One Dimensional Array Access Formula

AI Summary

An AI-generated summary of this video lecture.

This lecture introduces the memory address calculation formula for one-dimensional arrays. The instructor begins by presenting a slide titled 'One Dimensional array' with the prompt 'Address of the element at kth index' and an incomplete formula 'a[k] ='. A visual array diagram is constructed at the bottom of the slide, showing a row of boxes with red handwritten addresses 100, 104, 108, 112, 116, 120, and 124 below them, and red index numbers 0 through 7 above. The instructor then derives the general formula step-by-step: a[k] = B + W * (k - Lower bound). The variables are defined as B for the base address, W for the size of each element, k for the target index, and Lower bound for the starting index. A worked example uses B=100, W=4, and k=6 to calculate the address as 100 + 4 * (6 - 0) = 124, which matches the diagram. The final slide summarizes the formula and variable definitions for reference.

Chapters

1. 0:00 – 2:00 00:00-02:00

   The instructor introduces the concept of calculating memory addresses in a one-dimensional array. The slide displays 'One Dimensional array' and 'Address of the element at kth index' with the prompt 'a[k] ='. A row of array boxes is drawn at the bottom, labeled with red handwritten addresses 100, 104, 108, and 112. The instructor writes '100' below the first cell to establish the base address, then extends the addresses across the boxes to 124 and adds red index numbers 0 through 7 above them.

2. 2:00 – 4:45 02:00-04:45

   The instructor derives the formula a[k] = B + W * (k - Lower bound) by building it incrementally. The base address 'B' is written first, followed by the element size 'W', and finally the offset term '[k - L]'. A red cross marks index 6 in the diagram for the example k=6. The instructor substitutes B=100, W=4, and K=6 into the formula, calculating 100 + 4 * (6 - 0) = 124, which matches the diagram. A final slide summarizes the general formula and defines B as base address, W as element size, K as index, and Lower bound as the first element's index.

The lesson progresses from a concrete visual example to an abstract formula. The array diagram with addresses 100-124 and indices 0-7 provides the numerical foundation. The formula a[k] = B + W * (k - Lower bound) is derived by identifying each component: base address, element size, and index offset. The worked example (k=6 yielding 124) verifies the formula against the diagram. The lower bound term accounts for arrays not starting at zero, making the formula general.