Chapter 11: Reference Section 251
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 add-
ing 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 r-1
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 r-1
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.
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