Is it possible to use just one 1-of-8 decoder in order to generate a function with 16 possible minterms? ex) can i generate minterms 0,1,2,10,11,12 with just one 1-of-8 decoder

I think its only possible with 2x 1-of-8 decoders but am not entirely sure.

 

Decoders don't generate minterms. They decode a particular value of the three inputs. In other words they can recognize a single 3 bit minterm. Multiplexers are used to generate functions. What you want is a 16 input multiplexer with four select lines that can generate any boolean function of 4 inputs (the select lines). The values of the function are wired to the 16 multiplexer inputs. You wire a logic 1 for each minterm and a 0 for the rest

 

if i AND together all of the outputs that are not part of the function it will generate my function

 

You lost me -- the multiplexer has only a single output. What are you ANDing together?

 

No fair you edited the original question, and no you can't use decoders to realize arbitrary collections of minterms. Each decoder will recognize a single minterm and activate a unique output. With two decoders and a gate you can recognize a function of two minterms.

 

if my variables running to the decoder come from a counter it will run through the numbers and effectively produce a ONE for each one of my minterms and ZERO for any term that is not a minterm

 

No it won't. I guess you better show us a schematic because I don't think you understand a thing that I've said.

 

http://image.slidesharecdn.com/l25-...2/95/l25hegdeunlocked-8-638.jpg?cb=1414382670

 

As I said, "each decoder can recognize one single minterm at a time". A function composed of 2 to 15 minterms would require 1 decoder per minterm plus an OR gate with enough inputs to combine from 2 to 15 minterms. A function with 1 minterm can be realized with a single decoder, and a function with 16 unique 4 input minterms is always 1.

On the other hand you can use a single 16:1 multiplexer with no external gates.

And the answer to your original question is still no.

I'm done -- stick me with a fork.

 

If you have a 3-to-8 decoder then, with a suitable OR gate following it, you can generate an arbitrary function of three inputs. If you want an arbitrary function of four inputs, you need a way to deal with the fourth input. Using the enable input allows you to force the output to be zero for one state of one of the inputs, but that isn't enough in general. So you would need two such decoders, as you suspected, along with an inverter so that you enable one while disabling the other and also with an OR gate that has as many inputs as you have minterms in your function.

You do not want to AND them together because that will force the output to always be LO.

 

If you wanted to use a MUX, you could use a single 8:1 mux along with a single inverter in order to implement an arbitrary function of 4 variables.