Why I like ladder logic for boolean expressions

Example:
Take this boolean algebraic expression:

note: I'm using a single quote to denote negation as I can't place a bar over the letter.

(CA + B' + C + D') * C

When you reduce this expression:
1) CA + CB' + C*C + CD' // multiply C by what is in parens
2) CA + CB' + C + CD' // we replace (C * C) with C because: C * C = C because: C AND C = C
3) CA + CB' + C * (1 + D') // we factor out C from (C + CD').
4) CA + CB' + C * 1 // (1 + D') = 1 because: (1 OR NOT D) = 1
5) CA + CB' + C // because: C * 1 = C or C AND 1 = C
6) CA + C * (B' + 1) // we know that (B' + 1) = 1 because NOT B OR 1 = 1
7) CA + C * 1
8) CA + C // (C * 1) = C because C AND 1 = C
9) C * (A + 1) // (A + 1) also known as A OR 1 = 1
10) C * 1 // C AND 1 = C
= C

Not immediately apparent that (A + B' + C + D') * C = C

Now in ladder as (CA + CB' + CC + CD'):

if every one starts with C being high and C on its own can be high... then anything else is irrelevant other than C being high.

Yes, it is easy to see that OR'ing w/ C will make the output true if C is true;
Not as apparent if C is False.
It is not a perfect example, I just found it interesting.

When it comes to simplifying Boolean algebra, K-Maps for the win: https://en.wikipedia.org/wiki/Karnaugh_map

PreLC said:

When it comes to simplifying Boolean algebra, K-Maps for the win: https://en.wikipedia.org/wiki/Karnaugh_map

Click to expand...

K-maps are ok, but Ladder pretty clearly shows what can be eliminated or grouped together.

ganutenator said:

Not immediately apparent that (A + B' + C + D') * C = C

Click to expand...

It is to me. It is as simple as factoring out C. Also 20 years ago Terry Wood would show you how to use Karnaugh maps to simplify boolean equations.
https://en.wikipedia.org/wiki/Karnaugh_map

There are also some basic rules like de Morgan's theorem.
https://en.wikipedia.org/wiki/De_Morgan's_laws


The good think about ladder is that you can see what contacts are active. In my programming IDEs I can set up a watch window or just hold my cursor over the variable I want to check.

Peter Nachtwey said:

It is to me. It is as simple as factoring out C. Also 20 years ago Terry Wood would show you how to use Karnaugh maps to simplify boolean equations.
https://en.wikipedia.org/wiki/Karnaugh_map

There are also some basic rules like de Morgan's theorem.
https://en.wikipedia.org/wiki/De_Morgan's_laws


The good think about ladder is that you can see what contacts are active. In my programming IDEs I can set up a watch window or just hold my cursor over the variable I want to check.

Click to expand...

Well, if I remember correctly, you are quite the math genius. You in my opinion are not the norm.

ganutenator said:

Well, if I remember correctly, you are quite the math genius. You in my opinion are not the norm.

Click to expand...

I am not a math genius. I am good but not that good. I am at the point of "the more you know, the more you know you don't know".

Peter Nachtwey said:

I am not a math genius. I am good but not that good. I am at the point of "the more you know, the more you know you don't know".

Click to expand...

"Always be skeptical of those who claim to be the best"

-Dunning Kruger














or what would have been said if there was ever a quote

Karnough maps are for analyzing and possibly reducing logic.
Ladder (and other languages) is to implement the logic, reduced or not.
I agree that Ladder is the best language for logic. Sometimes and with a little practice you can cut down unnecessary logic just by looking at the Ladder rung. But .. sometimes I leave unnecessary logic in, because commenting more is better than cutting down to the minimum. When you remove unnecessary code, you actually hide the considerations that were the reason behind the removal of the unnecessary code.
Ease of throubleshooting and maintaining trumps perfect optimization.

By the way, Siemens have added a new language to their TIA programming platform called "cause-effect matrix" aka CEM. Does sound similar to karnough maps. But I dont think the intention is to optimize the logic, only to make it very simple to program.
Someone asked on Siemens own forum "do you find CEM language useful? Will you use it?". No-one anwered.
https://support.industry.siemens.co...17-cause-effect-matrix-will-you-use-it/277410