Roland Edirol PCR-1 Owner's Manual page 120

MIDI implementation
4. 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
Dec. Hex. Dec. Hex.
0 00H 32 20H
1 01H 33 21H
2 02H 34 22H
3 03H 35 23H
4 04H 36 24H
5 05H 37 25H
6 06H 38 26H
7 07H 39 27H
8 08H 40 28H
9 09H 41 29H
10 0AH 42 2AH
11 0BH 43 2BH
12 0CH 44 2CH
13 0DH 45 2DH
14 0EH 46 2EH
15 0FH 47 2FH
16 10H 48 30H
17 11H 49 31H
18 12H 50 32H
19 13H 51 33H
20 14H 52 34H
21 15H 53 35H
22 16H 54 36H
23 17H 55 37H
24 18H 56 38H
25 19H 57 39H
26 1AH 58 3AH
27 1BH 59 3BH
28 1CH 60 3CH
29 1DH 61 3DH
30 1EH 62 3EH
31 1FH 63 3FH
* 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
120
Dec. Hex. Dec. Hex.
64 40H 96 60H
65 41H 97 61H
66 42H 98 62H
67 43H 99 63H
68 44H 100 64H
69 45H 101 65H
70 46H 102 66H
71 47H 103 67H
72 48H 104 68H
73 49H 105 69H
74 4AH 106 6AH
75 4BH 107 6BH
76 4CH 108 6CH
77 4DH 109 6DH
78 4EH 110 6EH
79 4FH 111 6FH
80 50H 112 70H
81 51H 113 71H
82 52H 114 72H
83 53H 115 73H
84 54H 116 74H
85 55H 117 75H
86 56H 118 76H
87 57H 119 77H
88 58H 120 78H
89 59H 121 79H
90 5AH 122 7AH
91 5BH 123 7BH
92 5CH 124 7CH
93 5DH 125 7DH
94 5EH 126 7EH
95 5FH 127 7FH
<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
●Example of an actual MIDI message
<Example1> CE 04
CnH is the Program Change status. "n" is the MIDI channel number. EH = 14, and
04H = 04. Thus, this is a program change message on MIDI channel 15, for program
number 05.
●Checksum calculation
In order to verify that the message was received correctly, Roland exclusive
messages (RQ1, DT1) add a checksum following the end of the data (before the F7).
The checksum value is determined by the address and data (or size) of the
exclusive message that is transmitted.
❍Calculating the checksum
("H" has been added following hexadecimal values)
The checksum is a value that results in a lower 7 bits of 0 when the address, size,
and checksum itself are added together.
Specifically, the calculation will be as follows when the exclusive message you
want to transmit has an address of aa bb ccH and data or size of dd ee ffH.
aa + bb + cc + dd + ee + ff = total
total ÷ 128 = quotient ... remainder
128 - remainder = checksum
* However, as an exception, the checksum for a remainder of 0 is not 80H but
rather 00H.
00 04 0E 0AH