To calculate effective number of cycles required for operand fetch , we should know about the cycles required in each addressing mode..Let us find one by one :
a) No of cycles required in register addressing mode = 1(only for register reference)
b) For immediate no separate access is required since operand is in the instruction itself hence no of cycles = 0
c) For direct , 1 memory access , so no of cycles = 4
d) For memory indirect , 2 memory accesses , so no of cycles = 8
e) For base indexed ,1 register reference to read the index register value,1 arithmetic computation to add index to base address and 1 memory access to read the data = 1 + 2 + 4 = 7
Hence effective number of cycles required for operand fetch = (0.4 * 1) + (0.2 * 0) + (0.2 * 4) + (0.1 * 8) + (0.1 * 7)
= 0.4 + 0.8 + 0.8 + 0.7
= 2.7 cycles