the number of memory location needed in Direct form I are M+N+1 as given in praokis ,i think it should be M+N , im not able to understand from where extra one location is coming.


and
secondly while in IIR filter why summation limits are changed to zero to M while in FIR it is 0 to M-1??

 

FIR is finite so you have M samples so starting from 0th you moveonwards you will finish M samples at M-1 point...e.g. 10 points start with zero when you reach 9, you have 10 samples...

Similarly in IIR, you start at M so starting from 0, you need M+1 to reach to M...reconsider above example and do maths...you will get the answer