Hello Ive read the AAC Karnaugh e-book. How would I draw a map for: xy + y'z + xz I started with a 2x4 grid. X = row, YZ = column, using Grey code. When I look at the first term: xy, where would I put the 1? Do I need to separate the 3 variables: x, y, z? How? Is this technique shown in the e-book?
Each box in a Kmap is a combination of each of the inputs, in your case x, y, and z. So, for xy you need to put a one in any square where both x and y are 1. Notice that a 1 can go into more than one square. Using Boolean algebra you also notice that xy = xy*1 = xy(z + z') = xyz + xyz'. Both of those squares satisfy the requirement for x and y to be 1.
You received the correct guidance. Since a Karnaugh map is a visual aid it would be a good idea for you to post a drawing. This AAC forum is not only about receiving help for yourself. Q & A such as this one can be a great help to others.
Here's a good little exercise for you. Can you explain, in words using the proper technical terms, why and how a K-map works? The keys are the explanation given by StayatHomeElectronics and the fact that the map has to be written in Gray code order. How would you explain it to the next person trying to learn this.
I couldn't find an easy way of making a drawing to post, so I punted for words. I realise this could have been difficult to explain, but since StayatHomeElectronics understood the question, and I understand the answer, I suspect most will as well.
Your description was fine. I also tend to opt for word descriptions when I think I can get away with it. But anything that gets much more complicated will definitely benefit from a drawing. You can use BB Code to do tables (though nothing too fancy) or tex to do more extravagant ones. Cropped screen shots from Excel, Word, PowerPoint, Paint, or other programs is an option, too.
First step is labelling the horizontal and vertical so called axes. For example z' z x'y' x'y xy xy' counts from 00,01,11,10 (It goes 01 to 11 because only 1 variable can change for each row) Then in ur equation u said xy + y'z + xz So in the k map, label the given situations with '1' For example z' z x'y' 0 1 <--- to satisfy y'z x'y 0 0 xy 1 1 <-- to satisfy xy xy' 0 1 <--- to satisfy y'z as u can see after satisfying xy and y'z, xz i already filled with ones. so the job becomes a little bit more easier. Then next step is to group the ones. U can only group them in 1s, 2s,4s,8,16s etc 2^n numbers Try to group as many as u can in 1 loop first. But if not possible then group in 2s and 1s. Picture Attached. Then deriving the solution from the map is next. U have to take the common terms in each loop. If u see my picture, for the yellow loop, the common terms are xy, Thus this is your first term. for green loop, common term is y'z for red loop, common term is ? figure out yourself Then the answer is just the addition of all the terms. For eg. A= xy+y'z+ _ assuming A is the eqn they gave. I hope this helps