Q$1.(80$ points$)$ Considering $(no+17{)}_{10}=($ abcdefg ${)}_2,$ design a synchronous sequence detector circuit that detects 'abcdefg' from a one$-$bit serial input stream applied to the input of the circuit with each active clock edge. The sequence detector should detect overlapping sequences.

a$)$ Derive the state diagram, describe the meaning of each state clearly. Specify the type of the sequential circuit $($Mealy or Moore$),$

b$)$ Determine the number of state variables to use and assign binary codes to the states in the state diagram,

e$)$ Choose the type of the FFs for the implementation. Give the complete state table of the sequence detector, using reverse characteristics tables of the corresponding FFs

d$)$ Obtain Boolean functions for state inputs. Also obtain the output Boolean expression,

e$)$ Draw the corresponding logic circuit for the sequence detector.

f$)$ Verify your design by providing Logisim simulation of the obtained circuit and show the corresponding truth table in Logisim

Q$2.(20$ points$)$ Assign $10$#no h to $00($#no$)$:$0400$h and #no h to $0040$:$00$#no h write a program that store;

a$)$ The sum of these two numbers in $00$#no:$0600$h

b$)$ The difference of these two numbers in $00$#no:$0602$h

c$)$ The product of these two numbers in $00\%$no:$0604$h

d$)$ After the division of these two numbers, the quotient in $00$#no:$0608$h and remainder is in $00$#no:$0610$h

$($Ex: for $($:$\frac{122202099}{(99{)}_{10}}=(63{)}_{16},no=63H\}$

NOTE: You have to add comment line to your code that explain your code.

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