# Any digital logic help on this (rather basic) problem?

#### beer

##### Lifer
I'm just about done with the combinational-logic part of my logic design course. As a review, I have a lab that I need to do. I don't quite understand it, and I will go into the TA tomorrow, but if anyone could help, I'd appreciate it.

My inputs consist of a 4-bit BCD-coded digit, 0-9.
The output is a x1-x7, outputs that drive a 7-segment display, such as the one that you see on a digital alarm clock.

My job is to design a circuit that outputs the correct output, with no more than 17 NAND gates and inverters. However, I'm supposed to be able to do it by hand. Since I have seven outputs, I would have to do 7 karnaugh maps, right?

That is doable, but if I am to find a near-minimum solution to a 7-output system, a lot of gates are going to be shared. I don't think I'm supposed to be able to find multiple-output prime implicants over 7 4-variable maps. Is there an easier way to do it? Or am I stuck trying to find common factors over SEVEN maps?

#### tikwanleap

##### Senior member
I remember seeing this before. I think the first thing to do is to look at each number and figure out which number has the same segments in common....

next write out the logic for each segment using the four lines as input.

I drew a seven segment display below for reference. Ignore the dots.
.--
[..]
.--
[..]
.--

So for the topmost segment: which numbers will use this segment? 0,2,3,5,6,7,8,9

Ok now you have four inputs and 1 output. Create a karnaugh map with this information.

This will need to be done 7 times total... resulting in 7 karnaugh maps.

Draw out the logic gates and look visually for a gate or a set of gates that are being duplicated. Combine them together.

Hope that helps!

#### beer

##### Lifer
Originally posted by: tikwanleap
I remember seeing this before. I think the first thing to do is to look at each number and figure out which number has the same segments in common....

next write out the logic for each segment using the four lines as input.

I drew a seven segment display below for reference. Ignore the dots.
.--
[..]
.--
[..]
.--

So for the topmost segment: which numbers will use this segment? 0,2,3,5,6,7,8,9

Ok now you have four inputs and 1 output. Create a karnaugh map with this information.

This will need to be done 7 times total... resulting in 7 karnaugh maps.

Draw out the logic gates and look visually for a gate or a set of gates that are being duplicated. Combine them together.

Hope that helps!
I feel so honored. You used your one-post a month on my thread. I feel really special

Yea, your procedure is basically how I figured I would have to do it. Unfortunately, the methods we have for finding essential prime implicants - by hand - are bascially visual in nature, and thus, would be hard to do over the course of 7 different maps. I was hoping there was an easier way, but I guess there isn't. Oh well, time to start cracking

Thanks for your help. At least I know I'm on the right track now.

##### Diamond Member
Do you goto UofT? I have the same lab due on Monday. But I don't know about any restrictions, other than meeting criteria of being the cheapest.