Question

What's the memory address for the following elements arrays given:
Base Address: 1000, Dimensions: 10 rows, 5 columns, 4 byte elements.
Elements: 0,0; 9,4; 2,2; 4,1;
Base Address: 500, Dimensions: 10 rows, 15 columns, 4 byte elements.
Elements: 0,0; 9,14; 2,2; 4,11;
Base Address: 800, Dimensions: 4 rows, 5 columns, 2 byte elements.
Elements: 0,0; 3,4; 2,2; 3,4;

Answer 1

Solution:

(a)

Given,

=>Base address = 1000

=>Number of rows = 10

=>Number of columns = 5

=>Size of each element = 4 bytes

(i)

Explanation:

=>By default row-major order is assumed.

=>In row-major order first one full row is traversed before traversing another row,

Calculating address of 0,0:

=>Address of element = base address + size of element(i*number of rows + j*number of columns)

Where i = first index of array and j = second index of array

=>Address of element = 1000 + 4*(0*10 + 0*5)

=>Address of element = 1000

(ii)

Explanation:

Calcualting address of 9,4:

=>Address of element = 1000 + 4*(9*10 + 4*5)

=>Address of element = 1000 + 4*110

=>Address of element = 1000 + 440

=>Address of element = 1440

(iii)

Explanation:

Calcualting address of 2,2:

=>Address of element = 1000 + 4*(2*10 + 2*5)

=>Address of element = 1000 + 4*30

=>Address of element = 1000 + 120

=>Address of element = 1120

(iv)

Explanation:

Calculating address of 4,1:

=>Address of element = 1000 + 4*(4*10 + 1*5)

=>Address of element = 1000 + 4*45

=>Address of element = 1000 + 180

=>Address of element = 1180

(b)

Given,

=>Base address = 500

=>Number of rows = 10

=>Number of columns = 15

=>Size of each element = 4 bytes

(i)

Explanation:

Calculating address of 0,0:

=>Address of element = 500 + 4*(0*10 + 0*15)

=>Address of element = 500

(ii)

Explanation:

Calculating address of 9,14:

=>Address of element = 500 + 4*(9*10 + 14*15)

=>Address of element = 500 + 4*300

=>Address of element = 500 + 1200

=>Address of element = 1700

(iii)

Explanation:

Calculating address of 2, 2:

=>Address of element = 500 + 4*(2*10 + 2*15)

=>Address of element = 500 + 4*50

=>Address of element = 500 + 200

=>Address of element = 700

(iv)

Explanation:

Calculating address of 4,11:

=>Address of element = 500 + 4*(4*10 + 11*15)

=>Address of element = 500 + 4*205

=>Address of element = 500 + 820

=>Address of element = 1320

(c)

=>Base address = 800

=>Number of rows = 4

=>Number of columns = 5

=>Size of each element = 2 bytes

(i)

Explanation:

Calculating address of 0,0:

=>Address of element = 800 + 2*(0*4 + 0*5)

=>Address of element = 800

(ii)

Explanation:

Calculating address of 3,4:

=>Address of element = 800 + 2*(3*4 + 4*5)

=>Address of element = 800 + 64

=>Address of element = 864

(iii)

Explanation:

Calculating address of 2,2:

=>Address of element = 800 + 2*(2*4 + 2*5)

=>Address of element = 800 + 2*18

=>Address of element = 800 + 36

=>Address of element = 836

(iv)

Explanation:

Calculating address of 3,4:

=>Address of element = 800 + 2*(3*4 + 4*5)

=>Address of element = 800 + 2*32

=>Address of element = 800 + 64

=>Address of element = 864

I have explained each and every part with the help of statements attached to it.