123
MIDI Implementation
Appendices
3. Supplementary material
■
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.
* An “H” is appended to the end of numbers in hexadecimal notation.
+——————————————————————————————————————————————————————————+
| 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.
<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
■
Calculation of the Checksum of Exclusive
Messages
Roland Exclusive messages (RQ1, DT1) 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.
❍
How to calculate the checksum (hexadecimal numbers 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 cc ddH and the data or size is ee ff gg hhH.
aa + bb + cc + dd + ee + ff + gg + hh = sum
sum / 128 = quotient ... remainder
128 - remainder = checksum
(However, the checksum will be 0 if the remainder is 0.)
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