[20 pts] [urgent ] Boolean equation simplification

[AdvaRes]

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]

c+ab

 

[AdvaRes]

c+ab

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

 

[neoaspilet11]

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]

Thanks my friend.

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

Have you materials abouts Quine mcCluskey technique ?

 

[drDOC]

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]

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

/(/C*/(AB))

so NAND[inv(C),NAND(A,B)]

Nice idea ! Using Nand and NOR introduce less delay.

4 All :


I gave you each 7 points. Many thanks.

 

[neoaspilet11]

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

 

[Sadegh.j]

Draw a Karnaugh map and the result is:

ab+c