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Memory less system
A system is said to be memory less if for any time $ t_{0} $ the output $ y(t_{0}) $ depends only on the input at $ t_{0} $ i.e no past or future samples.
Example of memory less
Y(t)=2X(t)
the system is memory less because the output depends only on the present time t and not on the past time i.e t-1 etc or on the future time t+1 etc.
System with memory
A system is said to have memory if for any time $ t_{0} $ the output $ y(t_{0}) $ depends on more than just that time but also on the past or future time.
Example of as system with memory
Y(t)=X(t)+X(t-1)
the output of the system here depends on the present time t but also on the past time t-1. thus we can say that the system has a memory.
