ITI 1100 Lecture Notes - Karnaugh Map, Maurice Karnaugh, Binary Number

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Lecture 6 - gate level minimization (chapter 3 part 1) An alternate approach to representing boolean functions. Easy conversion from truth table to k-map. Much faster and more efficient than previous minimization techniques with boolean algebra. Assign the value of the outputs to the corresponding minterms in the k-map. F (a,b,c,d)= a"b"c"d"+a"bc"d"+ ab"c"d" + a"bc"d+ abc"d + abcd"+ab"cd". Consider the squares with 1"s to simplify sop. Consider the squares with 0"s to simplify pos. K-map is ideally suited for four or less variables, becoming cumbersome for five or more variables. Map is arranged such that two neighbors differ in only one variable (e. g. abc +abc") Two terms must be adjacent in the map. A k-map of n variables will have 2n squares. For a boolean expression, product terms are denoted by 1"s, while sum terms are denoted by 0"s or left blank (represented by minterms in the map) Groups of squares are formed in considering the following rules:

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