
Truth Table to EquationsAfter you have generated the truth table to describe the desired functionality of your circuit, you will need to convert this to a set of equations. One approach to reducing your equations is using Karnaugh maps, or Kmaps for short. This is a graphical reduction technique that will result in the same reductions as Boolean algebra for up to 4 variables. This technique is not generally useful for more than 4 variables (although it can be done with significant effort). Assume that we want to implement the following truth table
We start by drawing a blank Kmap. The digits across the top represent We then populate the next Repeat until the entire function has been entered into the table Now, we need to decide on the groups. A group must contain a power of 2
Repeat until all Next, we need to read these groups out since they represent the minimal sumofproducts. To do this, look at each group for each input variable (D, C, B, A). If the group is completely in or completely out of the region covered by the input variable, then that letter appears in the minterm or is complimented in the minterm. Looking at the largest group (2x2) we see the following This is completely outside the This is completely outside the Again we see that we cross the boundary of the Repeating the procedure for the next group we get If you would like to use these power point graphics for your reports, you may copy them here. Last Modified: 