canonical forms

[sulekha]

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??

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

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

 

[Rich Grise]

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??

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

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

This is sci.electronics.basics . All beginners are welcome here.

Problem is, even after reading the wiki article,
http://en.wikipedia.org/wiki/Canonical_form

I still don't know what it means. =:-O

I guess it's something like a standardized format, such that each
value can be uniquely represented in the same "formula" by just
plugging in the parameters.

I'm sure that someone will be happy to clarify that further.

Good Luck!
Rich

 

[John Larkin]

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_(Boolean_algebra)

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

 

[john jardine]

Hi all,

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

[...]

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.

[...]

"Great code". Yep. Fru-Fru, pretentious, pompous, affected.
An ongoing work but programmers can celebrate being nearly fully adrift
from the shores of reality.

 

[John Larkin]

Hi all,

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

[...]

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.

[...]

"Great code". Yep. Fru-Fru, pretentious, pompous, affected.
An ongoing work but programmers can celebrate being nearly fully adrift
from the shores of reality.

Well, that's what abstraction is for.

John