b$)$ A digital system is to count the number of bits in a register, $A,$ that has the value $1.$ A step$-$by$-$

step procedure, or algorithm, that can be used to perform the required task is as follows:

It assumes that $A$ is stored in a register that can

shift its contents in the left$-$to$-$right direction.

The answer produced by the algorithm is

stored in the variable named $B.$ The algorithm

terminates when A does not contain any more

$1s,$ that is when $A=0.$ In each iteration, if the

least$-$significant bit $($LSB$)$ of $A$ is $1,$ then $B$ is

incremented by $1$ ; otherwise, $B$ is not changed.

The contents of A are shifted one bit to the right

at the end of each iteration.

Fig. $3($b$)$ gives an ASM chart that represents

the algorithm. The state box for the starting

state, $S1,$ specifies that $B$ is initialized to $0.$ It

assumes that an input signal, $s,$ exists, which is used to indicate when the data to be processed

has been loaded into $A,$ so that the machine can start. The decision box labeled $\text{'}s\text{'}$ stipulates

that the machine remains in state $SI$ as long as $s=0.$ The conditional output box with Load $A$

written inside it indicates that $A$ is loaded from external data inputs if $s=0$ in state $S1.$

When $s$ becomes $1,$ the machine changes to state $S2.$ The decision box below the state box for

$S2$ checks whether $A=0.$ If so$,$ the bit$-$counting operation is complete; hence the machine

should change to state $S3.$ If not, the FSM remains in state $S2.$ The decision box at the bottom

of the chart checks the value of $a_0.$ If $a_0=1,B$ is incremented, which is indicated in the chart

as BlarrB$+1.$ If $a_0=0,$ then $B$ is not changed. In state $S3,B$ contains the result, which is the

number of bits in A that were $1.$ An output signal, Done, is set to $1$ to indicate that the algorithm

is finished; the FSM stays in $S3$ until $s$ goes back to $0.$

i$.$ Design the Datapath circuit of the ASM chart.

ii$.$ Give the ASM chart for the control circuit corresponding to part $($i$).$help