# Problem Quine-McClusky

M

#### Maurizio

Jan 1, 1970
0
Hi everyone,

I'd kindly ask some help with a problem using Quine-McClusky method.
I'm following the instruction on this web site:
http://www.embedded.com/columns/programmerstoolbox/29111968

Below I write the true table of the function that I'm trying to
minimize:

ROW ABCD OUTPUT
00 0000 1
01 0001 0
02 0010 0
03 0011 1
04 0100 0
05 0101 1
06 0110 0
07 0111 1
08 1000 0
09 1001 0
10 1010 0
11 1011 1
12 1100 0
13 1101 1
14 1110 0
15 1111 1

Step one: build a second table that contains only the minterms that
require the output to be true
ROW ABCD OUTPUT
00 0000 1
03 0011 1
05 0101 1
07 0111 1
11 1011 1
13 1101 1
15 1111 1

Matching up entries:

### 0000 ###
### 0011 ###
Matching: 0111 : 0111 <> 03,07 0x11 OK
Matching: 1011 : 1011 <> 03,11 x011 OK
### 0101 ###
Matching: 0111 : 0111 <> 05,07 01x1 OK
Matching: 1101 : 1101 <> 05,13 x101 1 <<<----- This entry is not
included
### 0111 ###
Matching: 0011 : 0011 <> 07,03 0x11 DUPLICATE
Matching: 0101 : 0101 <> 07,05 01x1 DUPLICATE
Matching: 1111 : 1111 <> 07,15 x111 OK
### 1011 ###
Matching: 0011 : 0011 <> 11,03 x011 DUPLICATE
Matching: 1111 : 1111 <> 11,15 1x11 OK
### 1101 ###
Matching: 0101 : 0101 <> 13,05 x101 DUPLICATE
Matching: 1111 : 1111 <> 13,15 11x1 OK
### 1111 ###
Matching: 0111 : 0111 <> 15,07 x111 DUPLICATE
Matching: 1011 : 1011 <> 15,11 1x11 DUPLICATE
Matching: 1101 : 1101 <> 15,13 11x1 DUPLICATE

I find all match described above.
Discarding duplicate entry I found seven matches.

The guide tell me that you should find a total of six matches:

03,07 0x11
03,11 x011
05,07 01x1
07,15 x111
11,15 1x11
13,15 11x1

My problem is here. Why only six matches?

I'd like to ask if somone know where I can find a simple guideline for
this problem.
Thank you very much for your help!

Ciao
Maurizio

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