Using T$-$ Flip FLops, design and implement a transfer register system which consists of two $5-$bit registers A and $B$ and which has the following operating features.

a$)$ Transfers the contents of register $A$ to register $B$ on receipt of the first clock pulse.

b$)$ Transfers the contents of register $B$ to register A shifted one position to the left on receipt of the second clock pulse.

c$)$ Increments the contents of register A on receipt of the third clock pulse.

e$)$ Resets both registers on receipt of the fourth clock pulse.