Karnaugh map for state table.

[snoggerT]

Derive the circuit that implements the state table
http://silvercurvemedia.com/alex/flyers/state%20table.jpg

The Attempt at a Solution

I know you can get your equations for the circuit from either the table itself or through a Karnaugh map, but I prefer using a karnaugh map. How exactly would you set one up with a table like this? The only examples we've seen have had only 2 inputs (y1,y2), so they were 4 columns and 2 rows (w= 0 and 1). Not sure how to set up a karnaugh map with 3 inputs and w=0/1.

 

[jhicks]

since Y3, Y2 and Y1 depend on w, that makes w an input. You can construct a k-map for each output using 4 columns and 4 rows, so whatever you did to construct that 4 column 2 row kmap, apply the 4 column idea to the rows to get 4 rows. It doesn't really matter which inputs you vary across rows or columns as long as each column/row is only different by 1 bit from its neighbor.

Hope I made sense.

 

[piercas]

To set up a Karnaugh map for a state table with 3 inputs and w=0/1, you would first need to list out all the possible combinations of inputs in binary form. In this case, there would be 8 combinations (2^3) since there are 3 inputs.

Next, you would need to label the Karnaugh map with the binary values of the inputs. For example, if the inputs are labeled as x, y, and z, the Karnaugh map would have rows labeled as 00, 01, 10, and 11 (representing the combinations of x and y) and columns labeled as 0 and 1 (representing the values of z).

Once the Karnaugh map is set up, you can then fill in the corresponding output values from the state table in each cell of the map. This will help you identify any patterns or groups of cells that have the same output values, which can then be used to simplify the circuit.

From the simplified Karnaugh map, you can then derive the circuit by identifying the necessary logic gates and their connections based on the simplified expressions. This circuit will implement the state table and provide the desired outputs for each input combination.