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Minimize term without Karnaugh map
simplifying using Boolean Algebra.Boolean function simplificationThree Boolean Algebra Proofs - I just don't get it!Boolean algebra question.Minimizing using a Karnaugh map when given as subscripts F4,2655How many minimized forms can a boolean expression have with 4 variables?How can i simplyfy this boolean equation?Simplifying a four term Boolean expression using Boolean algebraboolean algebra: simplify 3-term dnf form covering a|~aCircuit to Karnaugh map
$begingroup$
I have the following term, that should get minimized with Boolean algebra (no Karnaugh map!):
(a ∧ ¬b ∧ c) ∨ (a ∧ c ∧ d) ∨ (b ∧ d)
I already figured out, that the minimzed term is as follows (everything without the middle term) and it makes totally sense to me:
(a ∧ ¬b ∧ c) ∨ (b ∧ d)
However when I try to get same result with boolean algebra I am not able to reproduce it.
My first step is the following:
(a ∧ c) ∧ (¬b ∨ d) ∨ (b ∧ d)
When I apply distributivity-law I end up with the first (non-minimized) term.
Edit: Besides the question above, more general: Can every term that is minimizable by a Karnaugh map be minimized with boolean algebra?
propositional-calculus boolean-algebra
edited yesterday
Rodrigo de Azevedo
13k41960
asked yesterday
F.M.F.F.M.F.
1084
New contributor
F.M.F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I have the following term, that should get minimized with Boolean algebra (no Karnaugh map!):
(a ∧ ¬b ∧ c) ∨ (a ∧ c ∧ d) ∨ (b ∧ d)
I already figured out, that the minimzed term is as follows (everything without the middle term) and it makes totally sense to me:
(a ∧ ¬b ∧ c) ∨ (b ∧ d)
However when I try to get same result with boolean algebra I am not able to reproduce it.
My first step is the following:
(a ∧ c) ∧ (¬b ∨ d) ∨ (b ∧ d)
When I apply distributivity-law I end up with the first (non-minimized) term.
Edit: Besides the question above, more general: Can every term that is minimizable by a Karnaugh map be minimized with boolean algebra?
propositional-calculus boolean-algebra
edited yesterday
Rodrigo de Azevedo
13k41960
asked yesterday
F.M.F.F.M.F.
1084
New contributor
F.M.F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
What does KV mean?
$endgroup$
– Jens
yesterday
$begingroup$
The german abbreviation for the Karnaugh map... updated the question!
$endgroup$
– F.M.F.
yesterday
$begingroup$
Where is the Boolean algebra? Looks like propositional logic to me.
$endgroup$
– Rodrigo de Azevedo
yesterday
add a comment |
$begingroup$
I have the following term, that should get minimized with Boolean algebra (no Karnaugh map!):
(a ∧ ¬b ∧ c) ∨ (a ∧ c ∧ d) ∨ (b ∧ d)
I already figured out, that the minimzed term is as follows (everything without the middle term) and it makes totally sense to me:
(a ∧ ¬b ∧ c) ∨ (b ∧ d)
However when I try to get same result with boolean algebra I am not able to reproduce it.
My first step is the following:
(a ∧ c) ∧ (¬b ∨ d) ∨ (b ∧ d)
When I apply distributivity-law I end up with the first (non-minimized) term.
Edit: Besides the question above, more general: Can every term that is minimizable by a Karnaugh map be minimized with boolean algebra?
propositional-calculus boolean-algebra
edited yesterday
Rodrigo de Azevedo
13k41960
asked yesterday
F.M.F.F.M.F.
1084
New contributor
F.M.F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have the following term, that should get minimized with Boolean algebra (no Karnaugh map!):
(a ∧ ¬b ∧ c) ∨ (a ∧ c ∧ d) ∨ (b ∧ d)
I already figured out, that the minimzed term is as follows (everything without the middle term) and it makes totally sense to me:
(a ∧ ¬b ∧ c) ∨ (b ∧ d)
However when I try to get same result with boolean algebra I am not able to reproduce it.
My first step is the following:
(a ∧ c) ∧ (¬b ∨ d) ∨ (b ∧ d)
When I apply distributivity-law I end up with the first (non-minimized) term.
Edit: Besides the question above, more general: Can every term that is minimizable by a Karnaugh map be minimized with boolean algebra?
propositional-calculus boolean-algebra
propositional-calculus boolean-algebra
edited yesterday
Rodrigo de Azevedo
13k41960
asked yesterday
F.M.F.F.M.F.
1084
New contributor
F.M.F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Rodrigo de Azevedo
13k41960
asked yesterday
F.M.F.F.M.F.
1084
New contributor
F.M.F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
Rodrigo de Azevedo
13k41960
edited yesterday
Rodrigo de Azevedo
13k41960
edited yesterday
Rodrigo de Azevedo
13k41960
13k41960
asked yesterday
F.M.F.F.M.F.
1084
New contributor
F.M.F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
F.M.F.F.M.F.
1084
asked yesterday
F.M.F.F.M.F.
1084
1084
New contributor
F.M.F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
F.M.F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
F.M.F. is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
What does KV mean?
$endgroup$
– Jens
yesterday
$begingroup$
The german abbreviation for the Karnaugh map... updated the question!
$endgroup$
– F.M.F.
yesterday
$begingroup$
Where is the Boolean algebra? Looks like propositional logic to me.
$endgroup$
– Rodrigo de Azevedo
yesterday
add a comment |
$begingroup$
What does KV mean?
$endgroup$
– Jens
yesterday
$begingroup$
The german abbreviation for the Karnaugh map... updated the question!
$endgroup$
– F.M.F.
yesterday
$begingroup$
Where is the Boolean algebra? Looks like propositional logic to me.
$endgroup$
– Rodrigo de Azevedo
yesterday
$begingroup$
What does KV mean?
$endgroup$
– Jens
yesterday
$begingroup$
What does KV mean?
$endgroup$
– Jens
yesterday
$begingroup$
The german abbreviation for the Karnaugh map... updated the question!
$endgroup$
– F.M.F.
yesterday
$begingroup$
The german abbreviation for the Karnaugh map... updated the question!
$endgroup$
– F.M.F.
yesterday
$begingroup$
Where is the Boolean algebra? Looks like propositional logic to me.
$endgroup$
– Rodrigo de Azevedo
yesterday
$begingroup$
Where is the Boolean algebra? Looks like propositional logic to me.
$endgroup$
– Rodrigo de Azevedo
yesterday
add a comment |
1 Answer
1
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$begingroup$
beginalign
aoverlinebc+acd+bd & = aoverlinebc + acd(b+overlineb) + bd \
& = aoverlinebc + acdb+acdoverlineb + bd \
& = (aoverlinebc + aoverlinebcd) + (bd + bdac) \
& = aoverlinebc + bd \
endalign
answered yesterday
JensJens
3,90021031
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
beginalign
aoverlinebc+acd+bd & = aoverlinebc + acd(b+overlineb) + bd \
& = aoverlinebc + acdb+acdoverlineb + bd \
& = (aoverlinebc + aoverlinebcd) + (bd + bdac) \
& = aoverlinebc + bd \
endalign
answered yesterday
JensJens
3,90021031
$endgroup$
add a comment |
$begingroup$
beginalign
aoverlinebc+acd+bd & = aoverlinebc + acd(b+overlineb) + bd \
& = aoverlinebc + acdb+acdoverlineb + bd \
& = (aoverlinebc + aoverlinebcd) + (bd + bdac) \
& = aoverlinebc + bd \
endalign
answered yesterday
JensJens
3,90021031
$endgroup$
add a comment |
$begingroup$
beginalign
aoverlinebc+acd+bd & = aoverlinebc + acd(b+overlineb) + bd \
& = aoverlinebc + acdb+acdoverlineb + bd \
& = (aoverlinebc + aoverlinebcd) + (bd + bdac) \
& = aoverlinebc + bd \
endalign
answered yesterday
JensJens
3,90021031
$endgroup$
beginalign
aoverlinebc+acd+bd & = aoverlinebc + acd(b+overlineb) + bd \
& = aoverlinebc + acdb+acdoverlineb + bd \
& = (aoverlinebc + aoverlinebcd) + (bd + bdac) \
& = aoverlinebc + bd \
endalign
answered yesterday
JensJens
3,90021031
answered yesterday
JensJens
3,90021031
answered yesterday
JensJens
3,90021031
answered yesterday
JensJens
3,90021031
3,90021031
add a comment |
add a comment |
F.M.F. is a new contributor. Be nice, and check out our Code of Conduct.
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$begingroup$
What does KV mean?
$endgroup$
– Jens
yesterday
$begingroup$
The german abbreviation for the Karnaugh map... updated the question!
$endgroup$
– F.M.F.
yesterday
$begingroup$
Where is the Boolean algebra? Looks like propositional logic to me.
$endgroup$
– Rodrigo de Azevedo
yesterday