Theseus Research : Technical Papers : NULL Convention Logic™ Page 7 of 26
3. Two Value NULL Convention Logic

We have shown how to make Boolean logic purely symbolically complete as a four value logic system and practically symbolically complete as a three value logic system, but three and four value logic systems are not commercially viable. The next step is to show how the NULL Convention can be applied to a system with only two values such as our favorite digital electronic implementation environment.

If the logic is limited to two values (0 volts and 5 volts for instance) in its primitive mutually exclusive value assertion domain (a wire for instance) and one value must be assigned to express NULL (0 volts), this leaves only one value remaining to express data. This means that each wire can express only one data meaning which we will call DATA (5 volts). Two data meanings, True and False for instance, must be expressed with two wires (one wire asserting DATA means TRUE, the other wire asserting DATA means FALSE). With no inherent means to prevent any two wires from expressing their DATA values simultaneously there is no longer an inherently enforced mutually exclusive value assertion domain for data meanings as there was when two data meanings were by physical necessity mutually exclusively asserted by a single wire. Since there must be mutually exclusive assertion of DATA values it must be reestablished by convention.

Each wire is still an inherent mutually exclusive value assertion domain that asserts either DATA or NULL. To reestablish mutually exclusive assertion of data meanings, a convention that only one wire of a group of wires will assert its DATA value at a time. It is illegal or erroneous for two or more wires within this group to simultaneously assert DATA values. A group of wires that assert mutually exclusive data meanings will be called a mutually exclusive assertion group.

A mutually exclusive assertion group can be any size. A group of ten wires can directly express decimal numbers with each wire expressing a digit value. A group of two wires can directly express True and False. The two wire mutually exclusive assertion group is identical to dual rail encoding, which is traditionally used as a transmission protocol between speed independent circuits. The mutually exclusive assertion group in NULL Convention Logic is a much more general concept than dual rail transmission encoding. It is not just a transmission protocol but is inherent in the logic itself.

The Single Data Value Logic Gate

NULL expresses a control meaning and is meaningless with respect to data. In fact NULL means "not data", so the NULL value cannot be considered in resolving data value sets. Since each input to a gate can express only one DATA value (5 volts for instance) there can be no combinations of different data values as in Boolean logic. The only discriminable property available when combining wires at the input to a gate is how many DATA values are presented. Therefore, NULL Convention Logic gates must be discrete threshold gates. A complete input data set for a threshold gate is sufficient DATA values to meet its threshold. Figure 5 shows a 5 input/threshold 3 gate. If any three or more inputs are DATA the gate will assert a result DATA value. Otherwise it asserts a NULL value.