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RST Flip-Flop Input Equations

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2 Author(s)
Graham, Peter J. ; Dept. Elec. Engrg., University of Kentucky, Lexington, Ky. ; Distler, Raymond J.

There are several different usable combinations of the inputs of an RST flip-flop. It is shown how all of the possible combinations can be displayed simultaneously on three Karnaugh maps, facilitating the choice of the simplest input equations. The application equation for flip-flop Q characterized by a sequential problem is plotted on a map designated Qn+1. Additional maps, (Qn+1)* and (Qn+1)¿ are derived from Qn+1. Cells corresponding to prime implicants not containing the variable Q are identified on these maps, and are used to enter the properly designated arbitrary elements on the R, S, and T maps of flip-flop Q. The method is based on the following theorem: ``If Qn+1 = (g1Q + g2Q¿)n, and if F is the set of all prime implicants that do not contain the literals Q or ¿, then the Boolean function g1g2 is the union of all the prime implicants of Qn+1 that belong to the set F.'' A simple illustrative example is included.

Published in:

Electronic Computers, IEEE Transactions on  (Volume:EC-16 ,  Issue: 4 )