How to know if a certain number is a don't care in KMAP

[engineeringnoobie]

Homework Statement

given the function
$F(a,b,c,d)=Σ(0,1,2,4,5,10,12)$

how can i know for sure if 8 is a don't care?
and is it possible for 6 and 14 to be don't cares?

Homework Equations

it's part of a bigger exercise, so the boolean expression i got from previous parts is a'c'+c'd'+b'd'

The Attempt at a Solution

as it's a part of a bigger question, i solved the previous parts to obtain the boolean expression of a'c'+c'd'+b'd' and i don't know how to know if 8 is for sure a don't care, and if 6 and 14 might be don't cares.

 

[berkeman]

Welcome to the PF.

Don't cares are usually inputs to the K-Map, not the results from it. Why would 8 be a don't care ("X") in this K-Map?

 

[engineeringnoobie]

thank you for replying. i was asked in the sub question if 8 must be a don't care(and i don't know how to answer that)

 

[berkeman]

$F(a,b,c,d)=Σ(0,1,2,4,5,10,12)$

The way I interpret your notation, that is a list of the "1" values for the function F(abcd). That implies that all other terms are "0", no?

 

[berkeman]

https://en.wikipedia.org/wiki/Karnaugh_map#Don.27t_cares

Don't cares

The value of f ( A , B , C , D ) {\displaystyle f(A,B,C,D)}

for ABCD = 1111 is replaced by a "don't care". This removes the green term completely and allows the red term to be larger. It also allows blue inverse term to shift and become larger
Karnaugh maps also allow easy minimizations of functions whose truth tables include "don't care" conditions. A "don't care" condition is a combination of inputs for which the designer doesn't care what the output is. Therefore, "don't care" conditions can either be included in or excluded from any rectangular group, whichever makes it larger. They are usually indicated on the map with a dash or X.

 

[engineeringnoobie]

i think he meant something else that i understand but i don't know how to implement.
after simplifying f(a,b,c,d) in a karnaugh map, i should only get a'c'+c'd'+b'd', and i need to check if the given possibilities allow me to treat the other elements as don't cares. but i don't know how to do that

 

[berkeman]

i should only get a'c'+c'd'+b'd'

Hmm, my answer was not quite that simplified. I guess I'll try it again...

 

[berkeman]

Are you sure that the solution you show does not already include some don't cares? Is that the question? "Which terms to you need to make X in order to reach this simpler solution"?

 

[engineeringnoobie]

the question is to check if:

(i)if 6 and 14 might've been two of the don't cares
(ii)if 15 might've been one of the don't cares
(iii) if 8 must've been one of the don't cares

 

[berkeman]

the question is to check if:

(i)if 6 and 14 might've been two of the don't cares
(ii)if 15 might've been one of the don't cares
(iii) if 8 must've been one of the don't cares

Okay, that is a different question than your first post. Do a K-Map of just the function you were given, and notice how you get 4 minterms. Then compare that answer to the solution you are given, and then figure out which terms you need to be able to change from 0-->1 (or 0-->X) in order to get that simplified solution. It does look like you will need to change F(8)-->X at least, and maybe more... Can you post your work?

 

[engineeringnoobie]

c'.d' c'.d c.d c.d'
a'.b' 1 1 0 1
a'.b 1 1 0 x
a.b 1 0 x x
a.b' x 0 0 1

if m6, and m14 together, i get cd' which is not what i was looking for so i guess it's not possible.
if m15, it doesn't help me at all (it's not connected to anything, i can't pair it)
if m8, if i am right, then it simplifies the simplification of the given function. i am not sure if it is a must though

 

[berkeman]

$F(a,b,c,d)=Σ(0,1,2,4,5,10,12)$

the boolean expression i got from previous parts is a'c'+c'd'+b'd'

the question is to check if:

(i)if 6 and 14 might've been two of the don't cares
(ii)if 15 might've been one of the don't cares
(iii) if 8 must've been one of the don't cares

To get your first term a'c', you don't need any don't cares.

To get the second term c'd', you need 8 as a don't care, right?

To get the third term b'd', you still need 8 as a don't care, right?

You can simplify things more if you include 6 and 14 as don't cares (right?), but it looks like you can get to your expression that you listed with just the one don't care.

if m8, if i am right, then it simplifies the simplification of the given function. i am not sure if it is a must though

Sure looks needed to me...