h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Boolean Expressions from Truth Tables - A2062045
Author: Old Hairy - U241325

I offer A1269894 (Universal Functions of Boolean Algebra) for peer review, together with A1238889 (Boolean Function Reduction), A1340812 (Boolean Functions Classified) and A2069894 (Boolean Expressions from Truth Tables).

The first of these refers to all of the others, and so cannot stand alone. The others are complete within themselves.

I find the section where you introduce the concepts of minterms and maxterms are very difficult to understand, even though I did a course in Boolean Algebra (many years ago). There must be an easier way of stating this.

The table needs some work. Because you've put in four separate tables, they are independent. When the screen size is very narrow (for example when you;'re looking at h2g2 in a small window), some of the table cells change to two lines high, and then aren't lined up with the other ones. Perhaps you could make one big table of it.

Hello Gnomon.

Do not understand your posting.

Which part of minterms/maxterms is difficult? Is it that the example table is rather too far (more than a screen) from the descriptive text? I do describe how minterms and maxterms are formed, and even suggest why they are so named - something omitted from every conventional text that I have read on the matter.

Where I describe minterms, I could add something that says X1,X2,X3 being false,true,false leads to NOT X1 AND X2 AND NOT X3, that is in effect quote a line from the complete list given in the table, and similarly for maxterms, leading to X1 OR NOT X2 OR X3. Doing so would separate the text from the given table even more though.

All the tables in this entry are already contained within outer tables. If you view the entry in an unsuitably small window, the browser does its best but the tables break up. There is nothing I can do to fix that. Should I mention that full screen viewing is needed somewhere in the introduction?

The problem is that some tables "break up" while others don't, which causes they to be no longer aligned. If you had one table, then there wouldn't be a problem.

The problem with minterms/maxterms is not that there is anything incorrect. It is that I get confused by all the references to True and False - this is very far from normal modes of thought. I would prefer a gentler introduction. I know that you do not want to simplify this so much that the average News of the World reader can understand it, but at the moment it seems so complex that only someone who already understands it would be able to read it.

Hello Gnomon.

I still don't understand the tables thing. All the tables have the same structure. An outer table, borders on thick, has a single row and single column. Inside that, a placement table has borders off, one row, and several columns. This table controls the spacing between the main items, which are tables, borders on thin. From outer to inner, the CELLPADDING is 2, 6, 4. I have studiously avoided CAPTION, because of the problem in Brunel skin. I found that using HEIGHT did not lead to reliable alignment of the rows, therefore many of the tables have dummy &nbsp subscipts, to line up with other having real subscripts. I previewed the tables in every skin except plain, but always full screen. Which tables do you find that break?

I would like the entry to be widely accessible, but am not concerned whether the individual that reads only the Daily Sport can understand it - he won't be here. I am talking about truth tables, which contain only true and false, so if that is confusing, can you suggest a way out? I thought that maxterms might be the more confusing, because everthing in them is, in effect, complemented. For that reason, I described them in full, rather than invoking De Morgan on the minterms, which is technically correct and quicker to state. (I avoid using 0 and 1, because I might want to write an entry about binary arithmetic, which will need to separate logic from arithmetic.)

The tables I am talking about are in the section "Canonical Forms". I'm using Brunel skin, Internet Explorer 6 and have my window size set to about 800 pixels wide, which will be the full screen size for many readers.

There is an outer box. Inside this box are four tables. The two tables on the left have one line of text on each row, but the third table, entitled "minterms" has two lines of text for most rows, which means that the whole table is much taller than the other two, and the rows in it do not line up with the rows in the other tables.

The table problem should now be fixed. It was rather hard to find - you must be using a larger than normal text size in your browser.

Now the minterm/maxterm thing - any suggestions?

The tables are indeed now OK. By the way, I am using "Medium" text.

I'll think about the minterm/maxterm problem later.

Just a comment.

Clarifying the tables thing, and recording it for future reference. Text items are liable to get folded unless &nbsp is used throughout. Folding occurs differently in different skins, and in different screen resolutions. At 1024 pixels, I got no folding with medium chars in any skin, only with larger chars. With larger chars I got folding in Alabaster (normal for me).

this article is very accurate and descriptive, but not very accessible at the moment. I would put a different introduction, explaining the uses of these functions in processing information (is that right?) eg in computers as you've stated. Would it be useful to put in this introduction how true/false gives you a binary system? It depends which audience you are aiming at

Old Hairy,

you say that the methods give good compact expressions if the truth tables have been abbreviated, but later on you say that the methods as presented only work on unabbreviated truth tables.

Hello Gnomom.

Don't quite understand the problem. I state, in this order

1) 'The methods do give comparatively simple expressions if the truth table of the given function has been well abbreviated'

2) 'The methods are generalisations of the fundamental techniques producing the canonical forms of a function F from the complete, unabbreviated truth table'

3) 'The constructions given need only slight adaptation to be applied to abbreviated tables, to give expressions in the forms of a sum of products or a product of sums'

Then after (2) I develop the method for canonical forms, using maxterms or minterms. After (3) I give the modified procedure, which involves subexpressions which are neither true maxterms nor true minterms, but just sums and products. I also justify the modifications in terms of the abbreviation procedure.

Where do I say 'the methods as presented only work on unabbreviated truth tables', unless you mean (2)?

I took (2) to mean that unabbreviated tables are used with these methods. I didn't notice (3).

Hello Gnomon.

So does that mean its OK as it is, or does (3) need more emphasis?

I've had another look at this from start to finish.

in terms of the those arguments --> in terms of those arguments

I suggest putting a comma after the phrase "that is".

I think the paragraph explaining the formation of minterms really needs to be expanded. I don't understand it at present, and I think that explains the problems I was having with the rest of the entry.

Hello everyone. Sorry for any delays on my part.

I've just done a little edit, expanding on the formation of minterms. If necessary, I could expand further, describing the product chapter and verse, but hope that what I have added so far does the trick.

Is it good enough then just to say maxterms are similar, or do they need expanding too?

By the way, I'll fix up the minor typo's and stuff later. Just want to get the main substance right at this stage.

It's certainly good enough to say maxterms are done similarly to minterms.

I still find the explanation of minterms is a very complicated way of describing something which is basically very simple. I can just about understand it, even though I already know how to convert a truth table to a boolean function.

I'm suffering the usual problem of understanding it too well to appreciate the difficulty. Can you help?

Are you getting a lot of page faults and proxy errors today? I am.

RL will cut me off from h2g2 from about 10.00 until tomorrow.

I have completely rewritten the definitions of minterms and maxterms, so that they are now clear (I hope). The 'the those' typo has been fixed as well.

Can you change the subheaders to headers?