Disjunctive Normal form to Combinatorial Circuit

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Homework Help Overview

The discussion revolves around converting a disjunctive normal form (DNF) expression into a corresponding combinatorial circuit. The original poster presents a DNF expression for a function of three variables and seeks to understand the implications of simplifying the expression.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to simplify the DNF expression and questions whether certain terms would cancel out. Other participants point out potential inaccuracies in the DNF and challenge the assumptions made about the terms involved.

Discussion Status

Participants are actively questioning the correctness of the DNF provided and exploring the implications of de Morgan's Laws. There is a recognition of mistakes in the original expression, and some guidance has been offered regarding the interpretation of the terms.

Contextual Notes

There is a noted confusion regarding the application of negation in the DNF terms, and participants are discussing the implications of these assumptions on the overall expression. The original poster's understanding of the truth table corresponding to the DNF is also under scrutiny.

Kingyou123
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Homework Statement


Draw the combinatorial circuit corresponding to the disjunctive normal form.
2.PNG

Homework Equations


DNF of f(x,y,z)=xyz+Not(xy)z

The Attempt at a Solution


f(x,y,z)=xyz+not(xy)z
=z(xy+not(xy))
Wouldn't the xy and not xy cancel out? That's my current problem with this probelm.
 
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The problem is that your DNF is not correct. Presumably the first term is supposed to give the 1 in the second row of the last column. But z is 0 in that row. So why are none of x,y,z negated in the term?
Your second term is not correct either. Are you aware that not(xy) is not the same as not(x)not(y)? de Morgan's Laws can sort that out for you.
 
andrewkirk said:
The problem is that your DNF is not correct. Presumably the first term is supposed to give the 1 in the second row of the last column. But z is 0 in that row. So why are none of x,y,z negated in the term?
Your second term is not correct either. Are you aware that not(xy) is not the same as not(x)not(y)? de Morgan's Laws can sort that out for you.
Oh thank you for catching my mistake, I was looking at row 0 for some reason.
So I'm left with xynot(z) + not(x)not(y)z, wouldn't everything just cancel out?
 
Kingyou123 said:
wouldn't everything just cancel out?
No. In fact the expression cannot be factorized at all.
 

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