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277 Chapter 11: Reference Section
SYSEX TUTORIAL
14-BIT SIGNED 2'S COMPLEMENT NUMBERS
If the data value is negative, you must first take the 2's complement of the
number: In the case of a 14-bit number this is equivalent to adding 16384 to the
original negative value.
To fit the 7-bit MIDI protocol, numbers must be “nibble-ized”.
To get the 14-bit nibble-ized value (of a positive value or a 2's
complemented negative value):
msb = value DIV 128 (divide and ignore the remainder)
lsb = value MOD 128 (divide and use only the remainder)
To go the other way (convert 14 bit signed 2's complement to a signed real
number)
raw Value = (msb*128) + lsb (gives you the unsigned raw value) if
raw Value
≥
8192 (8192 = 2^13)
then signed Value = raw value - 16384 (16384 = 2^14)
Example: To find the “nibble-ized” Hex value of -127:
1) -127 + 16384 = 16257
2) 16257
÷
128 = 127 r1
3) 127 in Hex = 7F = msb
4) 1 in Hex = 01 = lsb
5) Parameter value would be transmitted as 01 7F
Example: To find the “nibble-ized” Hex value of parameter number 257:
1) 257
÷
128 = 2 r1
2) 2 in Hex = 02 = msb
3) 1 in Hex = 01 = lsb
4) Parameter number would be transmitted as 01 02
00000000 00000000
{ {
data bits data bits
Status
Bit
Status
Bit
Status Bit MUST be “0” in MIDI
data bytes.