Some modular synth manufacturers offer modules which perform Boolean logic functions using digital logic signal conventions that are compatible with the signal levels used in modular synths. Logic functions are sometimes used by modular synth performers to combine or make decisions about triggering gates (e.g. as driven by an analog sequencer), or to make more complex quasi-random patterns from simple inputs.
In Boolean logic, each signal can be in one of two states, known as "true" and "false", usually abbreviated T and F. Most manufacturers of logic modules implement a convention in which any signal with a voltage level of +5 volts are higher is considered true, and anything below +5V is considered false. There are only three basic Boolean operations:
- AND: Takes two or more inputs. The output is T if and only if all of the inputs are T; otherwise the output is F.
- OR: Takes two or more inputs. The output is T if at least one of the inputs is T. The output is F only when all of the inputs are F.
- NOT: Takes one input. The output is T when the input is F, and vice versa.
The theory of Boolean logic states that all other operations can be formed from combinations of the basic three. However, more complex operations are often offered as self-contained units, in order to save on circuits and patching. Here are a few compound operations:
- NAND: Takes two or more inputs. This is an AND with a NOT on the output. The output is T if at least one of the inputs is F. (In other words, the output is the opposite of the AND output.)
- NOR: Takes two or more inputs. The output is T when all of the inputs are F.
- XOR: Takes two inputs. The output is T when the inputs are different (the first input is T and the second is F, or vice versa). The output is F when the inputs are the same.
Most logic modules will output a level of +5V for a T output, and 0V for a F output. These levels are almost but not quite the same as the thresholds used by the 4000-series CMOS logic integrated circuits. Something to be aware of is that most logic circuits are not designed to take negative voltages on the inputs. Most logic modules take care of this, protecting the inputs and treating any negative voltage at the input as an F. However, it pays to read the manual before using.