A three dimensional array in 'C' is declared as int A[x][y][z]. Consider that…

Concept: The memory address of an element in a row-major multi-dimensional array equals the base address plus (word size × the number of elements stored before it in linear order). For an element A[p][q][r] in an array declared A[x][y][z], the count of elements skipped is found dimension by dimension, from the outermost index down to the innermost; each index contributes the size of one full 'block' at its own level, and the innermost index contributes its position directly.

Application:

1. In row-major order for A[x][y][z], the last index (r) varies fastest: all r-values for a fixed (p, q) are stored contiguously, then all q-values for a fixed p, then all p-values.

2. To reach the p-th plane, p complete planes must be skipped, and each plane holds y × z elements -- this skips p × (y × z) elements.

3. Within that plane, to reach the q-th row, q complete rows must be skipped, and each row holds z elements -- this skips q × z elements.

4. Within that row, to reach the r-th element, r elements are skipped directly.

5. Total elements skipped before A[p][q][r] = (y × z × p) + (z × q) + r.

6. Each element occupies w units of memory (the word length), so the total memory skipped = w × [(y × z × p) + (z × q) + r].

7. Address of A[p][q][r] = base address + memory skipped = &A[0][0][0] + w(y × z × p + z × q + r).

Cross-check:

• Setting p = q = r = 0 gives &A[0][0][0] + w × 0 = &A[0][0][0], the base address itself -- as expected for the first element.

• The largest valid offset, at p = x-1, q = y-1, r = z-1, evaluates to (x × y × z) - 1 elements -- exactly one less than the total element count x.y.z, confirming the formula stays within bounds across the whole array.

This confirms the address as &A[0][0][0] + w(y × z × p + z × q + r).