I have reached a simplified boolean expression
Y = C + A + B'.D' + B.D
and I was wondering if there was any way to expand this expression from its simplified version (how did it get to this current expression)
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1Sure, you can! For example, replace C with BC + B'C or replace A with ABD + ABD' + AB'. But that doesn't seem to have anything to do with StackOverflow – CiaPan Jan 14 '16 at 21:25
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1There are infinitely many boolean expressions that reduce to this one. Which one do you want to find? – jwodder Jan 14 '16 at 21:39
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There is no such thing as an irreversible Boolean identity. Of course you can use Boolean algebra to make expressions more complicated. – John Coleman Jan 14 '16 at 21:45
1 Answers
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Yes, it is possible expand rather than simplify a boolean expression.
Y = C + A + B'.D' + B.D
is, for example, equivalent to this expanded expression:
Y = C + A + B'.D' + B.D + B.D
No, it is not possible to recover the original non-simplified form of a boolean expression; that information is not preserved during simplification steps in any way within the simplified expression itself. This can easily be seen since
Y = C + A + B'.D' + B.D
might have started as
Y = C + A + B'.D' + B.D + B.D
but just as easily could have started as
Y = C + A + B'.D' + B.D + B.D + B.D
or
Y = C + A + B'.D' + B.D + B.D + B.D + B.D
(You get the idea.)
kjhughes
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