(Boolean Algebra) Did I write this logic expression correctly?

  • #1

Homework Statement


5c7c19e54a06b3c38414cbf3ad4e2750.png


My solution, is this correct?
This is what I came up with.
Y=A+((A*B)+B+C'+(B+C'*D)+D)
Is it safe to say that it is correct or did I make a mistake?
 

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  • #2
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I’d write the intermediate expressions at the gate output and put parentheses around them until you get to the final gate.

Also I’d use the bar over an expression to indicate negation.

Lastly. You can then apply Boolean algebra to reduce the long expression to get your final expression.

Try that and see if you can validate your own work. Doing it with intermediate results helps until you get good at it.
 
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  • #3
I’d write the intermediate expressions at the gate output and put parentheses around them until you get to the final gate.

Also I’d use the bar over an expression to indicate negation.

Lastly. You can then apply Boolean algebra to reduce the long expression to get your final expression.

Try that and see if you can validate your own work. Doing it with intermediate results helps until you get good at it.
487d6b7c22a98ebf0bf126817d93626b.png


I actually did these parts beforehand but i am not sure if what i came up with is correct and i would like to validate it before i start simplifying it.
Also i have no way to check if it correct because this is for an assignment which i will not get back with feedback but only with a grade.

If you would be so kind to help me on my mistakes and guide me to do this correctly, or just give me the answer i would appreciate it a lot. Either one is fine with me.
 

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  • #4
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Your paper is very messy and hard to read.

R = A + B
X = B + C'
Y = ( ( B + C' ) * D )'

Look at the Y gate again.
 
  • #5
Your paper is very messy and hard to read.

R = A + B
X = B + C'
Y = ( ( B + C' ) * D )'

Look at the Y gate again.
I am sorry for the paper quality.

I see i did a very silly mistake and forgot to add parentheses around B + C' and ofcourse It's a NAND gate so the expression needs a negation as a whole. I can see i did same mistake with E gate it should have been ((B+C'*D)'+D)'

This is the result i got now:

F=A+(A*B)+(B*C')+(((B+C')*D)'+D)'

It looks correct to me, does it so to you?
 
  • #6
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5,533
Students are always looking for the geodesic when the real geodesic is the step by step approach with intermediate values allowing someone to review it and check each step.

R = A * B (I made a mistake as it was an AND gate)
X = B + C'
Y = ( ( B + C' ) * D )'

E = ( Y + D )' = ( ( ( B + C' ) * D )' + D )'

G = R + X + E = (A * B) + (B + C') + ( ( ( B + C' ) * D )' + D )'

F = A + G = A + (A * B) + (B + C') + ( ( ( B + C' ) * D )' + D )'

Can you check my work?
 
  • #7
Students are always looking for the geodesic when the real geodesic is the step by step approach with intermediate values allowing someone to review it and check each step.

R = A * B (I made a mistake as it was an AND gate)
X = B + C'
Y = ( ( B + C' ) * D )'

E = ( Y + D )' = ( ( ( B + C' ) * D )' + D )'

G = R + X + E = (A * B) + (B + C') + ( ( ( B + C' ) * D )' + D )'

F = A + G = A + (A * B) + (B + C') + ( ( ( B + C' ) * D )' + D )'

Can you check my work?
It all looks correct and i can see this is an easy way to do it, thank you very much for your help!
 
  • #8
LCKurtz
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Hmmm, I don't check this forum often so I'm a bit late to the party, but I get$$C'+A+B$$when it's all said and done.
 
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