- #1
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.
ibcoding said:Alright, variable p is missing from that equation, but I get the idea.
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
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
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.
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.
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.
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.
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.