Explain and demonstrate the process of register allocation by the compiler for the given intermediate representation. Assume that the available number of registers is $3.$ Identify the variables which will be allocated in these registers.

Intermediate representation$($given in fig$)$

Assume the liveness of variables as follows

B$1$ Entry :$$B$,$ C$,$ D$,$ F

B$1$ Exit :$$A$,$ C$,$ D$,$ E$,$ F

B$2$ Entry :$$A$,$ C$,$ D$,$ E$,$ F

B$2$ Exit :$$B$,$ C$,$ D$,$ E$,$ F