All About Circuits

Listing minterms and maxterms

M

Thread Starter

mcc123pa

Joined Sep 12, 2010
40
Hi everyone:
For this problem I am given the following truth table:
x y z E F
0 0 0 0 1
0 0 1 1 0
0 1 0 1 1
0 1 1 0 0
1 0 0 1 1
1 0 1 0 0
1 1 0 1 0
1 1 1 0 1

part a) list the minterms and maxterms of each function, this is my answer

Minterms:
E: x'y'z
x'yz'
xy'z'
xyz'
Maxterms:
x'y'z'
x'yz
xy'z
xyz

Minterms:
F: x'y'z'
x'yz'
xy'z'
xyz
Maxterms:
xyz'
xy'z
x'yz
x'y'z

part B) says to find the max and min terms of E' and F' ,but won't that just be the reverse of the answers from part A?

Could someone please tell me if I am correct and if I am wrong could someone please post the correct answer (with steps to the solution if possible)? Thanks!!
 
Last edited:
Georacer

Georacer

Joined Nov 25, 2009
5,182
The maxterms are sums specificaly specified, i.e. M0=x+y+z by definition. Correct all the maxterms of part a.

As for part b, yes, the solution is to swap min and maxterms.
 
M

Thread Starter

mcc123pa

Joined Sep 12, 2010
40
Thanks for the help!

so say that the term "abc" was a maxterm for part a. Should it be written as a+b+c?

are the minterms correct and written correctly for part a? Could you give me the correct answer if they're wrong?

for part b, do I litterally just list the minterms from part a as maxterms for part b and vice versa?
 
Georacer

Georacer

Joined Nov 25, 2009
5,182
I will quote wikipedia's article on Canonical Forms (http://en.wikipedia.org/wiki/Canonical_form_(Boolean_algebra) ):

Indexing minterms

In general, one assigns each minterm an index based on a conventional binary encoding of the complementation pattern of the variables (where the variables in all the minterms are written in the same order, usually alphabetical). This convention assigns the value 1 to the direct form (xi) and 0 to the complemented form (x'i). For example, we assign the index 6 to the minterm abc' (110) and denote that minterm as m6. Similarly, m0 of the same three variables is a'b'c' (000), and m7 is abc (111).


Indexing maxterms

Each maxterm is assigned an index based on the opposite conventional binary encoding used for minterms. The maxterm convention assigns the value 0 to the direct form (xi) and 1 to the complemented form (x'i). For example, we assign the index 6 to the maxterm a' + b' + c (110) and denote that maxterm as M6. Similarly M0 of these three variables is a + b + c (000) and M7 is a' + b' + c' (111).
Click to expand...
So, since you have found correctly the indexes of minterms and maxterms, use the above information to convert them to sums of products of variables.

For the second part, just invert the truth table of the original function and to the same process. This will result giving the minterms the indexes of the former maxterms and vice versa.
 
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