Theory

The decoder is like a backwards multiplexer, it uses the selector bits to output a DATA 1 on a single output, and DATA 0 on the others. This can be used to enable one of many modules, or just to change encoding from binary to one-hot.

Design

If you remember how we made the MUX module, we had a loop that generated a set of selector lines (DATA0 or DATA1 from each selector input) for each case. We will re-use this, but we will generate a TRUE and FALSE signal for each case (DATA0 and DATA1 of the corresponding output). The TRUE gate for each case will be a THNN, and the FALSE gate will be a TH1N. Here is what a Decoder2 module would look like:

The inputs to the TH1N gates (FALSE) are the opposing rails to the THNN gate of the same case.

• CaseTrue='All bits for this case set'
• CaseFalse='Any other bit set'

Any NULL input produces some NULL output: The THNN gates (TRUE) can’t set because they will always be missing an input, and for any particular input (missing a bit) there are two possible outputs: one with the bit set and one with it clear; these FALSE outputs will remain off as they need the DATA0 and DATA1 respectively from the missing input.

The decoder is actually a fairly simple gate. It is possible to split the DMUX into two parts: DMUX1, and DMUX0. These components would output the DATA1 and DATA0 lines respectively. They are not valid as complete NCL components, but they are useful: You can make a MUX by using a DMUX1 and 2*NumOptions TH22 gates. This might be especially useful when making a MUX that takes in multi-bit options. A single DMUX1 would be used to generate the control signals, and each signal of each bit of each option would be gated with the TH22 gates.