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Boolean Expression to Logic Gates Diagram - Page 3

post #21 of 47
Thread Starter 
F = xy¹z + x¹y¹z + w¹xy + wx¹y + wxy. I get the basic concept, but I don't know how to approach this? Can you kind of lead me through this?
    
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post #22 of 47
each of the terms will have an and gate and then you or all of those together. youve done this in other problems with fewer terms, its exactly the same
    
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post #23 of 47
Thread Starter 
This is what I got
F = xy¹z + x¹y¹z + w¹xy + wx¹y + wxy
= (x + x¹)y¹z + (w¹ + w)xy + wx¹y
= y¹z + xy + wx¹y
= y¹z + y(x + w) Where did x¹ go?

= y¹z + y(w + x) This is the right answer from my teacher
    
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post #24 of 47
Quote:
Originally Posted by Buster;12470526 
This is what I got
F = xy¹z + x¹y¹z + w¹xy + wx¹y + wxy
= (x + x¹)y¹z + (w¹ + w)xy + wx¹y
= y¹z + xy + wx¹y
= y¹z + y(x + w) Where did x¹ go?

= y¹z + y(w + x) This is the right answer from my teacher
xy+wx'y=y(x+x'w)
y(x+x'w)=y(x+w)

xw+xw'+x'w=x+x'w
xw+xw'+xw+x'w=x+x'w
x(w+w')+w(x'+x)=x+x'w
x+w=x+x'w
    
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post #25 of 47
Thread Starter 
for xw+xw'+xw+x'w=x+x'w
how did you add another xw?
It is from the theorem 1a x + x = x so xw + xw = xw?
Edited by Buster - 2/21/11 at 11:56am
    
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post #26 of 47
Quote:
Originally Posted by Buster;12470859 
for xw+xw'+xw+x'w=x+x'w
how did you add another xw?
It is from the theorem 1a x + x = x so xw + xw = xw?
yes that is exactly it
    
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post #27 of 47
Thread Starter 
If there are two expression together like this
y1 = a (c + d + e)
y2 = ((b¹(c + d + e)f)¹)¹


and they are from one logic diagram

Do I draw one truth table for both? 6 characters with 32 values?
    
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post #28 of 47
yes, there will be 32 y1's and 32 y2's or you can do 2 truth tables with 16 values for each y and disregard the missing variable in each equation
    
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post #29 of 47
Thread Starter 
Since both equations don't have all the same characters, if I draw one truth table, what do I do with the chars that is missing from one equation? leave it blank? Which way is the default way?
    
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post #30 of 47
Quote:
Originally Posted by Buster;12471535 
Since both equations don't have all the same characters, if I draw one truth table, what do I do with the chars that is missing from one equation? leave it blank? Which way is the default way?

ignore it, it doesnt matter so if one equation uses b-f you would ignore "A" and do all proper combinations of b-f

b+c=y

a b c y
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
    
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