# Boolean Algebra

Discussion in 'Electronic Basics' started by Beanq, Oct 19, 2003.

1. ### BeanqGuest

How can I simplify this? I need to implement it using NAND gates only. I
thought maybe Demorgan, but I don't see how.

2. ### CFoley1064Guest

How can I simplify this? I need to implement it using NAND gates only. I
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\$

.---.
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

3. ### petrus bitbyterGuest

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:

= /(/(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

4. ### SHAUNGuest

chris wrote:

Shaun writes: great answer!, even though I don't understand one word you
wrote, but it did sound great

5. ### BaphometGuest

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

6. ### Roger JohanssonGuest

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.

7. ### BaphometGuest

Thanks for the tip Roger -

I guess I'm just old fashioned. I still prefer a good schematic but I'll try

8. ### Roger JohanssonGuest

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.

9. ### BaphometGuest

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

10. ### Lord GarthGuest

In OE, one clicks 'view' then 'text size' then 'fixed'.
One can also set the default font to couier ....