Reading Assignment Sections 2.6 and 2.7 from the text Elec 326 2 Karnaugh Maps Karnaugh Map Definitions A Karnaugh map is a two-dimensional truth-table. However, 5 and 6 variable K-map is … The map also includes the three don’t-care conditions. •If M i is a maxterm of f, then place a 0 in cell i. Unlike ordinary (i.e., one-dimensional) truth tables, Don’t care “x” should also be included while grouping to make a larger possible group. K-maps for Product-of-Sum Design Product-of-sums design uses the same principles, but applied to the zeros of the function.
Karnaugh Maps (K-map) • Alternate representation of a truth table Red decimal = minterm value ... “don’t care” conditions for logic minimization • The output for a don’t care condition can be either 0 or 1 WE DON’T CARE!!! The function Y() is the function to simplify, the function d() is the list of don't care conditions. K-maps basically deal with the technique of inserting the values of the output variable in cells within a rectangle or square grid according to a definite pattern.
You are not looking for anything. To ﬁnd the desired SOP expression, we must ﬁnd the least-expensive set of prime implicants that covers all 1s in the map. Example: Designing with Don't-Care Values In some situations, we don't care about the value of a logic function. Use a 4-variable K-Map with don't cares to simply the functions given by the following two equations. K-maps are also referred to as 2D truth tables as each K-map is nothing but a different format of representing the values present in a one-dimensional truth table. The way the K-Map works is by grouping the numbers that their binary representation has a Hamming distance = 1 [Only 1 bit difference] In the image you posted Don't-care values in a Karnaugh map relate to output that is generally not reachable under normal circumstances and allow you to simplify the logic more than you would normally be able to. In those cases, treat the don’t care value as ‘1’. This will have an optimal behavior if the map has no "don't cares" [reference needed]. Example •If d i is a don’t care of f, then place a d or x in cell i. The term x1x2x4 speciﬁesminterms1and3. Your answer is NOT correct; This is not the proper way to group a 5 variables K-map. Lets first look why a K-map is not practical for functions with more than 4 variables . Introduce the concept of "don't care" entries and show how to extend Karnaugh map techniques to include maps with don't care entries. To have optimal behavior with "don't care", you have to consider that an X can be either a 1 or a 0. The fourth product term represents the minterm 13. That means that for each X, you have two versions of you map.
• Don’t Care conditions denoted by: Karnaugh map of 2 to 4 variables is very easy. in the map, comprising minterms 3, 7, 11, and 15. Consider only the don’t cares ‘x’ that are helpful for grouping maximum number of adjacent ones. Karnaugh Maps (K-maps) •If m i is a minterm of f, then place a 1 in cell i of the K-map.
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