Variable Entered K-Map (VEM)

Question

From the given K-map for the function F=(a,b,c,d,e), answer the following questions: 

In the minimized form of the function how many minterms are free from e, e’ (The term should not include any of e, e’)

1.    2
2.    3
3.    1
4.    0

Comments

Can you pls tell the source of the question ?
K-Map function and table you provided doesnt sync . Might have badly formed .

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@arjun sir can u pls check this question ? Here K-Map is defined for 5 variables and displayed for 4 variables only . Is this possible ?

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yes, because they used the final one inside the map.

Answer 1

[ @arjun Sir pls check the approach and correct me if wrong ]

Minimization In Varialbe Entered K-MAP

Step 1 : Set all the variables in the cell as '0' (here put e and e' as 0) and obtain SOP Expression

Step 2 a : Making one variable  in the cell as '1' ( here put e as 1 and e' as 0 ) and obtain SOP by making ear;ier minterms as dont care (here earlier '1' will now be set as dont care $\phi$)

Step 2b : Multiply Above SOP with concerned variable

Repeat Step 2 untill all varialbes are covered

Step 3 : SOP of VEM is obtainned by ORing all the obtained SOP

Step 1
In place of variables put it as '0' and obtain SOP

Step 2 a
In place of one variable e  denote it as 1 and minterm 1 as dont care and e' as 0 and obtain SOP

Step 2 a
In place of one variable e'  denote it as 1 and minterm 1 as dont care and e as 0 and obtain SOP

SOP : $b\bar{c}\bar{d} + \bar{b}cd+e(b\bar{c}+a\bar{b}d)+\bar{e}(cd)$

Only 2 minterms will be  free from e and e' . Hence Option a

Good Read

• http://www.ie.itcr.ac.cr/jdiaz/licenciatura/DISENO_LOGICO/MATERIALES/LECTURAS/VEM.pdf

Comments

In step 2A i think you are unnecessary adding dont care in 2 cells.. you can form essential using 1 1

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@meivinay but we should try to form the largest subcube possible, so we can use the don't cares and make a quad

Answer 2

3 minterms are free from e and e'

Comments

explaination

Answer 3

3 terms, each corresponding to each 1 in the map.
This can be obtained by putting e and ~e to 0. Putting e and ~e to 0 will eliminate e.

Comments

@agoh What are the 3 min terms ?