Re: canonical forms

On Mon, 08 Oct 2007 14:09:46 -0000, sulekha <aarklon@xxxxxxxxx> wrote:

Hi all,

I was recently reading the book "Write Great code by ryndall Hyde" in
this in chapter 8 the following are given.

given n input variables there are two raised to two raised to n
unique Boolean functions ex:- for 2 i/p variables there are 16
different functions.

then he mentions about canonical forms. he says about sum of min terms
and sum of product form.

now my questions are as follows

1) what exactly is the purpose of canonical forms,especially sum of
min terms, where is it applied??

It is a little abstract, and you can go through life happily designing
logic without dealing with this stuff. But it doesn't hurt, either.

http://en.wikipedia.org/wiki/Canonical_form_%28Boolean_algebra%29

Classic PAL and PEEL (cpld) architectures hardware implemented logic
equations as sums of products, ie in minterm form.

Nowadays, manual logic minimization is not done a lot. Logic tends to
be done in FPGAs, which are lookup-table based; a LUT can directly map
any n-bit input (say, 4 or 5 input bits) into any 1-bit output
function, by brute force. And logic compilers handle the gory details
for you, so nowadays it's more important to write clear,
comprehensable (but not minimal) equations, and let the compiler map
it to the hardware.


2)author says that for each different Boolean function, we can choose
a single canonical representation of that function.
I am not getting this point, can any one explain

I think he's saying that any function can be unambiguously factored
into a standard form. Or something. If you were writing a compiler,
that sort of thing probably matters.


pls note i am by no means an expert in these matters so please be
kind. only a beginner

I just design logic, without ever being taught how. That 'canonical'
stuff seems kinda fru-fru to me.

John


.

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