This question concerns a synchronous sequential counter, which counts an arbitrary

sequence. The properties of the counter include the following:

The counter has two inputs, input $x$ and $CLK($Clock$),$ and three outputs, $A,B$ and $C.$ A

is the most significant digit in the counting value, and C is the least significant digit.

The counter counts under a POSITIVE clock edge.

When $x$ is $0,$ the counting sequence is:

$1,Y,4,2,5,1,Y,4,2,5,1,$dots

When $x$ is $1,$ the counting sequence is:

$1,Z,6,0,3,1,Z,6,0,3,1,$dots

Values of Y and Z are based on the $7^{th}$ and $8^{th}$ digits of your student identity number:

$($E$,$g$.,$: if your student identity number is $22358285$ A $,$ the counting sequence is:

Input $x$ is $0$:$,1,6,4,2,5,1,6,4,2,5,1,$dots

Input $x$ is $1$:$,1,5,6,0,3,1,5,6,0,3,1,$dots

use the following SID number to solve this question $21084996$A

$($a$)$ Write down the counting sequence of your counter under different input $x$ values,

starting from $1$ until it returns to $1.$

$($b$)$ Write down the state table of your counter. You can assume that the states that do not

occur are don't care conditions.

$($c$)$ The counter is designed using JK flip$-$flops. List the required flip$-$flop inputs to the

flip$-$flops for each row in the state table. Hence, derive the flip$-$flop input equations of

the counter.