Is This Logic Diagram Correct?

In summary, the boolean expression I am working with is: ((ab)'(b'c)' + a'bpc') where ' is the NOT symbol.
  • #1
ibcoding
11
0
The boolean expression I am working with is:

((ab)'(b'c)' + a'bpc') where ' is the NOT symbol.

I have the following logic circuit diagram. Is it correct?








 

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  • #2
Welcome to PF!

The diagram is confusing a bit, because one of the a lines is very close to one of the b lines. However it looks correct to me.
 
  • #3
Ok, I know exactly which line you are talking about; I thought the same thing. I'll change that around. Thanks!
 
  • #4
I think you can simplify this a lot using DeMorgan's and other things. For instance, take the first input to the OR gate:

(ab)' * (b'c)'

Using DeMorgan's theorem (xy)' = x' + y', you can expand each thing in parentheses:

= (a' + b') * (b + c') [eq. 1]

and now using the distributive property of AND operator (which I believe is present for Boolean algebra?)

= a'b + a'c' + b'b + b'c'

and using the associative property:

a'(b + c') + 0 + b'c'

Anything OR'd with 0 is just itself, so this becomes:

a'(b + c') + b'c' [eq. 2]

I'm not sure that this is any simpler in this case, but the point is that you could, in principle, try to minimize the number of gates. I wrote a little program to generate the truth tables for eq. 1 and eq. 2 and they came out the same.
 
Last edited:
  • #5
Alright, variable p is missing from that equation, but I get the idea. On that note, is this the correct truth table outputs:

1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
 
  • #6
cepheid said:
I think you can simplify this a lot using DeMorgan's and other things. For instance, take the first input to the OR gate:

(ab)' * (b'c)'

Using DeMorgan's theorem (xy)' = x' + y', you can expand each thing in parentheses:

= (a' + b') * (b + c') [eq. 1]

and now using the distributive property of AND operator (which I believe is present for Boolean algebra?)

= a'b + a'c' + b'b + b'c'

and using the associative property:

a'(b + c') + 0 + b'c'

Anything OR'd with 0 is just itself, so this becomes:

a'(b + c') + b'c' [eq. 2]

I'm not sure that this is any simpler in this case, but the point is that you could, in principle, try to minimize the number of gates. I wrote a little program to generate the truth tables for eq. 1 and eq. 2 and they came out the same.

Ahh, the a' a' are adjacent so it is absorbed, got ya
 
  • #7
So the equation should be a'(b + c') + b'pc'
 
  • #8
which gives me three and gates and two or gates
 
  • #9
ibcoding said:
Alright, variable p is missing from that equation, but I get the idea.


Well, I was ONLY considering the (ab)'(b'c)' in the original equation, as an example. I wasn't trying to simplify the whole thing.

ibcoding said:
On that note, is this the correct truth table outputs:
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0

Here's what I get:

Code:
a	|	b	|	c	|	p	|	f
0 	|	0 	|	0 	|	0 	|	1
0 	|	0 	|	0 	|	1 	|	1
0 	|	0 	|	1 	|	0 	|	0
0 	|	0 	|	1 	|	1 	|	0
0 	|	1 	|	0 	|	0 	|	1
0 	|	1 	|	0 	|	1 	|	1
0 	|	1 	|	1 	|	0 	|	1
0 	|	1 	|	1 	|	1 	|	1
1 	|	0 	|	0 	|	0 	|	1
1 	|	0 	|	0 	|	1 	|	1
1 	|	0 	|	1 	|	0 	|	0
1 	|	0 	|	1 	|	1 	|	0
1 	|	1 	|	0 	|	0 	|	0
1 	|	1 	|	0 	|	1 	|	0
1 	|	1 	|	1 	|	0 	|	0
1 	|	1 	|	1 	|	1 	|	0
 
  • #10
Sorry, I wasn't complaining. :) Alright, that's the same as what I have.
 
  • #11
The equation breaks down to a'b + b'c' + a'bp, I believe.
 

1. How do I know if a logic diagram is correct?

To determine if a logic diagram is correct, you should first check if it follows the standard conventions and symbols for logic gates. Then, you can simulate the logic diagram using a logic simulator and compare the results with the expected output. Finally, you can verify the logic diagram by hand using truth tables or other logical methods.

2. What are the common mistakes to avoid when creating a logic diagram?

Some common mistakes to avoid when creating a logic diagram include using incorrect symbols for logic gates, not following the correct order of operations, and not properly labeling inputs and outputs. It is also important to check for any logical errors, such as feedback loops or floating inputs.

3. Can I use any software to create a logic diagram?

Yes, there are many software programs available that allow you to create logic diagrams, such as Microsoft Visio, Lucidchart, and draw.io. It is important to choose a software that has the necessary features and symbols for creating accurate logic diagrams.

4. Is it necessary to include a legend/key in a logic diagram?

Yes, it is important to include a legend or key in a logic diagram to explain the symbols and their corresponding logic gates. This helps to ensure that the diagram is easily understandable to others and reduces the risk of misinterpretation.

5. Can a logic diagram be used to represent any logical function?

Yes, a logic diagram can be used to represent any logical function, as long as it follows the standard conventions and symbols for logic gates. However, for more complex functions, it may be necessary to break them down into smaller sub-functions and use multiple diagrams to represent the entire function.

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