Null Convention Logic Signals

If you don’t yet know what asynchronous logic is, I recommend reading this post (or using Google).

For the time being, I will be focusing my efforts on Null Convention Logic (NCL). NCL is technically a separate logic system from boolean logic. For now, I’ll stick to considering it in the context of a boolean system. What that means is that all signals in the design will still be boolean, they will just represent something a little different.

In NCL, each signal (boolean value) still has 2 meanings, but they are changed. A value of 0 means NO_DATA/NULL and a value of 1 means DATA. Different signals have different Data assigned. To represent a standard boolean variable, 2 lines are needed, the encoding:

• FALSE (0): DATA0=1, DATA1=0
• TRUE (1): DATA0=0, DATA1=1
• Null/Unknown: DATA0=0, DATA1=0

The new state, NULL is used when the circuit hasn’t determined a value for the line yet. Detecting completion of the circuit is then as simple as seeing if one line in each group is set. When all the outputs are assigned a value, the values are saved, and the circuit resets to NULL outputs.

Note, it is entirely possible to have more than two lines in a group. Imagine If I made a circuit that took in an 8-bit color value and outputted if it was mostly one of {Red, Green, Blue}. Instead of having 2 boolean variables for 3 states (wasting a combination), I can have 1 three-state variable: {DATA_RED, DATA_BLUE, DATA_GREEN}. When the circuit is reset, the output is unknown, so all three go to NULL, when the inputs are received and the result found, the circuit sets one of the lines. This is not that different from ‘one-hot’ encoding in synchronous logic, except that it does have a defined all-off state that carries meaning (not data, but it does indicate circuit state). In synchronous logic, such a state would be an error.

The most common encodings I’ve come across so far are 2-rail {DATA0 and DATA1} and 4-rail {DATA0, DATA1, DATA2, DATA3}, representing 1 and 2 boolean variables respectively.

Anyways, that’s the basics of NCL signaling. The thing to remember is that the signals have to go to NULL between calculations, otherwise, there’s no way to know when they are ready.