Answer $6\mathrm{.}11.$ Please do the solution by pen$/$pencil and paper. Because last time I sent this question to an expert I got a solution that I couldn't read because it appeared like the following:

"The input$-$output relationship is:

$\backslash [$

y$($t$)=\backslash$int$\_\{$t$-$T$\}^$t $($t$-\backslash$tau$)^2$ x$(\backslash$tau$)\backslash ,$ d$\backslash$tau

$\backslash ]$

The impulse response $\backslash ($ h$($t$)\backslash )$ is the output when $\backslash ($ x$($t$)=\backslash$delta$($t$)\backslash ).$ Substitute $\backslash ($ x$($t$)=\backslash$delta$($t$)\backslash )$:

$\backslash ["$ CHAPTER $6$

$-$ Synchronous Sequential Circuits

that produces $\backslash ($ z$=1\backslash )$ when it detects that either the sequence $\backslash ($ w: $0010\backslash )$ or $\backslash ($ w: $1110\backslash )$ has been applied; otherwise, $\backslash ($ z$=0\backslash ).$ After the fourth clock pulse, the machine has to be again in the reset state, ready for the next sequence. Minimize the number of states needed.