K-map for 4 inputs and 7 outputs - hex decoder

Thread Starter

StrongPenguin

Joined Jun 9, 2018
287
I am still in the mist of trying to get better at solving gate problems using K-maps, as I feel this helps with the understanding of how my 8-bit computer works.

In one ("Designing a 7 segment hex decoder") video, Ben Eater (who's computer recipe I'm following) shows a decoder built from scratch. And my first reaction was "how in the world did he do that gate circuit???"

I've been trying to google and Youtube some tutorials on bigger Kmaps, but none of them have more than 2 outputs. From the looks of it, It seems that it is just the same with 2 outputs, as it is with 7, I just do one map per output.

Is this correct? Which programs do you use to test such a monstrosity, if I were to do one? LTspice?
 

WBahn

Joined Mar 31, 2012
26,398
Yes, you can treat each output as a separate logic circuit and do seven independent K-maps. That will probably not result in the smallest circuit as there are likely terms that can be shared between circuits and this approach will not identify them and might even obscure them. But it is a viable way to start and to get a circuit that works.

You can use any of a number of simulators to verify your circuit. LTspice is one option. There are other logic-only options that might be easier if you don't already know how to use LTspice.
 

Thread Starter

StrongPenguin

Joined Jun 9, 2018
287
@WBahn Ok, nice. You say it's a viable way to get things started, but will not yield the most optimal circuit. If I were to create a least possible gates circuit like this, how would I proceed? Is it custom to just start the way like I mentioned, and from there start "cutting" gates out? Or are there other methods when working with a circuit like this, if one wants the most optimal circuit?

@dl324 Manually, as in breadboard? That's what I call discipline, but I guess it also gives good practice.
 

WBahn

Joined Mar 31, 2012
26,398
@WBahn Ok, nice. You say it's a viable way to get things started, but will not yield the most optimal circuit. If I were to create a least possible gates circuit like this, how would I proceed? Is it custom to just start the way like I mentioned, and from there start "cutting" gates out? Or are there other methods when working with a circuit like this, if one wants the most optimal circuit?
I'm not sure that an algorithmic way exists for optimizing multiple-output circuits. There might be, but I'm not aware of one. Looking for common groupings among the various K-maps should reveal most of the common logic.

Also, the very notion of "optimal" is misleading as there are several different metrics by which to say that Solution A is "more optimal" than Solution B. K-maps can be used to optimize against a particular metric, namely minimizing SOP or POS forms.
 

Thread Starter

StrongPenguin

Joined Jun 9, 2018
287
@WBahn Agree very much on the optimal situation. I was more implying on getting down to a reasonable number of gates, and not having 7 gates doing the same thing.

@dl324 I just downloaded Logism, which I've heard good things about. Gonna try and have some fun with that.
 
Top