Mixing
How do i work this Boolean Algebra?
$begingroup$
Simplify: ~P~VSTC + ~PV~STC + ~PVS~TC + ~PVSTC + P~V~STC + P~VS~TC + P~VSTC + PV~S~TC + PV~S TC + PVS~TC + PVST~C + PVSTC (hint: ending value only has seven terms...) I have no clue how or why that's answer... If someone can please explain to me that would be sooooo great The answer is PVST + STC + VTC + VSC + PTC + PSC + PVC Thanks for the help guys... I got the answer from a calculator thing
abstract-algebra boolean-algebra
asked Jan 27 at 0:40
MeeksMeeks
34
$endgroup$
add a comment |
$begingroup$
Simplify: ~P~VSTC + ~PV~STC + ~PVS~TC + ~PVSTC + P~V~STC + P~VS~TC + P~VSTC + PV~S~TC + PV~S TC + PVS~TC + PVST~C + PVSTC (hint: ending value only has seven terms...) I have no clue how or why that's answer... If someone can please explain to me that would be sooooo great The answer is PVST + STC + VTC + VSC + PTC + PSC + PVC Thanks for the help guys... I got the answer from a calculator thing
abstract-algebra boolean-algebra
asked Jan 27 at 0:40
MeeksMeeks
34
$endgroup$
add a comment |
$begingroup$
Simplify: ~P~VSTC + ~PV~STC + ~PVS~TC + ~PVSTC + P~V~STC + P~VS~TC + P~VSTC + PV~S~TC + PV~S TC + PVS~TC + PVST~C + PVSTC (hint: ending value only has seven terms...) I have no clue how or why that's answer... If someone can please explain to me that would be sooooo great The answer is PVST + STC + VTC + VSC + PTC + PSC + PVC Thanks for the help guys... I got the answer from a calculator thing
abstract-algebra boolean-algebra
asked Jan 27 at 0:40
MeeksMeeks
34
$endgroup$
Simplify: ~P~VSTC + ~PV~STC + ~PVS~TC + ~PVSTC + P~V~STC + P~VS~TC + P~VSTC + PV~S~TC + PV~S TC + PVS~TC + PVST~C + PVSTC (hint: ending value only has seven terms...) I have no clue how or why that's answer... If someone can please explain to me that would be sooooo great The answer is PVST + STC + VTC + VSC + PTC + PSC + PVC Thanks for the help guys... I got the answer from a calculator thing
abstract-algebra boolean-algebra
abstract-algebra boolean-algebra
asked Jan 27 at 0:40
MeeksMeeks
34
asked Jan 27 at 0:40
MeeksMeeks
34
edited Jan 27 at 1:25
Meeks
asked Jan 27 at 0:40
MeeksMeeks
34
asked Jan 27 at 0:40
MeeksMeeks
34
asked Jan 27 at 0:40
MeeksMeeks
34
34
add a comment |
add a comment |
1 Answer
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$begingroup$
Here are some general principles that will help:
Adjacency
$PQ+PQ'=P$
For example, the last two terms from your starting expression can be combined to form $PVST$. But you can also combine $PVSTC$ with $P'VSTC$ to form $VSTC$. Fortunately, you don't have to choose one, since you can always create a copy by:
Idempotence
$P=P+P$
Another useful one is:
Reduction
$P+P'Q= P +Q$ (the $P$ term 'reduces' the $P'Q$ term to $Q$)
and this one actually generalizes to:
Generalized Reduction
$PR+P'QR=PR+QR$
In your expression, for example, after obtaining $VSTC$, you can use that to reduce $P'V'STC$ to $P'STC$
Good luck!
answered Jan 27 at 1:21
Bram28Bram28
63.9k44793
$endgroup$
$begingroup$
Thank you so much!
$endgroup$
– Meeks
Jan 27 at 1:26
add a comment |
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1 Answer
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1 Answer
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$begingroup$
Here are some general principles that will help:
Adjacency
$PQ+PQ'=P$
For example, the last two terms from your starting expression can be combined to form $PVST$. But you can also combine $PVSTC$ with $P'VSTC$ to form $VSTC$. Fortunately, you don't have to choose one, since you can always create a copy by:
Idempotence
$P=P+P$
Another useful one is:
Reduction
$P+P'Q= P +Q$ (the $P$ term 'reduces' the $P'Q$ term to $Q$)
and this one actually generalizes to:
Generalized Reduction
$PR+P'QR=PR+QR$
In your expression, for example, after obtaining $VSTC$, you can use that to reduce $P'V'STC$ to $P'STC$
Good luck!
answered Jan 27 at 1:21
Bram28Bram28
63.9k44793
$endgroup$
$begingroup$
Thank you so much!
$endgroup$
– Meeks
Jan 27 at 1:26
add a comment |
$begingroup$
Here are some general principles that will help:
Adjacency
$PQ+PQ'=P$
For example, the last two terms from your starting expression can be combined to form $PVST$. But you can also combine $PVSTC$ with $P'VSTC$ to form $VSTC$. Fortunately, you don't have to choose one, since you can always create a copy by:
Idempotence
$P=P+P$
Another useful one is:
Reduction
$P+P'Q= P +Q$ (the $P$ term 'reduces' the $P'Q$ term to $Q$)
and this one actually generalizes to:
Generalized Reduction
$PR+P'QR=PR+QR$
In your expression, for example, after obtaining $VSTC$, you can use that to reduce $P'V'STC$ to $P'STC$
Good luck!
answered Jan 27 at 1:21
Bram28Bram28
63.9k44793
$endgroup$
$begingroup$
Thank you so much!
$endgroup$
– Meeks
Jan 27 at 1:26
add a comment |
$begingroup$
Here are some general principles that will help:
Adjacency
$PQ+PQ'=P$
For example, the last two terms from your starting expression can be combined to form $PVST$. But you can also combine $PVSTC$ with $P'VSTC$ to form $VSTC$. Fortunately, you don't have to choose one, since you can always create a copy by:
Idempotence
$P=P+P$
Another useful one is:
Reduction
$P+P'Q= P +Q$ (the $P$ term 'reduces' the $P'Q$ term to $Q$)
and this one actually generalizes to:
Generalized Reduction
$PR+P'QR=PR+QR$
In your expression, for example, after obtaining $VSTC$, you can use that to reduce $P'V'STC$ to $P'STC$
Good luck!
answered Jan 27 at 1:21
Bram28Bram28
63.9k44793
$endgroup$
Here are some general principles that will help:
Adjacency
$PQ+PQ'=P$
For example, the last two terms from your starting expression can be combined to form $PVST$. But you can also combine $PVSTC$ with $P'VSTC$ to form $VSTC$. Fortunately, you don't have to choose one, since you can always create a copy by:
Idempotence
$P=P+P$
Another useful one is:
Reduction
$P+P'Q= P +Q$ (the $P$ term 'reduces' the $P'Q$ term to $Q$)
and this one actually generalizes to:
Generalized Reduction
$PR+P'QR=PR+QR$
In your expression, for example, after obtaining $VSTC$, you can use that to reduce $P'V'STC$ to $P'STC$
Good luck!
answered Jan 27 at 1:21
Bram28Bram28
63.9k44793
answered Jan 27 at 1:21
Bram28Bram28
63.9k44793
answered Jan 27 at 1:21
Bram28Bram28
63.9k44793
answered Jan 27 at 1:21
Bram28Bram28
63.9k44793
63.9k44793
$begingroup$
Thank you so much!
$endgroup$
– Meeks
Jan 27 at 1:26
add a comment |
$begingroup$
Thank you so much!
$endgroup$
– Meeks
Jan 27 at 1:26
$begingroup$
Thank you so much!
$endgroup$
– Meeks
Jan 27 at 1:26
$begingroup$
Thank you so much!
$endgroup$
– Meeks
Jan 27 at 1:26
add a comment |
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