simplifying logic

I'm building a simple circuit to hook up to a 7segment LED, from the truth tables I get:

Out = (A'B'C'D') + (AB'C'D') + (ABCD') + (A'B'CD)

Out = B'C'D'(A' + A) + C((ABD') + (A'B'D))

Out = B'C'D' + C((ABD') + (A'B'D))

Apparently it can be expressed more simple (and so use less gates), but I can't see it?

Are you using an Arduino?

If so, use a little array for each LED.

I assume that this is an assignment but try combining the first and fourth terms and the 2nd and 3rd.


Ah, thanks Pete - yes, it's a tutorial exercise.

Out = (A'B'C'D') + (AB'C'D') + (ABCD') + (A'B'CD)

Out = A'B'(C'D' + CD) + AD'(B'C' + BC)

Out = A'B'(CxorD) + AD'(BxorC)

That was obvious once it was pointed out, I must have tried every arrangement except that one :slight_smile:
Now to build it :slight_smile:

Is that really the simplest form of this circuit I wonder?
They both use 10 gates, although the first one needs three 3input AND gates so I suppose the second circuit is a bit simpler.

Why not use an 4511, all problems solved.


Karnaugh maps look interesting.

Hmm, that gives my first solution again - doh! :~

Then there's the "look at a display decoder/driver data sheet" method:

Easier to just shift the code into a shift register from an array.

Sadly I can't use a chip, I'm building the decoder from gates and so I need the most efficient solution.

I don't have any issue with that.,
So you don't think the decoder implemented by manucturer's is efficient?
I doubt you could improve it it much.
You need to control all 7 segments? You only seem to be decoding for 1 at the moment.

I can't comment on the efficiency of Texus Instruments ICs, I suspect they are quite good considering they've been doing it a while 8)

I need to build it using basic logic gates using the minimum number of gates and as that would get a bit busy for all 7 segments, I only need to get 1 element working.

I guess there is a clue in that Ti circuit diagram, but it's a bit tricky to follow.

Not really. Look at the LS49 diagram.
Each input becomes A, A/, B, B/, C, C/ and D, D/ using the inverter and the NAND gate.
Ignore the blanking input, and you can get by with the original signal and the inverter to make A, A/, etc.
Then each output is just the 3 AND gates and the following gate to collect the AND gate outputs. If you make the AND gates all NAND gates, the final stage is just a 2 or 3 input AND gate.
So, A just becomes this:

And you could make the whole thing with 4 input NAND gates, tieing any unused inputs HIGH.

Using all NAND gates.

Thanks for all the help, I've certainly learnt a great deal about boolean algebra :slight_smile: