Mixing
Boolean expression: how to find “don't care†numbers?
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The boolean expression z+w' is received after simplification of the expression
vw'y+v'wz+vyz+v'w'x'y'+v'w'xyz+vw'y'z'+vw'xy'z+v'w'yz'
We don't know what are the don't care numbers, what are the numbers that are for sure don't care expressions?
I tried solving this a few ways, but none of them worked.
I find it more important for me to understand the way to solve this question, so please provide a detailed answer.
I tried to use a truth table with 5 variables, and then a Karnaugh map, but I'm still struggling.
Thanks.
boolean-algebra
edited Jul 21 at 9:14
Chandler Watson
417320
asked Jul 21 at 7:05
OO1
61
add a comment |Â
up vote
1
down vote
favorite
The boolean expression z+w' is received after simplification of the expression
vw'y+v'wz+vyz+v'w'x'y'+v'w'xyz+vw'y'z'+vw'xy'z+v'w'yz'
We don't know what are the don't care numbers, what are the numbers that are for sure don't care expressions?
I tried solving this a few ways, but none of them worked.
I find it more important for me to understand the way to solve this question, so please provide a detailed answer.
I tried to use a truth table with 5 variables, and then a Karnaugh map, but I'm still struggling.
Thanks.
boolean-algebra
edited Jul 21 at 9:14
Chandler Watson
417320
asked Jul 21 at 7:05
OO1
61
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 21 at 7:07
Are you saying that the large expression reduces to the smaller expression if certain input combinations are designated as "don't cares"? And you want to know what these combinations are?
– Jens
Jul 21 at 9:08
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
The boolean expression z+w' is received after simplification of the expression
vw'y+v'wz+vyz+v'w'x'y'+v'w'xyz+vw'y'z'+vw'xy'z+v'w'yz'
We don't know what are the don't care numbers, what are the numbers that are for sure don't care expressions?
I tried solving this a few ways, but none of them worked.
I find it more important for me to understand the way to solve this question, so please provide a detailed answer.
I tried to use a truth table with 5 variables, and then a Karnaugh map, but I'm still struggling.
Thanks.
boolean-algebra
edited Jul 21 at 9:14
Chandler Watson
417320
asked Jul 21 at 7:05
OO1
61
The boolean expression z+w' is received after simplification of the expression
vw'y+v'wz+vyz+v'w'x'y'+v'w'xyz+vw'y'z'+vw'xy'z+v'w'yz'
We don't know what are the don't care numbers, what are the numbers that are for sure don't care expressions?
I tried solving this a few ways, but none of them worked.
I find it more important for me to understand the way to solve this question, so please provide a detailed answer.
I tried to use a truth table with 5 variables, and then a Karnaugh map, but I'm still struggling.
Thanks.
boolean-algebra
edited Jul 21 at 9:14
Chandler Watson
417320
asked Jul 21 at 7:05
OO1
61
edited Jul 21 at 9:14
Chandler Watson
417320
edited Jul 21 at 9:14
Chandler Watson
417320
edited Jul 21 at 9:14
Chandler Watson
417320
417320
asked Jul 21 at 7:05
OO1
61
asked Jul 21 at 7:05
OO1
61
asked Jul 21 at 7:05
OO1
61
61
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 21 at 7:07
Are you saying that the large expression reduces to the smaller expression if certain input combinations are designated as "don't cares"? And you want to know what these combinations are?
– Jens
Jul 21 at 9:08
add a comment |Â
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 21 at 7:07
Are you saying that the large expression reduces to the smaller expression if certain input combinations are designated as "don't cares"? And you want to know what these combinations are?
– Jens
Jul 21 at 9:08
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 21 at 7:07
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 21 at 7:07
Are you saying that the large expression reduces to the smaller expression if certain input combinations are designated as "don't cares"? And you want to know what these combinations are?
– Jens
Jul 21 at 9:08
Are you saying that the large expression reduces to the smaller expression if certain input combinations are designated as "don't cares"? And you want to know what these combinations are?
– Jens
Jul 21 at 9:08
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
Hint
Set up a Karnaugh map with $vwx$ on top and $yz$ on the side, like this:
$$beginarrayc
textvwxbackslash textyz&000&001&011&010&110&111&101&100\hline
00\hline
01\hline
11\hline
10
endarray$$
Now fill in the map with 1's in the places given by the larger expression. In order for the larger expression to reduce to z+w', there must be 1's or "don't care"s in row 2 and 3 as well as in columns 1,2,7,8.
You will find that 6 "don't care"s are needed.
answered Jul 21 at 13:05
Jens
3,0732826
Hi, many thanks for the answer but that's what I have tried. for example: if I take a look at the larger expression and I choose the first number combination it gives me $vw'y = 101 = 5$ then i mark it in the table at the place of number 5 as 1 right? then I fill the rest of the numbers same technique as mentioned above... if that's the way, then what's next?
– OO1
Jul 22 at 6:19
First, don't think of the bit combinations as numbers, just as bit combinations. Second, the columns give combinations of $vwx$, not $vwy$. So in which columns is $vw=10$? And in which rows is $y=1$? Put a 1 in the intersection of those columns and rows. Continue in the same way with the rest of the expression.
– Jens
Jul 22 at 6:48
Ok got you, i made my K-map as $vw$ rows and $xyz$ columns but lets do your way!. but the example you give me there are 2 options to put 1 for $vw=10$ and $y=1$ how can i know which one of them?
– OO1
Jul 22 at 16:36
Put 1 in all of them.
– Jens
Jul 22 at 19:24
Many thanks! sometimes all you need is to put it in the tables and the answer is in front of your eyes.
– OO1
Jul 22 at 20:52
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
Hint
Set up a Karnaugh map with $vwx$ on top and $yz$ on the side, like this:
$$beginarrayc
textvwxbackslash textyz&000&001&011&010&110&111&101&100\hline
00\hline
01\hline
11\hline
10
endarray$$
Now fill in the map with 1's in the places given by the larger expression. In order for the larger expression to reduce to z+w', there must be 1's or "don't care"s in row 2 and 3 as well as in columns 1,2,7,8.
You will find that 6 "don't care"s are needed.
answered Jul 21 at 13:05
Jens
3,0732826
Hi, many thanks for the answer but that's what I have tried. for example: if I take a look at the larger expression and I choose the first number combination it gives me $vw'y = 101 = 5$ then i mark it in the table at the place of number 5 as 1 right? then I fill the rest of the numbers same technique as mentioned above... if that's the way, then what's next?
– OO1
Jul 22 at 6:19
First, don't think of the bit combinations as numbers, just as bit combinations. Second, the columns give combinations of $vwx$, not $vwy$. So in which columns is $vw=10$? And in which rows is $y=1$? Put a 1 in the intersection of those columns and rows. Continue in the same way with the rest of the expression.
– Jens
Jul 22 at 6:48
Ok got you, i made my K-map as $vw$ rows and $xyz$ columns but lets do your way!. but the example you give me there are 2 options to put 1 for $vw=10$ and $y=1$ how can i know which one of them?
– OO1
Jul 22 at 16:36
Put 1 in all of them.
– Jens
Jul 22 at 19:24
Many thanks! sometimes all you need is to put it in the tables and the answer is in front of your eyes.
– OO1
Jul 22 at 20:52
add a comment |Â
up vote
1
down vote
Hint
Set up a Karnaugh map with $vwx$ on top and $yz$ on the side, like this:
$$beginarrayc
textvwxbackslash textyz&000&001&011&010&110&111&101&100\hline
00\hline
01\hline
11\hline
10
endarray$$
Now fill in the map with 1's in the places given by the larger expression. In order for the larger expression to reduce to z+w', there must be 1's or "don't care"s in row 2 and 3 as well as in columns 1,2,7,8.
You will find that 6 "don't care"s are needed.
answered Jul 21 at 13:05
Jens
3,0732826
Hi, many thanks for the answer but that's what I have tried. for example: if I take a look at the larger expression and I choose the first number combination it gives me $vw'y = 101 = 5$ then i mark it in the table at the place of number 5 as 1 right? then I fill the rest of the numbers same technique as mentioned above... if that's the way, then what's next?
– OO1
Jul 22 at 6:19
First, don't think of the bit combinations as numbers, just as bit combinations. Second, the columns give combinations of $vwx$, not $vwy$. So in which columns is $vw=10$? And in which rows is $y=1$? Put a 1 in the intersection of those columns and rows. Continue in the same way with the rest of the expression.
– Jens
Jul 22 at 6:48
Ok got you, i made my K-map as $vw$ rows and $xyz$ columns but lets do your way!. but the example you give me there are 2 options to put 1 for $vw=10$ and $y=1$ how can i know which one of them?
– OO1
Jul 22 at 16:36
Put 1 in all of them.
– Jens
Jul 22 at 19:24
Many thanks! sometimes all you need is to put it in the tables and the answer is in front of your eyes.
– OO1
Jul 22 at 20:52
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Hint
Set up a Karnaugh map with $vwx$ on top and $yz$ on the side, like this:
$$beginarrayc
textvwxbackslash textyz&000&001&011&010&110&111&101&100\hline
00\hline
01\hline
11\hline
10
endarray$$
Now fill in the map with 1's in the places given by the larger expression. In order for the larger expression to reduce to z+w', there must be 1's or "don't care"s in row 2 and 3 as well as in columns 1,2,7,8.
You will find that 6 "don't care"s are needed.
answered Jul 21 at 13:05
Jens
3,0732826
Hint
Set up a Karnaugh map with $vwx$ on top and $yz$ on the side, like this:
$$beginarrayc
textvwxbackslash textyz&000&001&011&010&110&111&101&100\hline
00\hline
01\hline
11\hline
10
endarray$$
Now fill in the map with 1's in the places given by the larger expression. In order for the larger expression to reduce to z+w', there must be 1's or "don't care"s in row 2 and 3 as well as in columns 1,2,7,8.
You will find that 6 "don't care"s are needed.
answered Jul 21 at 13:05
Jens
3,0732826
answered Jul 21 at 13:05
Jens
3,0732826
answered Jul 21 at 13:05
Jens
3,0732826
answered Jul 21 at 13:05
Jens
3,0732826
3,0732826
Hi, many thanks for the answer but that's what I have tried. for example: if I take a look at the larger expression and I choose the first number combination it gives me $vw'y = 101 = 5$ then i mark it in the table at the place of number 5 as 1 right? then I fill the rest of the numbers same technique as mentioned above... if that's the way, then what's next?
– OO1
Jul 22 at 6:19
First, don't think of the bit combinations as numbers, just as bit combinations. Second, the columns give combinations of $vwx$, not $vwy$. So in which columns is $vw=10$? And in which rows is $y=1$? Put a 1 in the intersection of those columns and rows. Continue in the same way with the rest of the expression.
– Jens
Jul 22 at 6:48
Ok got you, i made my K-map as $vw$ rows and $xyz$ columns but lets do your way!. but the example you give me there are 2 options to put 1 for $vw=10$ and $y=1$ how can i know which one of them?
– OO1
Jul 22 at 16:36
Put 1 in all of them.
– Jens
Jul 22 at 19:24
Many thanks! sometimes all you need is to put it in the tables and the answer is in front of your eyes.
– OO1
Jul 22 at 20:52
add a comment |Â
Hi, many thanks for the answer but that's what I have tried. for example: if I take a look at the larger expression and I choose the first number combination it gives me $vw'y = 101 = 5$ then i mark it in the table at the place of number 5 as 1 right? then I fill the rest of the numbers same technique as mentioned above... if that's the way, then what's next?
– OO1
Jul 22 at 6:19
First, don't think of the bit combinations as numbers, just as bit combinations. Second, the columns give combinations of $vwx$, not $vwy$. So in which columns is $vw=10$? And in which rows is $y=1$? Put a 1 in the intersection of those columns and rows. Continue in the same way with the rest of the expression.
– Jens
Jul 22 at 6:48
Ok got you, i made my K-map as $vw$ rows and $xyz$ columns but lets do your way!. but the example you give me there are 2 options to put 1 for $vw=10$ and $y=1$ how can i know which one of them?
– OO1
Jul 22 at 16:36
Put 1 in all of them.
– Jens
Jul 22 at 19:24
Many thanks! sometimes all you need is to put it in the tables and the answer is in front of your eyes.
– OO1
Jul 22 at 20:52
Hi, many thanks for the answer but that's what I have tried. for example: if I take a look at the larger expression and I choose the first number combination it gives me $vw'y = 101 = 5$ then i mark it in the table at the place of number 5 as 1 right? then I fill the rest of the numbers same technique as mentioned above... if that's the way, then what's next?
– OO1
Jul 22 at 6:19
Hi, many thanks for the answer but that's what I have tried. for example: if I take a look at the larger expression and I choose the first number combination it gives me $vw'y = 101 = 5$ then i mark it in the table at the place of number 5 as 1 right? then I fill the rest of the numbers same technique as mentioned above... if that's the way, then what's next?
– OO1
Jul 22 at 6:19
First, don't think of the bit combinations as numbers, just as bit combinations. Second, the columns give combinations of $vwx$, not $vwy$. So in which columns is $vw=10$? And in which rows is $y=1$? Put a 1 in the intersection of those columns and rows. Continue in the same way with the rest of the expression.
– Jens
Jul 22 at 6:48
First, don't think of the bit combinations as numbers, just as bit combinations. Second, the columns give combinations of $vwx$, not $vwy$. So in which columns is $vw=10$? And in which rows is $y=1$? Put a 1 in the intersection of those columns and rows. Continue in the same way with the rest of the expression.
– Jens
Jul 22 at 6:48
Ok got you, i made my K-map as $vw$ rows and $xyz$ columns but lets do your way!. but the example you give me there are 2 options to put 1 for $vw=10$ and $y=1$ how can i know which one of them?
– OO1
Jul 22 at 16:36
Ok got you, i made my K-map as $vw$ rows and $xyz$ columns but lets do your way!. but the example you give me there are 2 options to put 1 for $vw=10$ and $y=1$ how can i know which one of them?
– OO1
Jul 22 at 16:36
Put 1 in all of them.
– Jens
Jul 22 at 19:24
Put 1 in all of them.
– Jens
Jul 22 at 19:24
Many thanks! sometimes all you need is to put it in the tables and the answer is in front of your eyes.
– OO1
Jul 22 at 20:52
Many thanks! sometimes all you need is to put it in the tables and the answer is in front of your eyes.
– OO1
Jul 22 at 20:52
add a comment |Â
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Jul 21 at 7:07
Are you saying that the large expression reduces to the smaller expression if certain input combinations are designated as "don't cares"? And you want to know what these combinations are?
– Jens
Jul 21 at 9:08