Circuit minimization

I have a circuit that I've minimized using two different methods that have
produced two different answers.

The circuit is (A(B+C))+(A'BC')

Which I then expanded to disjunctive form:

AB+AC+A'BC'

Using a Karnaugh map I got the expression minimized to AB+AC+BC'

However using Venn diagrams I got the circuit minimized to AC+BC'

The thing I don't understand is that I thought Karnaugh maps always produced
a completely minimized circuit so what is it I'm doing wrong?

 

Your Karnaugh map solution is correct. You erred somewhere in the
Venn diagram. Maybe you left out the "don't care" states?

...Jim Thompson

 

You know, I've just looked over it again and it appears the Karnaugh map
solution is actually *wrong*.

I used three circles when I only need to use two.

 

It is wrong- you have AB + AC +A'BC' so that AB term expands to ABC+ABC'
obviously- then the ABC+AC=AC obviously, and the
ABC'+A'BC'=(A+A')BC'=BC' so that the finished expression is AC+BC'.

 

See- I warned you about that pill....

 

Hi James,

You need all 3 circles to avoid race hazard.

 

Ehhhh? I think it's YOU that needs to check his pills ;-)

...Jim Thompson

 

LOL!!- The only pills I take are an occasional vitamin-C....

 

Do some Bs, too. They're really good for you.

John

 

No, not wrong. Just not minimal. Apparently you did use "three
circles". Only two are required. Your third term, AB, is included
within the other two, (AC + BC').

 

Are you still saying that BC' + AC + AB is not correct? <Big Frown>

Better double-up on the vitamin-C ;-)

...Jim Thompson

 

Aha! Missed that :-(

...Jim Thompson

 

Nevermind! Duh! I overlooked minimal :-(

I'll plead that it was a pill problem ;-)

Doc took me off of Atenolol on Friday since it wasn't controlling my
BP and put me on atacand HCT.

Saturday night had a rebound effect from going off of Atenolol and
went tachycardia (100 BPS).

Added back in 1/2 dose of Atenolol and will wean slowly.

Everything seems OK now.

...Jim Thompson

 

Hi Michael,

Yes, but there is a risk of race hazard between ABCD and AB'CD which will
need at least a circle around ABD and to minimize that, you go for the
entire column which gives AB, making it AB+AC+BC' - if it to be used in
the real world.

 

Don't beat yourself up too bad, Jim. I had to actually map both
(AB+AC+BC') and (AC+BC') to see whuddup wi' with the first.

 

Naw, not really. Here we always interpose a latch between combinatorial
and down-stream stuff.

 

I was using KarnaughMap v4.4.5, but didn't trust it, and also did a
hand check before I fessed up ;-)


...Jim Thompson

 

My doctor (a very nice Chinese lady) put me on Atenolol. It's a beta
blocker and makes bp go down by reducing heart output. That made me
get so easily winded that I couldn't get any decent exercize, which
makes one get fat, raising bp! Not good to mess with your heart!

Now I'm taking cheap stuff, an ace inhibitor and a diuretic, and they
work great for me. I tune the dosage to just below the point when I
fall over getting out of a chair or bed. 115/75 is easy, with a little
exercize and weight control. Some MDs think everybody over 45 should
take these routinely, along with aspirin and a statin.

This is relevant to electronic design: older people have the tricks
and experience (and just plain balls) to do great design, but they
have to stay in tune, not to mention alive, to keep their brains
working at top form. I know too many engineers who have gotten fat and
lazy, and mostly sleep at their desks in the afternoon.

John

back to hacking this uP code. Some days, like today, I seem to break
everything I touch. This keypad thing - membrane switch, up/down the
menu list, variable jogging, typematic, title flashing, special error
messages with timeouts, raw 16-segment VF drive - is getting hairy.
Time to test the latest pass.

VSEGS: ; VF DISPLAY SEGMENTS ARE :

N = 0800h ; AAAAAAAAAAAAAAA
P = 1000h ; FH L KB
D = 0008h ; F H L K B
R = 2000h ; F H L K B
C = 0004h ; F H L K B
H = 0080h ; F H L K B
K = 0100h ; F HLK B
L = 0200h ; GGGGGGG MMMMMMM
A = 0001h ; E RPN C
B = 0002h ; E R P N C
F = 0020h ; E R P N C
G = 0040h ; E R P N C
M = 0400h ; E R P N C
E = 0010h ; ER P NC
VDP = 4000h ; DDDDDDDDDDDDDDD VDP

 

Same here... put on weight (about 25#) since going on Atenolol. So I
finally confronted the doc about it last Friday. She switched me to
atacand HCT, but neglected to consider that you need to wind down from
the Atenolol, otherwise your heart goes bananas and ups the rate
precipitously :-(

IMHO statins SUCK... they're destructive of muscle tissue. Just eat a
handful of walnuts daily.

I don't have a falling asleep problem, but I'm distinctly
out-of-shape, and determined to get back to high-school weight ;-)

[snip]

...Jim Thompson

 

Where did D come from?