An $8$-bit data path is to be set up using two $4$-bit ALU’s and suitable multiplexers. The ALU’s accept two operands $A$ and $B$ on which a total of $16$ operations can be performed. The operand $A$ is from one of two register-arrays each consisting of $8$ registers, or from a temporary register, or is a constant. The operand $B$ is from a register-array consisting of $4$ registers, or is a constant. The output of the ALU may be routed to a destination register-array consisting of $8$ registers, or placed on a bus. List the data path control signals, and estimate the minimum width of a signal microcode word needed for the generation of these signals.