Memory Address Calculation in an Array

Address Calculation in single (one) Dimension Array:

Array of an element of an array say "A[ I ]" is calculated using the following formula:

Address of A [ I ] = B + W * ( I - LB )

Where, B = Base address W = Storage Size of one element stored in the array (in byte) I = Subscript of element whose address is to be found LB = Lower limit / Lower Bound of subscript, if not specified assume 0 (zero)

Example:

Given the base address of an array B[1300.....1900] as 1020 and size of each element is 2 bytes in the memory. Find the address of B[1700].

Solution:

The given values are: B = 1020, LB = 1300, W = 2, I = 1700

Address of A [ I ] = B + W * ( I - LB )

= 1020 + 2 * (1700 - 1300) = 1020 + 2 * 400 = 1020 + 800 = 1820 [Ans]

Address Calculation in Double (Two) Dimensional Array:

While storing the elements of a 2-D array in memory, these are allocated contiguous memory locations. Therefore, a 2-D array must be linearized so as to enable their storage. There are two alternatives to achieve linearization: Row-Major and Column-Major.

Address of an element of any array say "A[ I ][ J ]" is calculated in two forms as given: (1) Row Major System (2) Column Major System

Row Major System:

The address of a location in Row Major System is calculated using the following formula:

Address of A [ I ][ J ] = B + W * [ N * ( I - Lr ) + ( J - Lc ) ]

Column Major System: The address of a location in Column Major System is calculated using the following formula: Address of A [ I ][ J ] Column Major Wise = B + W * [( I - Lr ) + M * ( J - Lc )] Where, B = Base address I = Row subscript of element whose address is to be found J = Column subscript of element whose address is to be found W = Storage Size of one element stored in the array (in byte) Lr = Lower limit of row/start row index of matrix, if not given assume 0 (zero) Lc = Lower limit of column/start column index of matrix, if not given assume 0 (zero) M = Number of row of the given matrix N = Number of column of the given matrix

Important : Usually number of rows and columns of a matrix are given ( like A[20][30] or A[40][60] ) but if it is given as A[Lr- - - - - Ur, Lc- - - - - Uc]. In this case number of rows and columns are calculated using the following methods:

Number of rows (M) will be calculated as = (Ur - Lr) + 1 Number of columns (N) will be calculated as = (Uc - Lc) + 1

And rest of the process will remain same as per requirement (Row Major Wise or Column Major Wise).

Examples:

Q 1. An array X [-15..........10, 15...............40] requires one byte of storage. If beginning location is 1500 determine the location of X [15][20].

Solution:

As you see here the number of rows and columns are not given in the question. So they are calculated as:

Number or rows say M = (Ur - Lr) + 1 = [10 - (- 15)] +1 = 26 Number or columns say N = (Uc - Lc) + 1 = [40 - 15)] +1 = 26

(i) Column Major Wise Calculation of above equation

The given values are: B = 1500, W = 1 byte, I = 15, J = 20, Lr = -15, Lc = 15, M = 26

Address of A [ I ][ J ] = B + W * [ ( I - Lr ) + M * ( J - Lc ) ]

= 1500 + 1 * [(15 - (-15)) + 26 * (20 - 15)] = 1500 + 1 * [30 + 26 * 5] = 1500 + 1 * [160] = 1660 [Ans]

(ii) Row Major Wise Calculation of above equation The given values are: B = 1500, W = 1 byte, I = 15, J = 20, Lr = -15, Lc = 15, N = 26 Address of A [ I ][ J ] = B + W * [ N * ( I - Lr ) + ( J - Lc ) ] = 1500 + 1* [26 * (15 - (-15))) + (20 - 15)] = 1500 + 1 * [26 * 30 + 5] = 1500 + 1 * [780 + 5] = 1500 + 785 = 2285 [Ans] More Questions to follow