Master Boolean's Algebra with SOP: Simplifying F(X, Y) to XY' + XY

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Discussion Overview

The discussion centers around the simplification of the Boolean function F(X, Y) expressed as XY' + XY, with participants exploring the validity of this expression and the steps involved in simplifying it. The scope includes Boolean algebra techniques and potential misprints in the original expression.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant questions the simplification of F(X, Y) to XY' + XY, suggesting it should be X'Y' + X'Y + XY' + XY.
  • Another participant suggests using Boolean algebra rules, specifically that X + X' = 1, to simplify the expression.
  • A participant shares their own reduction process, arriving at XY + Y' + X'Y, but expresses uncertainty about the simplification.
  • There is a discussion about common factors in the terms, specifically regarding the first and third terms having a common Y.
  • One participant claims that the expression is a misprint and suggests it represents the exclusive OR function, X'Y + XY', rather than simplifying further.
  • Another participant notes that F(X, Y) results from the addition of the last two terms and questions why the first two terms are not included in this outcome.

Areas of Agreement / Disagreement

Participants express differing views on the simplification of F(X, Y), with some suggesting it is a misprint while others attempt to justify the simplification steps. The discussion remains unresolved regarding the correct interpretation and simplification of the expression.

Contextual Notes

There are indications of potential misprints in the original expression, and participants rely on various Boolean algebra rules without reaching a consensus on the simplification process.

desmond iking
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Can someone please explain why the F( X, Y ) is XY' + XY ? IMO , it is X'Y' + X'Y +XY' +XY ... or the author simplified it to become XY' + XY ? how to simplify it?
 

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Use boolean algebra to reduce it. In boolean algebra X+X' = 1 and use algebra to extract common factors.

Is this a homework assignment?
 
jedishrfu said:
Use boolean algebra to reduce it. In boolean algebra X+X' = 1 and use algebra to extract common factors.

Is this a homework assignment?
no, i am studying myself during the holiday.
 
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Did my advice make sense?

Boolean algebra rules are the same as ordinary algebra with the added concepts X=X'=1 and X.X'=0 and X=0 means X=false and X=1 means X=true. Engineers start with a truth table for a circuit, construct boolean expressions, reduce them down using boolean algebra ruls and then construct a circuit from the reduced expressions.
 
jedishrfu said:
Did my advice make sense?

Boolean algebra rules are the same as ordinary algebra with the added concepts X=X'=1 and X.X'=0 and X=0 means X=false and X=1 means X=true. Engineers start with a truth table for a circuit, construct boolean expressions, reduce them down using boolean algebra ruls and then construct a circuit from the reduced expressions.
i only managed to reduce it to XY +Y' +X'Y
here's my working:
(X'Y') + (X'Y) + (XY') + (XY)
=XY +Y'(X' +X ) +X'Y
= XY +Y' +X'Y
 
what about the 1st and 3rd term? they have a common Y.
 
jedishrfu said:
what about the 1st and 3rd term? they have a common Y.

continue form the previous post , i still didnt get the ans
XY +Y' +X'Y = Y(X +X') +Y' = Y+Y'
 
desmond iking said:
Can someone please explain why the F( X, Y ) is XY' + XY ?
Hi Desmond. No one can explain it. It's a misprint. :oops:

It is just the exclusive OR function, X'Y + XY'. It doesn't simplify, except you can write it as X ⨁ Y.
Good luck with your self-study. http://thumbnails112.imagebam.com/37333/0363e9373324851.jpg
 
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I noticed that theF(X , Y) is the outcome of the addition of the last two. *correct me if I m wrong* , why it only involve the addition of last two term? Why not also the first two terms??
 
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desmond iking said:
I noticed that theF(X , Y) is the outcome of the addition of the last two. *correct me if I m wrong* , why it only involve the addition of last two term? Why not also the first two terms??
It's a misprint. F(X,Y) is true when either of these is true: X'Y or XY'
 
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