H || 117 | 75H |
| 22 | 16H || 54 | 36H || 86 | 56H || 118 | 76H |
| 23 | 17H || 55 | 37H || 87 | 57H || 119 | 77H |
| 24 | 18H || 56 | 38H || 88 | 58H || 120 | 78H |
| 25 | 19H || 57 | 39H || 89 | 59H || 121 | 79H |
| 26 | 1AH || 58 | 3AH || 90 | 5AH || 122 | 7AH |
| 27 | 1BH || 59 | 3BH || 91 | 5BH || 123 | 7BH |
| 28 | 1CH || 60 | 3CH || 92 | 5CH || 124 | 7CH |
| 29 | 1DH || 61 | 3DH || 93 | 5DH || 125 | 7DH |
| 30 | 1EH || 62 | 3EH || 94 | 5EH || 126 | 7EH |
| 31 | 1FH || 63 | 3FH || 95 | 5FH || 127 | 7FH |
+------+------++------+------++------+------++------+------+
D: decimal
H: hexadecimal
* Decimal values such as MIDI channel, bank select, and program change are listed as
one (1) greater than the values given in the above table.
* A 7-bit byte can express data in the range of 128 steps. For data where greater
precision is required, we must use two or more bytes.
For example, two hexadecimal numbers aa bbH expressing two 7-bit bytes would
indicate a value of aa x 128 + bb.
* In the case of values which have a ± sign, 00H = -64, 40H = ±0, and 7FH = +63, so
that the decimal expression would be 64 less than the value given in the above
chart. In the case of two types, 00 00H = -8192, 40 00H = ±0, and 7F 7FH = +8191.
For example if aa bbH were expressed as decimal, this would be
aa bbH - 40 00H = aa x 128 + bb - 64 x 128.
* Data marked “nibbled” is expressed in hexadecimal in 4-bit units. A value expressed
as a 2-byte nibble 0a 0bH has the 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 value 12 34H given as hexadecimal for each 7
bits?
From the preceding table, since 12H = 18 and 34H = 52
18 x 128 + 52 = 2356
<Example3>
What is the decimal expression of the nibbled value 0A 03 09 0D?
From the preceding table, since 0AH = 10, 03H = 3, 09H = 9, 0DH = 13
((10 x 16 + 3) x 16 + 9) x 16 + 13 = 41885
<Example4>
What is the nibbled expression of the decimal value 1258?
16) 1258
16) 78... 10
16) 4... 14
0... 4
Since from the preceding table, 0 = 00H, 4 = 04H, 14 = 0EH, 10 = 0AH, the answer is
00 04 0E 0AH.
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Examples of Actual MIDI Messages
<Example1> 92 3E 5F
9n is the note on status, and n is the MIDI channel number. Since 2H = 2, 3EH = 62,
and 5FH = 95, this is a note on message with MIDI CH = 3, note number 62 (note
name is D4), and velocity 95.
<Example2> CE 49
CnH is the Program Change status, and n is the MIDI channel number. Since EH = 14
and 49H = 73, this is a Program Change message with MIDI CH = 15, program number
74 (Flute in GS).
<Example3> EA 00 28
EnH is the Pitch Bend Change status, and n is the MIDI channel number. The 2nd byte
(00H = 0) is the LSB and the 3rd byte (28H = 40) is the MSB, but Pitch Bend Value is a
signed number in which 40 00H (= 64 x 128 + 0 = 8192) is 0, so this Pitch Bend Value
is 28 00H - 40 00H = 40 x 128 + 0 - (64 x 128 + 0) = 5120 - 8192 = -3072
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Example of an Exclusive Message and Calculating a
Checksum
Roland Exclusive messages are transmitted with a checksum at the end (before F7)
to make sure that the message was correctly received. The value of the checksum is
determined by the address and data (or size) of the transmitted exclusive message.
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How to Calculate the Checksum (Hexadecimal Num-
bers are Indicated by ‘H’)
The checksum is a value derived by adding the address, size and checksum itself and
inverting the lower 7 bits.
Here’s an example of how the checksum is calculated. We will assume that in the
exclusive message we are transmitting, the address is aa bb ccH and the data or size
is dd ee ffH.
aa + bb + cc + dd + ee + ff = sum
sum / 128 = quotient ... remainder
128 - remainder = checksum
(However, the checksum will be 0 if the remainder is 0.)
