  We report the propagation of a square wave signal in a quasi-periodically
driven Murali-Lakshmanan-Chua (QPDMLC) circuit system. It is observed that
signal propagation is possible only above a certain threshold strength of the
square wave or digital signal and all the values above the threshold amplitude
are termed as 'region of signal propagation'. Then, we extend this region of
signal propagation to perform various logical operations like AND/NAND/OR/NOR
and hence it is also designated as the 'region of logical operation'. Based on
this region, we propose implementing the dynamic logic gates, namely
AND/NAND/OR/NOR, which can be decided by the asymmetrical input square waves
without altering the system parameters. Further, we show that a single QPDMLC
system will produce simultaneously two outputs which are complementary to each
other. As a result, a single QPDMLC system yields either AND as well as NAND or
OR as well as NOR gates simultaneously. Then we combine the corresponding two
QPDMLC systems in a cross-coupled way and report that its dynamics mimics that
of fundamental R-S flip-flop circuit. All these phenomena have been explained
with analytical solutions of the circuit equations characterizing the system
and finally the results are compared with the corresponding numerical and
experimental analysis.
