$2$Design a $101$ sequence recognizer using Moore model.$(6,10)$

$(1)$ Draw the state diagram with the state $a,b,c,d.$

$(2)$List the next$-$state table and $(3)$List the output table$($ table$)$

$(4)$ With State assignment $a(00),b(01),c(10),d(11),$ To drive the next$-$state equation using Kmap Optimization: $D1=,D2=$

$(5)$To drive the output equation $y=?$

$(6)$ Draw the result sequential circuit.