Refer to the following Algorithmic State Machine $($ASM$)$ chart in FIGURE Q$1.$

The ASM chart depicts a bit$-$counter circuit counting the number of $1$ s stored in register $A.$ The number$-$of$-1-$count is stored in register $B.$

a$.$ Given that register A has $8$ bits, analyze the number of bits required for register $B$ to store the number$-$of$-1-$count from register $A?$ Justify your answer.

b$.$ Derive the state diagram of the bit counter from the ASM chart.

c$.$ Derive the register transfer notation from the ASM chart.