Could you simplify this one: x'y'w' + yzw' + xz'w + x'zw' so I can get: x'y'w' + yzw' + xz'w?

Thread Starter

Nikoleta Ulama

Joined Aug 10, 2017
3
I got the Minterm already simplified: x'y'w' + yzw' + xz'w and the Maxterm: x'y'w' + yzw' + xz'w + x'zw', but they should be equal..
 

MrChips

Joined Oct 2, 2009
30,712
Moved thread from The Projects Forum to Homework Help.
If this is not homework then please identify the nature of your work.
 

Thread Starter

Nikoleta Ulama

Joined Aug 10, 2017
3
None of those are either minterm or maxterm expressions.

You have four variables, a minterm is a product involving all four and a maxterm is a sum of all four.

https://forum.allaboutcircuits.com/blog/boolean-logic-sop-and-pos-forms.583/

What you need to go between the two expressions in your title is an awareness of concensus terms.

https://forum.allaboutcircuits.com/blog/boolean-logic-working-with-consensus-terms.663/
Thank you for answer! Yes, I got it. Here are both Maxterm and Minterm, but I need to simplify both of expressions and they should be equal.
 

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RBR1317

Joined Nov 13, 2010
713
So you have a Boolean equation with the same 3 terms, but one side has an extra term (X'⋅Z⋅W'). Is this extra term a consensus term that is redundant and can be eliminated? One approach is to expand each 3-variable term in the equation into 4-variable minterms, e.g., (X'⋅Z⋅W')⋅(Y+Y') = (X'⋅Y⋅Z⋅W')+(X'⋅Y'⋅Z⋅W') then determine whether the minterms for the consensus term are contained within the minterm expansion of the other 3 terms. If the answer is YES then the consensus term is redundant and can be eliminated.

A recent post concerning consensus terms is here:
https://forum.allaboutcircuits.com/...-whats-the-simplest-way-to-prove-this.137259/
 

Thread Starter

Nikoleta Ulama

Joined Aug 10, 2017
3
So you have a Boolean equation with the same 3 terms, but one side has an extra term (X'⋅Z⋅W'). Is this extra term a consensus term that is redundant and can be eliminated? One approach is to expand each 3-variable term in the equation into 4-variable minterms, e.g., (X'⋅Z⋅W')⋅(Y+Y') = (X'⋅Y⋅Z⋅W')+(X'⋅Y'⋅Z⋅W') then determine whether the minterms for the consensus term are contained within the minterm expansion of the other 3 terms. If the answer is YES then the consensus term is redundant and can be eliminated.

A recent post concerning consensus terms is here:
https://forum.allaboutcircuits.com/...-whats-the-simplest-way-to-prove-this.137259/
Thank you so much! It helped.
Best regards.
 
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