Hi, how can i identify where to place my truth table input in K-map cell ?

[nyame]

Hi, for any given truth table how can i identify where to place my input in a k map,

[Benta]

Do you mean a Karnaugh map? Never heard of a k map.

[rstofer]

Divide the number of bits by two and use some for the horizontal legend (across the top) and the rest for the vertical legend (down the left side).

The trick when assigning values to the rows or columns is to use a Gray Code encoding such that only one bit changes between adjacent rows or  adjacent columns.

For your example, with just 3 bits, you could lay it out like:

Code: [Select]

AB  |C   0   1
==============
00  |    0   0
01  |    0   1
11  |    1   1
10  |    0   1


[nyame]

Yes, please I need to understand  From basic the technics use to identify where to place input from the truth table, with a practical demonstration to enable me understand better, I mean for a given truth table how can you determine this is were your input should be in the map cell ?

[Nitrousoxide]

You first draw out a map with Gray code for the appropriate amount of variables. For example, this is a 3 variable map:


Notice how there is only one bit changing per adjacent cell. The bits simply correspond to the variables. You can group the variables however you want. i.e. A/BC or AB/C. They will give you an identical result.

An example using the truth table you have provided: (please excuse the messy/quick drawing)


But, as we can see there are three SOP terms that form the output function:
Y = BC + AC + AB

[rstofer]

Do you understand the minimization that happened in the sketch?

Note the column where BC = 11.  The vertical encirclement shows that as long as B=1 and C=1, it doesn't matter what A equals.  So the output term is B&C

The bottom left encirclement shows that as long as A=1 and C=1, it doesn't matter what B equals.  So the output term in A&C

The bottom right encirclement shows that as long as A=1 and B=1, it doesn't matter what C equals,  The output term is A&B.

Combining the 3 terms (from the 3 loops) we get B&C + A&C + A&B

There are hundreds of videos on the subject plus many other tutorials.  Google can help!