Circuit minimization

James · May 15, 2004

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?

Jim Thompson · May 15, 2004

On Sat, 15 May 2004 18:36:31 +0100, "James" <james@spamco.com> wrote:

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?

480)460-2350 | |
| E-mail Address at Website Fax

James · May 15, 2004

"Jim Thompson" <thegreatone@example.com> wrote in message
news:3kmca051r9n0ga4d15gna101heb8ul3sf8@4ax.com...

On Sat, 15 May 2004 18:36:31 +0100, "James" <james@spamco.com> wrote:

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?

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.

Fred Bloggs · May 15, 2004

James wrote:

"Jim Thompson" <thegreatone@example.com> wrote in message
news:3kmca051r9n0ga4d15gna101heb8ul3sf8@4ax.com...

On Sat, 15 May 2004 18:36:31 +0100, "James" <james@spamco.com> wrote:

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?

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'.

Fred Bloggs · May 15, 2004

Jim Thompson wrote:

On Sat, 15 May 2004 18:36:31 +0100, "James" <james@spamco.com> wrote:

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

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

Soeren · May 15, 2004

Hi James,

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.

You need all 3 circles to avoid race hazard.

--
Regards,
Soeren

* If it puzzles you dear... Reverse engineer *

Jim Thompson · May 15, 2004

On Sat, 15 May 2004 22:08:04 GMT, Fred Bloggs <nospam@nospam.com>
wrote:

Jim Thompson wrote:
On Sat, 15 May 2004 18:36:31 +0100, "James" <james@spamco.com> wrote:

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

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

480)460-2350 | |
| E-mail Address at Website Fax

Fred Bloggs · May 16, 2004

Jim Thompson wrote:

On Sat, 15 May 2004 22:08:04 GMT, Fred Bloggs <nospam@nospam.com
wrote:

Jim Thompson wrote:

On Sat, 15 May 2004 18:36:31 +0100, "James" <james@spamco.com> wrote:

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

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

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....

John Larkin · May 16, 2004

On Sun, 16 May 2004 16:23:26 GMT, Fred Bloggs <nospam@nospam.com>
wrote:

Jim Thompson wrote:
On Sat, 15 May 2004 22:08:04 GMT, Fred Bloggs <nospam@nospam.com
wrote:

Jim Thompson wrote:

On Sat, 15 May 2004 18:36:31 +0100, "James" <james@spamco.com> wrote:

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

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

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

Michael · May 16, 2004

James wrote:

"Jim Thompson" <thegreatone@example.com> wrote in message
news:3kmca051r9n0ga4d15gna101heb8ul3sf8@4ax.com...
On Sat, 15 May 2004 18:36:31 +0100, "James" <james@spamco.com> wrote:

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?

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.

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').

Jim Thompson · May 16, 2004

On Sun, 16 May 2004 16:23:26 GMT, Fred Bloggs <nospam@nospam.com>
wrote:

Jim Thompson wrote:
[snip]
Your Karnaugh map solution is correct. You erred somewhere in the
Venn diagram. Maybe you left out the "don't care" states?

...Jim Thompson

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

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....

480)460-2350 | |
| E-mail Address at Website Fax

Jim Thompson · May 16, 2004

On Sun, 16 May 2004 16:43:16 GMT, Michael <NoSpam@att.net> wrote:

James wrote:

"Jim Thompson" <thegreatone@example.com> wrote in message
news:3kmca051r9n0ga4d15gna101heb8ul3sf8@4ax.com...
On Sat, 15 May 2004 18:36:31 +0100, "James" <james@spamco.com> wrote:

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?

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.

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').

480)460-2350 | |
| E-mail Address at Website Fax

Jim Thompson · May 16, 2004

On Sun, 16 May 2004 09:49:27 -0700, Jim Thompson
<thegreatone@example.com> wrote:

On Sun, 16 May 2004 16:23:26 GMT, Fred Bloggs <nospam@nospam.com
wrote:
[snip]
See- I warned you about that pill....

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....

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

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

...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
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice

480)460-2350 | |
| E-mail Address at Website Fax

Soeren · May 16, 2004

Hi Michael,

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').

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.

--
Regards,
Soeren

* If it puzzles you dear... Reverse engineer *

Michael · May 16, 2004

Jim Thompson wrote:

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').

Aha! Missed that :-(

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice480)460-2350 | |
| E-mail Address at Website Fax480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

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.

Michael · May 16, 2004

Soeren wrote:

Hi Michael,

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').

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.

--
Regards,
Soeren

* If it puzzles you dear... Reverse engineer *

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

Jim Thompson · May 16, 2004

On Sun, 16 May 2004 20:37:15 GMT, Michael <NoSpam@att.net> wrote:

Jim Thompson wrote:
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').

Aha! Missed that :-(

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice480)460-2350 | |
| E-mail Address at Website Fax480)460-2142 | Brass Rat |
| http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

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.

480)460-2350 | |
| E-mail Address at Website Fax

John Larkin · May 16, 2004

On Sun, 16 May 2004 10:26:03 -0700, Jim Thompson
<thegreatone@example.com> wrote:

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

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

Jim Thompson · May 16, 2004

On Sun, 16 May 2004 14:26:18 -0700, John Larkin
<jjlarkin@highSNIPlandTHIStechPLEASEnology.com> wrote:

On Sun, 16 May 2004 10:26:03 -0700, Jim Thompson
thegreatone@example.com> wrote:

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

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!

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 :-(

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.

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

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.

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

John

[snip]

480)460-2350 | |
| E-mail Address at Website Fax

Richard Henry · May 17, 2004

"Soeren" <Look@iNO-SPAMt.dk.invalid> wrote in message
news:Xns94EBDCE8586CFo8oLOOKatHOMEo8o@212.242.40.196...

Hi Michael,

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').

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.

Where did D come from?

Circuit minimization

James

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