help simplifying boolean algebra please

Thread Starter


Joined Jun 19, 2011
Can someone please help with the following, I have to build a circuit for a for a 7 segment display starting from 00 going to 15.
I have done the K-Maps and i'm trying to simplify the equations i have from them to reduce the number of gates i need, but i am getting stuck.
The equation is -x + -wyz + wy-z + wz-y + x-y-z
I keep factoring out and am left with -x + (w+x) but this does not work on the display. The programme i am using to build it is logic works 4.0.
Any and all help will be much appreciated. Thanks.


Joined Oct 2, 2009
Secondly, -x + (w+x) is not correct so you are doing something wrong in your reduction.

Firstly, the purpose of Karnaugh maps is to reduce the formula in the first place. You are not using the K-map correctly.

(I'm using an iPad - makes it difficult to edit.)


Joined Jun 19, 2011
try to use Espresso for minimisation.......also it would be easier to help if the question was more comprehensive....!


Joined Nov 25, 2009
Ok, let's start from the basics:
When you want to write the complement of a Boolean variable, say x, the way to do it is to write x' or \(\bar{x}\). -x is out of convention and has no meaning.

Afterwards, one single Boolean expression isn't enough to drive all of the 8 inputs of the 7-segment display. One is needed for each input.

But assuming that the expression you posted is one of them, let's try to simplify it through a K-map.

First, we fill a 4-variable truth table, according to the expression given (x=A, y=B, z=C and w=D):

Do you understand how is the table filled?

Next we fill the K-map:

Is that the map you built too? Can you simplify the expression following the shading of the various sets?

Write the final expression.