Boolean Algebra

B

Beanq

Guest
How can I simplify this? I need to implement it using NAND gates only. I
thought maybe Demorgan, but I don't see how.
F=AB+AC+AD+BC+BD+CD
 
How can I simplify this? I need to implement it using NAND gates only. I
thought maybe Demorgan, but I don't see how.
F=AB+AC+AD+BC+BD+CD
Hi, Bean. Straight homework help here. Cool.

Beginning digital logic classes are given three tools -- truth table, Karnaugh
mapping, and Demorgan, right? First thing I did was just draw a truth table.
Inspection shows there are only five cases where F is not true, so I decided to
do this inverted -- that is, solve for what's not true, rather than what's
true.

Let Q = (A! AND B! AND C!)
Let R = (A! AND B! AND D!)
Let S = (A! AND C! AND D!)
Let T = (B! AND C! AND D!)

It should be obvious looking at the table that F! = Q + R + S + T (with A! AND
B! AND C! AND D! being the redundant case which is true for all). Now, you can
Demorganize that, and come up with what you have below, with the last NAND
being used to invert again from F! to F. View in fixed font (like M$
Notepad)...

.---.
A!----| |
B!----| |o----------
C!----|& | |
| | |
'---' |
.---. |
A!----| | | .-----.
B!----| |o------- | | |
D!----|& | | '-- | | __
| | | | | |-----| |
'---' '----- | |o------| |& |o-
.---. | & | ------|__|
A!----| | .------| |
C!----| |o------- | |
D!----|& | .---| |
| | | '-----'
'---' |
.---. |
B!----| | |
C!----| |o----------
D!----|& |
| |
'---'

created by Andy´s ASCII-Circuit v1.22.310103 Beta www.tech-chat.de

This is pretty similar to factoring quadratics back in high school -- your
ability improves with practice. Try solving problems in different ways, and
just do what works.

Good luck.
Chris
 
"Beanq" <bean@yahoo.ca> schreef in bericht
news:bmt2e2$qtjbs$1@ID-198839.news.uni-berlin.de...
How can I simplify this? I need to implement it using NAND gates only. I
thought maybe Demorgan, but I don't see how.
F=AB+AC+AD+BC+BD+CD


Looks like schoolwork. But nevertheless:

It's (almost) written in NANDS and there is nothing to simplify. (Just draw
a Karnaugh map to see it.) Just use De Morgan:

f=ab+ac+ad+bc+bd+cd
=//(ab+ac+ad+bc+bd+cd)
= /(/(a*b) * /(a*c) * /(a*d) * /(b*c) * /(b*d) * /(c*d))

So you need six two inputs NAND and one six inputs NAND.

(N)AND that's it.

pieter


---
Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6.0.525 / Virus Database: 322 - Release Date: 9-10-2003
 
chris wrote:

"CFoley1064" <cfoley1064@aol.com> wrote in message
news:20031019133527.28188.00000930@mb-m12.aol.com...
How can I simplify this? I need to implement it using NAND gates only.
I
thought maybe Demorgan, but I don't see how.
F=AB+AC+AD+BC+BD+CD


Hi, Bean. Straight homework help here. Cool.

Beginning digital logic classes are given three tools -- truth table,
Karnaugh
mapping, and Demorgan, right? First thing I did was just draw a truth
table.
Inspection shows there are only five cases where F is not true, so I
decided to
do this inverted -- that is, solve for what's not true, rather than what's
true.

Let Q = (A! AND B! AND C!)
Let R = (A! AND B! AND D!)
Let S = (A! AND C! AND D!)
Let T = (B! AND C! AND D!)

It should be obvious looking at the table that F! = Q + R + S + T (with A!
AND
B! AND C! AND D! being the redundant case which is true for all). Now,
you can
Demorganize that, and come up with what you have below, with the last NAND
being used to invert again from F! to F. View in fixed font (like M$
Notepad)...

.---.
A!----| |
B!----| |o----------
C!----|& | |
| | |
'---' |
.---. |
A!----| | | .-----.
B!----| |o------- | | |
D!----|& | | '-- | | __
| | | | | |-----| |
'---' '----- | |o------| |& |o-
.---. | & | ------|__|
A!----| | .------| |
C!----| |o------- | |
D!----|& | .---| |
| | | '-----'
'---' |
.---. |
B!----| | |
C!----| |o----------
D!----|& |
| |
'---'

created by Andy´s ASCII-Circuit v1.22.310103 Beta www.tech-chat.de

This is pretty similar to factoring quadratics back in high school -- your
ability improves with practice. Try solving problems in different ways,
and
just do what works.

Good luck.
Chris
Shaun writes: great answer!, even though I don't understand one word you
wrote, but it did sound great
 
"SHAUN" <camba850@bellsouth.net> wrote in message
news:cJAkb.11429$W77.9636@bignews6.bellsouth.net...
chris wrote:

"CFoley1064" <cfoley1064@aol.com> wrote in message
news:20031019133527.28188.00000930@mb-m12.aol.com...
How can I simplify this? I need to implement it using NAND gates only.
I
thought maybe Demorgan, but I don't see how.
F=AB+AC+AD+BC+BD+CD


Hi, Bean. Straight homework help here. Cool.

Beginning digital logic classes are given three tools -- truth table,
Karnaugh
mapping, and Demorgan, right? First thing I did was just draw a truth
table.
Inspection shows there are only five cases where F is not true, so I
decided to
do this inverted -- that is, solve for what's not true, rather than
what's
true.

Let Q = (A! AND B! AND C!)
Let R = (A! AND B! AND D!)
Let S = (A! AND C! AND D!)
Let T = (B! AND C! AND D!)

It should be obvious looking at the table that F! = Q + R + S + T (with
A!
AND
B! AND C! AND D! being the redundant case which is true for all). Now,
you can
Demorganize that, and come up with what you have below, with the last
NAND
being used to invert again from F! to F. View in fixed font (like M$
Notepad)...

.---.
A!----| |
B!----| |o----------
C!----|& | |
| | |
'---' |
.---. |
A!----| | | .-----.
B!----| |o------- | | |
D!----|& | | '-- | | __
| | | | | |-----| |
'---' '----- | |o------| |& |o-
.---. | & | ------|__|
A!----| | .------| |
C!----| |o------- | |
D!----|& | .---| |
| | | '-----'
'---' |
.---. |
B!----| | |
C!----| |o----------
D!----|& |
| |
'---'

created by Andy´s ASCII-Circuit v1.22.310103 Beta www.tech-chat.de

This is pretty similar to factoring quadratics back in high school --
your
ability improves with practice. Try solving problems in different ways,
and
just do what works.

Good luck.
Chris

Shaun writes: great answer!, even though I don't understand one word you
wrote, but it did sound great
It must be those cheesy ASCII representations Shaun ;-) I don't think
anybody understands them with the possible exception of the poster!
 
"Baphomet" <fandaDEATH2SPAMMERS@catskill.net> wrote:

It must be those cheesy ASCII representations Shaun ;-) I don't think
anybody understands them with the possible exception of the poster!
You are using Outlook Express and it is not easy to see the ASCII
schematics in it.

You need to right-click the message in the message list, choose
"properties", details, source code, maximize window. then you will see
the message in notepad, with a fixed font, and these ASCII schematics
will make sense to you.


--
Roger J.

(My email address is a spam trap, don't use it)
 
"Roger Johansson" <no-email@home.se> wrote in message
news:u438pvoajfuk0d82b7i6bfmi5rp0rl2grq@4ax.com...
"Baphomet" <fandaDEATH2SPAMMERS@catskill.net> wrote:

It must be those cheesy ASCII representations Shaun ;-) I don't think
anybody understands them with the possible exception of the poster!

You are using Outlook Express and it is not easy to see the ASCII
schematics in it.

You need to right-click the message in the message list, choose
"properties", details, source code, maximize window. then you will see
the message in notepad, with a fixed font, and these ASCII schematics
will make sense to you.


--
Roger J.
Thanks for the tip Roger -

I guess I'm just old fashioned. I still prefer a good schematic but I'll try
your advice ;-)
 
"Baphomet" <fandaDEATH2SPAMMERS@catskill.net> wrote:

You need to right-click the message in the message list, choose
"properties", details, source code, maximize window. then you will see
the message in notepad, with a fixed font, and these ASCII schematics
will make sense to you.

I'm still too stupid to figure out how to do this in O.E., but I did look at
the post in Google and it made perfect sense, even to a dolt like me...DUH
It works, if you only try to do it step by step.
First rightclick the message, and choose properties at the bottom of
the menu which appears, then choose the "details tab" at the top of
that window, then use the button named source (there is only one
button there so it doesn't matter what it says really), and maximize
that new popup window. There is the raw message and it starts with a
lot of headers, scroll down to see the real message.


--
Roger J.

(My email address is a spam trap, don't use it)
 
"Roger Johansson" <no-email@home.se> wrote in message
news:u438pvoajfuk0d82b7i6bfmi5rp0rl2grq@4ax.com...
"Baphomet" <fandaDEATH2SPAMMERS@catskill.net> wrote:

It must be those cheesy ASCII representations Shaun ;-) I don't think
anybody understands them with the possible exception of the poster!

You are using Outlook Express and it is not easy to see the ASCII
schematics in it.

You need to right-click the message in the message list, choose
"properties", details, source code, maximize window. then you will see
the message in notepad, with a fixed font, and these ASCII schematics
will make sense to you.
I'm still too stupid to figure out how to do this in O.E., but I did look at
the post in Google and it made perfect sense, even to a dolt like me...DUH
 
"Roger Johansson" <no-email@home.se> wrote in message
news:u438pvoajfuk0d82b7i6bfmi5rp0rl2grq@4ax.com...
"Baphomet" <fandaDEATH2SPAMMERS@catskill.net> wrote:

It must be those cheesy ASCII representations Shaun ;-) I don't think
anybody understands them with the possible exception of the poster!

You are using Outlook Express and it is not easy to see the ASCII
schematics in it.

You need to right-click the message in the message list, choose
"properties", details, source code, maximize window. then you will see
the message in notepad, with a fixed font, and these ASCII schematics
will make sense to you.


--
Roger J.

(My email address is a spam trap, don't use it)
In OE, one clicks 'view' then 'text size' then 'fixed'.
One can also set the default font to couier ....
 
Baphomet wrote:
"Roger Johansson" <no-email@home.se> wrote in message
news:u438pvoajfuk0d82b7i6bfmi5rp0rl2grq@4ax.com...
"Baphomet" <fandaDEATH2SPAMMERS@catskill.net> wrote:

It must be those cheesy ASCII representations Shaun ;-) I don't think
anybody understands them with the possible exception of the poster!

You are using Outlook Express and it is not easy to see the ASCII
schematics in it.

You need to right-click the message in the message list, choose
"properties", details, source code, maximize window. then you will see
the message in notepad, with a fixed font, and these ASCII schematics
will make sense to you.

I'm still too stupid to figure out how to do this in O.E., but I did look at
the post in Google and it made perfect sense, even to a dolt like me...DUH
-------------
Save the whole message to a text file and view it.

-Steve
--
-Steve Walz rstevew@armory.com ftp://ftp.armory.com/pub/user/rstevew
Electronics Site!! 1000's of Files and Dirs!! With Schematics Galore!!
http://www.armory.com/~rstevew or http://www.armory.com/~rstevew/Public
 

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