Question

Suppose an array with six rows and eight columns is stored in row major order starting at address 50 (base ten). If each entry in the array requires two memory cells, what is the address of the entry in the fifth row and seventh column? What will it be if each entry requires three memory cells?

Short answer

For 2-cell entries, address is 126. For 3-cell entries, address is 164.

Step-by-step solution

Understand the Problem

We are given a 6x8 array. The entries are stored in row-major order which means we list all the elements of a row continuously before continuing to the next row. We need to find the address of the entry in the fifth row and seventh column.

Calculate Address for 2-Cell Entries

Each entry takes up 2 memory cells. The row-major starting address is 50. To find the address of an entry at a position (row, column), calculate how many entries are before it. For position (5, 7), the row index is 4 (0-based). The total entries before this position are the first 4 rows of 8 entries each plus 6 entries of the 5th row. So, total entries = (4 * 8) + 6 = 38. Total memory cells = 38 * 2 = 76. The address of (5, 7) will be 50 + 76 = 126.

Calculate Address for 3-Cell Entries

Now suppose each entry requires 3 memory cells, the total entries remain the same. The entry (5, 7) is preceded by 38 entries. Total memory cells = 38 * 3 = 114. Starting from address 50, the address of (5, 7) will be 50 + 114 = 164.

Key concepts

Row-Major Order

In computer science, arrays are a fundamental data structure used to store collections of elements. When dealing with multidimensional arrays, like a 2D array, two significant ways to store these in memory are row-major and column-major orders. Row-major order means that all elements of a row are stored in contiguous memory cells before moving to the next row.

This way of storage is akin to reading lines of text from left to right and top to bottom. For a 6x8 array, row-major order helps by storing the first row's 8 elements first, followed by the second row's 8 elements, and so forth until all rows are stored.

This ordering facilitates efficient data retrieval and manipulations when processing row-oriented data in programming languages like C and Python, which commonly use row-major order.

Understanding row-major order crucially affects how you calculate memory addresses in memory-intensive applications like graphics or scientific computing.

Memory Address Calculation

Memory address calculation is a method used to find where a specific element in an array is stored in computer memory. In a 2D array stored in row-major order, the memory address of an element located at \(i, j\) in an array starts by determining the base address. The base address is where the first element (upper-left corner) of the array is stored in memory.

• Calculate the total number of entries before the element (i,j).
• Multiply this count by the number of memory cells per entry.
• Add this product to the starting address.

For example, the address calculation for an element at position (5,7) involves counting all elements preceding it and multiplying by the memory cells required per entry. Memory address calculation ensures that you accurately pinpoint where any given element is stored, which is crucial in programming for memory efficiency.

Memory Cells

Memory cells are the basic units of storage in computer memory. Each cell holds a specific amount of data, usually one byte. When referring to arrays, each entry or element may occupy multiple memory cells. For example, an integer may take up to 2 or 4 memory cells depending on the architecture.

In the exercise, the problem involves handling entries that occupy either 2 or 3 memory cells. Determining the number of memory cells per entry is imperative in accurately calculating the total memory footprint of an array and finding specific element addresses.

Understanding how many memory cells are used directly influences how efficiently one can manage memory space and access speed, especially when creating large-scale data applications or handling high-performance computing tasks.

Two-Dimensional Arrays

Two-dimensional arrays are a collection of rows and columns, forming a grid-like structure in memory. They are perfect for representing matrices or tables, with applications in mathematics, simulations, images, and more. A 2D array consists of a definite number of rows and columns, and each position can store a data value.

This structure is analogous to a spreadsheet, with data organized neatly in cells. For instance, a 6x8 array indicates 6 rows and 8 columns. Programming languages adopt various methods to implement these arrays, with row-major order being a predominant approach.

Handling 2D arrays requires understanding their layout and memory usage to maximize computing efficiency. Memory address calculations hinge on knowing the dimensions of the array and how data is packed together, helping optimize computational tasks.