Roland VK-8 owner manual Midi Implementation Supplementary material, How to calculate the checksum

MIDI Implementation

4. Supplementary material

■Decimal/Hexadecimal Table

MIDI uses 7-bit hexadecimal values to indicate data values and the address and size of exclusive messages. The following table shows

the correspondence between decimal and hexadecimal numbers.

*Hexadecimal values are indicated by a following ‘H.’

+——————+——————++——————+——————++——————+——————++——————+——————+ 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 expressions such as used for MIDI channel, Bank Select, and Program Change will be the value 1 greater than the decimal value given in the above table.

*Since each MIDI byte carries 7 significant data bits, each byte can express a maximum of 128 different values. Data for which higher resolution is required must be transmitted using two or more bytes. For example a value indicated as a two-byte value of aa bbH would have a value of aa x 128 + bb.

*For a signed number (±), 00H = -64, 40H = ±0, and 7FH = +63. I.e., the decimal equivalent will be 64 less than the decimal value given in the above table. For a two-byte signed number, 00 00H = -8192, 40 00H = ±0, and 7F 7FH = +8191. For example the decimal expression of aa bbH would be aa bbH - 40 00H = aa x 128 + bb - 64 x 128.

Hexadecimal notation in two 4-bit units is used for data indicated as “nibbled.” The nibbled two-byte value of 0a 0b H would be a x 16 + b.

<Example1> What is the decimal equivalent of 5AH?

From the above table, 5AH = 90.

<Example2> What is the decimal equivalent of the 7-bit hexadecimal values 12 34H?

From the above table, 12H = 18 and 34H = 52

Thus, 18 x 128 + 52 = 2356

■Examples of Actual MIDI Messages

<Example1> 93 3E 5F

9n is the Note On status and ‘n’ is the MIDI channel number. Since 3H = 3, 3EH = 62, and 5FH = 95, this is a Note On message of MIDI CH = 4, note number 62 (note name D4) and velocity 95.

<Example2> C0 25

CnH is the Program Change status and ‘n’ is the MIDI channel number. Since 0H = 0, and 25H = 37, this is a Program Change message of MIDI CH = 1, Program number 38

■Examples of System Exclusive Messages and

Calculating the Checksum

Roland exclusive messages (RQ1, DT1) are transmitted with a checksum at the end of the data (before F7) to check that the data was received correctly. The value of the checksum is determined by the address and data (or size) of the exclusive message.

●How to calculate the checksum

The checksum consists of a value whose lower 7 bits are 0 when the address, size and checksum itself are added. The following formula shows how to calculate the checksum when the exclusive message to be transmitted has an address of aa bb cc ddH, and data or size of ee ffH.

aa+ bb + cc + dd + ee + ff = total total ÷ 128 = quotient ... remainder 128 - remainder = checksum

<Example1> Turn the Temporary Preset Organ percussion switch ON

(DT1).

The “Parameter address map” indicates that the starting address of the Temporary Preset is 10 00 00 00H, that the Preset Organ Parameter offset address is 10 00H, and that the “PERCUSSION SWITCH” address is 00 14H. Thus, the address is:

	10 00		00	00H
			10	00H
+)			00 14H
---------------
	10 00		10	14H
Since “ON” is parameter value 01H,
F0	41	10		00 4D	12 10 00 10 14	01	??	F7
(1)	(2)	(3)		(4)	(5) address	data	checksum	(6)
(1) Exclusive status					(2) ID number (Roland)		(3) device ID(17)
(4) model ID (VK-8)					(5) command ID (DT1)		(6) EOX

Next we calculate the checksum.

10H + 00H + 10H + 14H + 01H = 16 + 0 + 16 + 20 + 1 = 53 (sum) 53 (total) ÷ 128 = 0 (quotient)... 53 (remainder)

checksum = 128 - 53 (quotient) = 75 = 4BH

This means that the message transmitted will be F0 41 10 00 4D 12 10 00 10 14 01 4B F7.

<Example2> Obtain preset organ parameter data for User Preset: 02

(RQ1).

The “Parameter address map” indicates that the starting address of USER: 02 is 20 01 00 00H, and that the offset address of Organ Parameter is 10 00H. Thus, the address is:

	20 01		00	00H
+)			10 00H
---------------
	20 01		10	00H
Since the size of the Performance Part is 00 00 00 1AH,
F0	41	10		00 4D	11	20 01 10 00	00 00 00 1A	??	F7
(1)	(2)	(3)		(4)	(5)	address	data	checksum	(6)
(1) Exclusive status					(2) ID number (Roland)			(3) Device ID (17)
(4) Model ID (VK-8)					(5) Command ID (RQ1)			(6) EOX

Next we calculate the checksum.

20H + 01H + 10H + 00H + 00H + 00H + 00H + 1AH = 32 + 1 + 16 + 0 + 0 + 0 + 0 + 26 = 75 (sum)

75 (total) ÷ 128 = 0 (product)... 75 (remainder) checksum = 128 - 75 (remainder) = 53 = 35H

Thus, a message of F0 41 10 00 4D 11 20 01 10 00 00 00 00 1A 35 F7 would be transmitted.

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