Quine–McCluskey algorithm: Difference between revisions

Revision as of 12:14, 18 March 2024

Revision as of 15:05, 18 March 2024

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==Example==

===Input===

In this example, the input is a Boolean function in four variables, <math>f :\{0,1\}^4 \to \{0,1\}</math> which evaluates to <math>1</math> on the values <math>4,8,10,11,12</math> and <math>15</math>, evaluates to an unknown value on <math>9</math> and <math>14</math>, and to <math>0</math> everywhere else (where these integers are interpreted in their binary form for input to <math>f</math> for succinctness of notation). The inputs that evaluate to <math>1</math> are called 'minterms'. We encode all of this information by writing

The Quine-McCluskey method is a systematic approach to minimize Boolean expressions. Let's apply it to the given Boolean expression:

F:<math>f(WA,XB,YC,ZD) = Σ\sum m(04,18,410,5) and F(W11,X12,Y,Z15) = Σ+ d(129,1314). \,</math>

This expression says that the output function f will be 1 for the minterms <math>4,8,10,11,12</math> and <math>15</math> (denoted by the 'm' term) and that we don't care about the output for <math>9</math> and <math>14</math> combinations (denoted by the 'd' term). The summation symbol <math>\sum</math> denotes the logical sum (logical OR, or disjunction) of all the terms being summed over.

===Step 1: finding prime implicants===