Encoding of Incompletely Specified Boolean Matrices

The problem discussed in this paper is a generalization of the problem of choosing the binary codes for the various operations of a digital computer with a view towards minimizing the gating circuitry in the computer's central control. The general procedure is a systematic method for the simultaneous encoding of a large number of arbitrary Boolean functions in an economical manner. The method is applicable to those cases where the designer is allowed to choose the independent variables so as to minimize the circuit which realizes the given Boolean functions. Other applications of the procedure are indicated. The method given includes a means for determining a lower bound on the cost of the circuit which realizes the given Boolean functions. The entire procedure is systematic and lends itself well to mechanization via a digital computer program. A discussion of the advantages and limitations of the method presented here is included, and the method is compared with a previously published procedure for attacking the same problem.