Size of an Array

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An AI-generated summary of this video lecture.

This lecture introduces how to calculate the size of an array using bounds and element byte sizes. It begins with the formula Number of elements = (Upper bound – Lower Bound) + 1, defining lower and upper bounds as the first and last indices. The instructor then uses a hand-drawn array diagram with indices 1 through 8, labeling LB at index 1 and UB at index 8, and substitutes values to show (8 - 1) + 1. Additional examples include zero-based indexing and negative indices, such as (2-0)+1=3 and (1-(-6))+1 = 7+1 = 8, demonstrating that the formula works regardless of indexing style. The lesson transitions to types of array indexing—zero-based, one-based, and n-based—and later returns to the size formula. Finally, it introduces memory size calculation using Size = number of elements * Size of each element in bytes, with a worked example showing 8 × 2B = 16B. A memory location table maps indices to stored letters, reinforcing how array elements occupy consecutive addresses.

Chapters

1. 0:00 – 2:00 00:00-02:00

   The slide titled “Size of an array” displays the formula “Number of elements = (Upper bound – Lower Bound) + 1,” with bullets defining the lower bound as the index of the first element and the upper bound as the index of the last element. The instructor gestures with a pen while explaining, then draws a row of boxes to represent an array. Numbers 1 through 8 are written above the boxes, and arrows label the first index as LB and the last as UB. The instructor substitutes these values into the formula, showing (8 - 1) + 1 to calculate the number of elements.

2. 2:00 – 5:00 02:00-05:00

   The instructor continues applying the size formula to different indexing schemes. A second example uses indices from 0 to -7, with calculations such as (2-0)+1=3 and (1-(-6))+1 = 7+1 = 8, illustrating that negative bounds still yield the correct element count. The lecture then shows a slide titled “Types of indexing in array:” listing zero-based, one-based, and n-based indexing, with red underlines emphasizing the options. Returning to the “Size of an array” slide, the instructor writes 8 - 1 + 1 above the formula and reinforces the LB/UB diagram. A cartoon appears with a doctor saying “Array Index starts from 1,” humorously reinforcing one-based indexing.

3. 5:00 – 5:18 05:00-05:18

   The final section shifts to calculating total memory size using the formula “Size = number of elements * Size of each element in bytes.” A green table labeled “Memory Location” shows columns 200–206 containing letters U, B, F, D, A, E, C over indices 0–6. The instructor underlines “number of elements” and then the entire formula, followed by a red worked example: = 8 X 2B, then = 16B. This connects the earlier element-count formula to byte-level memory allocation for a one-dimensional array.

The lecture progresses from defining array bounds to applying the element-count formula across multiple indexing conventions, then extends to memory size calculation. The central idea is that array size in elements depends only on the difference between upper and lower bounds plus one, independent of whether indices are positive, negative, zero-based, or one-based. The instructor supports this with visual diagrams and step-by-step substitutions, ensuring students can identify LB and UB in any array representation. The final transition to byte size introduces the practical memory formula, linking logical element count to physical storage requirements. Key exam-relevant points include memorizing both formulas, recognizing indexing types, and interpreting memory location tables.