Karnaugh Maps: Plot F(W,X,Y,Z) = sum m(1,3,4,5,6,7,9,11,13)

[benderzfloozy]

Hi. I have done this problem but the answer is troubling me. Here is the problem:

Plot the function F(W,X,Y,Z) = summation symbol m(1,3,4,5,6,7,9,11,13). Use the K-map to simplify the function F. Also, display F in SOP form and display the complemented function ~F is SOP form.

What I've done:

The simplified equation I got was ~wz + ~wx + ~yz + w~xz. The ~ symbol refers to negation. Is this right?
The SOP form for F I got: w~x~yz + ~w~xyz + ~wx~y~z + ~wx~yz + ~wxy~z + ~wxyz + w~x~yz + w~xyz + wx~yz
The SOP form for ~F I got: wxy + w~z + ~w~x~z.

Could someone verify these? I would greatly appreciate it! Thnx.

 

[stapel]

Hi. I have done this problem but the answer is troubling me.

I'm sorry, but I don't understand...? What aspect of your answer disturbs you?

Plot the function F(W,X,Y,Z) = summation symbol m(1,3,4,5,6,7,9,11,13). Use the K-map to simplify the function F. Also, display F in SOP form and display the complemented function ~F is SOP form.

How do the inputs W, X, Y, and Z relate to the formula? Is "m" a variable, or something else? What is being summed? What is "the K-map"? What is "SOP form"? (I'm assuming it's something other than the usual "standard operating procedure".) What does it mean to "plot" this function? (You aren't plotting points on a graph, I don't think, so "plot" must mean something else here.) :?:

The simplified equation I got was ~wz + ~wx + ~yz + w~xz. The ~ symbol refers to negation. Is this right?

For what is the above the "simplified equation"? Does this relate to the "plot"? How do these variables relate to the other ones, given previously? Or don't they?

Please pardon my confusion and reply with clarification. Thank you!

Eliz.

 

[benderzfloozy]

I apologize for the confusion.

A K-map is a graphical interpretation of a truth table. You are supposed to be able to come up with a boolean equation of a function from the K-map. The function I was given, F(W,X,Y,Z) was expressed as the sum of the minterms listed in the parantheses. So, F(W,X,Y,Z) = m1 + m3 + m4 + m5 + m6 + m7 + m9 + m11 + m13.

Since each square in the K-map represents a minterm, you just place a 1 in the cell representing that minterm. In my k-map, I placed a one for each cell representing each of the above minterms. (The image seems to fuzzy things up, but those are 1s in the cells). Once the graph is filled in, the object is to group many ones as you can together in rectangles that are the size of power of twos. This means that the rectangle size can be 2, 4, or 8 squares. I have colored the diferent squares and gave its corresponding equation. That's how I obtained the boolean expression for F.

SOP stands for sum of products. I think that's where you sum up each minterm that has a value of 1. I have done so for F, and it's complement F'.

Basically, using K-maps are another way to obtain boolean expressions for a function. What I was unsure about was if my equations were correct; they just don't appear right to me. I hope this clarifies things. Thnx.