Is there a way to simplify of the next boolean expression?

Question

Im trying to simplify the next expression

$$A\bar{B}E+\bar{A}B\bar{E}$$

so the approach is to factor $E$ and ·$\bar{E}$ to get something like
$$A\bar{B}+\bar{A}B (E+\bar{E})$$
(this step before is not allowed, so how to get last one?) $$A\bar{B}+\bar{A}B (1)$$
and finally
$$A\bar{B}+\bar{A}B$$

but how can factor $E$ and their negation?

How can it be simplified any more than the first expression? — copper.hat, Feb 24 '19 at 05:40
At least two terms are necessary and each term must have three literals. — copper.hat, Feb 24 '19 at 06:16
@riccs_0x this is not correct $A\bar{B}+\bar{A}B (E+\bar{E}).$ — user376343, Feb 25 '19 at 22:15
Yes, that exactly what Im asking, is there a "legal" way to do these step? — riccs_0x, Feb 26 '19 at 03:24

score 1 · Accepted Answer · answered Feb 26 '19 at 04:04

Going from:

$AB'E+A'BE'$

To:

$(AB'+A'B)(E +E')$

is not correct.

That is like going from

$2\cdot 3 \cdot 5+4\cdot 7\cdot 6$

To:

$(2\cdot 3+4 \cdot 7)(5 +6)$

which you can easily verify are not the same!

And indeed, with $A=T$, $B=F$, and $E=F$, we have that

$AB'E+A'BE'=TTF+FFT=F+F=F$

But

$(AB'+A'B)(E+E')=(T+F)(F+T)=TT=T$

So, these two are not equivalent!

Is there a way to simplify of the next boolean expression?

1 Answers1