$9\mathrm{.}1$ Sequential Logic Circuit Design with D$-$type flip$-$flops

Design a sequential circuit that detects the occurrences of $"110"$ binary sequence in a string of bits coming through an input line $\backslash ($ X $\backslash ).$ If the binary input sequence $"110"$ is detected on the input line $\backslash ($ X $\backslash ),$ then the output $\backslash ($ Y $\backslash )$ must be equal to $1.$ For example if a binary sequence $"000001100011011"$ applied to the input X $,$ the output Y must indicate that the binary sequence $"110"$ came through the input $\backslash ($ X $\backslash ).$

Table $5\mathrm{.}1$

i$)$ Derive a state diagram for the circuit using Moore Model and if necessary reduce the number of states.

ii$)$ Derive the flip$-$flop input and output equations.

iii$)$ Simplify the flip$-$flop input and output equations using K$-$Maps.

iv$)$ Draw the logic diagram of the sequential circuit using D$-$type flip$-$flops. $9\mathrm{.}2$ Experimental Work

$9\mathrm{.}2$ Sequential Logic Circuit Design with D$-$type flip$-$flops

$1.$ Implement the designed Sequential Logic Circuit in the Preliminary Work $9\mathrm{.}1.$

$2.$ Determine the state table for the design. Record the results to the Table $9\mathrm{.}2$

Table $9\mathrm{.}2$