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[20 pts] [urgent ] Boolean equation simplification

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AdvaRes

AdvaRes

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Hi all,
In my design the datapath delay let me use only frequencies below 1 Ghz.
The logic of the datapath is given by the relation shown in the figure. I need to simplify this relation as possible in order to reduce the delay introduced by the datapath so I can rise in frequency.

Is the relation provided simplifiable ?
 

treehugger said:
c+ab
Click to expand...

Thanks.
Unfortunately your reply is wrong. In fact when a=1 my relation gives b+/bc your relation gives c+b.
 

I think: c+ab

your minterms are {1,3,5,6,7} you can K-map it or Quine mcCluskey you get the simplified form above.

Resulting into:

1 AND
1 OR


your concern when a = 1; your orig equation becomes b+/bc is actually equal to b + c when you take the minterms.

A quick check for the orig and simplified form if they are the same is plug in all possible values of a, b and c; you will get the same result;

if you want to implement it via NAND or NOR gates, you may not get a simplified form.

Thanks,
 

    AdvaRes

    AdvaRes

    Points: 2
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Thanks my friend.

I found by K-Map that you're right !

Have you materials abouts Quine mcCluskey technique ?
 

Only using Nands seems quicker since an AND normally is an NAND and an invertor.

/(/C*/(AB))

so NAND[inv(C),NAND(A,B)]
 

    AdvaRes

    AdvaRes

    Points: 2
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drDOC said:
Only using Nands seems quicker since an AND normally is an NAND and an invertor.

/(/C*/(AB))

so NAND[inv(C),NAND(A,B)]
Click to expand...

Nice idea ! Using Nand and NOR introduce less delay.

4 All :


I gave you each 7 points. Many thanks.
 

Hello AdvaRes:

Here's a link to Quine McCluskey https://en.wikipedia.org/wiki/Quine_McCluskey

It is usually useful if you have more than 4 inputs of your combinatorial logic circuit. Since your app is just 3- inputs, K-map method should be fine.

The link also has some links of automated (software) for Quine McCluskey which makes life easier. :-D
 

Draw a Karnaugh map and the result is:

ab+c
 

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