Binary Logic Math

stream byter - binary logic math - midi messages - midi designer pro - dk70

This is all a bit "low level", but I needed that.

Bit operators for Stream Byter

MAT I0 = I0 & 0F # AND
MAT I0 = I0 | 0F # OR
MAT I0 = I0 ^ FF # XOR

Binary math

Most of the time, you can not use bitpatterns in your code. Unfortunately.
Everything has to be converted to hex or to dec first (binary boolean calculator).
So you need comments to explain what you did there.

Bottom line.
You basically need an "on" and "off" switch, a toggle switch and a "leave the bit alone" operator function.
You could do all this with just AND and OR, but the XOR is a nice addition, because it makes programming lazier.

Examples

AND (get value of one bit)
# TEST BIT 3 VALUE
result = 0111 AND 0100 # result = 0100, meaning bit 3 is 'On'
result = 7 & 4 # result = 4

# result for 'Off' is 0
# because you cunningly filtered out the rest of the bits with '0' so they are not a part of the result
# possible results for 'On' are 8, 4, 2 and 1, depending on which bit you tested
# however, '>= 1' or 'not 0' would suffice, because you already know which bit you tested

# TEST BIT 3 VALUE
result = 1011 AND 0100 # result = 0000, meaning bit 3 is 'Off'
result = A & 4 # result = 0

OR (set one bit to 1)
# SET BIT 2 TO ON
result = 0100 OR 0010 # result = 0110, set bit 2 to 'On'
result = 4 | 2 # result = 6, which you can use to set the variable

AND (set one bit to 0)
# SET BIT 2 TO OFF
result = 0110 AND 1101 # result = 0100, set bit 2 to 'Off'
result = 6 & 13 # result = 4, the only calculation with a right part that has a higher number than the left

XOR (toggle one bit)
# TOGGLE BIT 3 VALUE
result = 0110 XOR 0100 # result = 0010
result = 6 ^ 4 # result = 2

So there. Very handy for working with SysEx messages.
And programming in assembly.

The next part is just for fun. Curiosity educates the cat.

Boolean Operators

The 4 possible results for logical operation on a bit:
- switch the bit on
- switch the bit off
- toggle the bit (from 1 to 0 or vice versa)
- don't change the bit

Every logical operator (AND, NOT, OR..) can only execute two ['what does 0 do, and what does 1 do'] of the above four possible operations in one go.
You could say that the operator is basically defined, by which 2 operations of the possible 4 it executes.

result = bitpatternA <operator> bitpatternB

The table focuses on what the right side (B) of the operator does to the left side (A) of the operator.
The table lists all possible (16 minus 2) results from 0001 to 1110 in the 'res' row.
The 2 results '0000' and '1111' are omitted, because the have no use.
The yellow cells show useless functions, or functions that can be achieved easily with existing operators.
See also Boolean Operators.

result = bitpatternA <operator> bitpatternB

'On' and 'Off' are "hard settings". When an operator results in only hard settings, you don't need that operator and you might as well have set the value with a simple assign. Or, as one developer put it: "The best time to use them (truth tables) is when you map your logic and realize you have a function that takes two inputs, and has the same outputs as those operators :)".

result of A when
B = 1	B = 0	operator
on	on	no use
	off	no use
	toggle	IMPLIES
	no change	OR
off	on	no use
	off	no use
	toggle	NOR
	no change
toggle	on	NAND
	off
	toggle
	no change	XOR
no change	on
	off	AND
	toggle	XNOR
	no change

Funny that an on/off switch can have so much theory.

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