Practice Question
Duration: 3 min
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This educational video demonstrates how to calculate the memory address of a specific element within a two-dimensional array using the Row Major Order storage scheme. The instructor presents a specific problem where the array A has non-standard indexing ranges: rows from 5 to 15 and columns from -8 to 8. The total dimensions are given as A[11][17]. The problem asks for the address of element A[8][5]. Essential parameters are provided: a Base Address of 800 and an element size of 4 memory cells. The lecture walks through the derivation of the address calculation formula and applies it to solve the numerical problem, highlighting the handling of negative lower bounds.
Chapters
0:00 – 2:00 00:00-02:00
The session begins with the problem statement displayed on screen: Q A[5.....15, -8.....8] is A[11][17] and we are supposed to find A[8][5]. The instructor identifies the given values: Row Major Order, Base Address = 800, and element size w = 4. He writes the general formula for Row Major Order on the board: A[i, j] = B + w * [(i - li) (ul - ll + 1) + (j - lj)]. He explicitly defines the lower and upper limits for rows (li=5, ui=15) and columns (lj=-8, uj=8). He notes that the term (ul - ll + 1) represents the total number of columns, which is 17. He sets up the substitution for the target element A[8][5], identifying i=8 and j=5.
2:00 – 3:14 02:00-03:14
The instructor performs the arithmetic substitution. He writes 800 + 4 * [(8 - 5) * 17 + (5 - (-8))]. He calculates the row difference (8 - 5) as 3. He calculates the column difference (5 - (-8)) as 13. He multiplies the row difference by the column count: 3 * 17 = 51. He adds the column difference to this product: 51 + 13 = 64. This sum represents the total number of elements skipped. He multiplies this by the element size: 4 * 64 = 256. Finally, he adds this offset to the base address: 800 + 256, resulting in the final address 1056.
The video provides a clear, step-by-step guide to memory address calculation for 2D arrays. It emphasizes the formula's structure, particularly how the row index is weighted by the total column count. The example with negative lower bounds serves as a practical test of understanding the (index - lower_limit) component of the formula. The final calculation confirms the address is 1056, reinforcing the method for handling non-zero-based indexing in programming and data structures.