Address Calculation in Two Dimensional Arrays

Addresses of  Two Dimensional arrays can be calculated by using

1. Row Major representation

2. Column major Representation

1. Row Major representaion: Let X be an array of M Rows and N Columns

Address Location (X [i, j]) = Base Adress of  X + S [N (i-LBofrow) + (j -LBofCol)]

i and j indicates index value of the element whose address you want to search.

Base Adress of  X  is the starting address of the given array. 

S is the memory word required to store given array’s element. 

LBofrow is Lower Boundary of Rows

LBofCol is Lower Boundary of Columns

Example : 

Rows:  2   Columns : 3

   0         1         2     

Let base address be 200

w be 2 bytes(int)

Address of x[1,0]=200+2[3[1-0]+[0-0]]

                         =200+2[3-0]

                         =200+6

                         =206

2 Column Major Representation

Address Location (X [i, j]) =  Base Adress of  X + S [(j- LBofrow) +M(i - LBofCol)]