✅ Representation of Two-Dimensional Arrays in Memory (Detailed BCA Exam Answer)

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✅ 1. Introduction

A Two-Dimensional Array (2D Array) stores elements in the form of rows and columns, like a matrix.

✅ Example:

int A[3][4];

It has:

• 3 rows
• 4 columns
• Total elements = 3 × 4 = 12

📌 Although it looks like a table, memory in computer is linear (1D), so a 2D array is stored in memory in a continuous sequence.

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✅ 2. Methods of Memory Representation of 2D Arrays

There are two common methods to store 2D arrays in memory:

✅ 1. Row-Major Order (used in C/C++)
✅ 2. Column-Major Order (used in FORTRAN / MATLAB)

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✅ 3. Row-Major Order Representation

✅ Meaning

In Row-Major Order, elements are stored row by row.

👉 First, all elements of Row 0, then Row 1, then Row 2, and so on.

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✅ Example

Let:

int A[3][3] = {
  {1, 2, 3},
  {4, 5, 6},
  {7, 8, 9}
};

📌 Table form:

A[0][0] A[0][1] A[0][2]
A[1][0] A[1][1] A[1][2]
A[2][0] A[2][1] A[2][2]

✅ Stored in memory (Row-Major):

1, 2, 3, 4, 5, 6, 7, 8, 9

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✅ Address Calculation Formula (Row-Major)

[
LOC(A[i][j]) = Base(A) + [(i \times N) + j] \times W
]

Where:

• LOC(A[i][j]) = address of element A[i][j]
• Base(A) = address of first element A[0][0]
• i = row index
• j = column index
• N = number of columns
• W = size of each element (bytes)

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✅ Example Calculation

Assume:

• Base(A) = 1000
• W = 4 bytes
• N = 3 columns
  Find address of A[2][1]

[
LOC(A[2][1]) = 1000 + [(2 \times 3) + 1] \times 4
]
[
= 1000 + (6+1)\times 4
= 1000 + 28
= 1028
]

✅ Address of A[2][1] = 1028

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✅ 4. Column-Major Order Representation

✅ Meaning

In Column-Major Order, elements are stored column by column.

👉 First all elements of Column 0, then Column 1, then Column 2, etc.

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✅ Example (Same Array)

Matrix:

1 2 3
4 5 6
7 8 9

✅ Stored in memory (Column-Major):

1, 4, 7, 2, 5, 8, 3, 6, 9

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✅ Address Calculation Formula (Column-Major)

[
LOC(A[i][j]) = Base(A) + [(j \times M) + i] \times W
]

Where:

• M = number of rows

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✅ Example Calculation

Assume:

• Base(A) = 1000
• W = 4 bytes
• M = 3 rows
  Find address of A[2][1]

[
LOC(A[2][1]) = 1000 + [(1 \times 3) + 2] \times 4
]
[
= 1000 + (3+2)\times 4
= 1000 + 20
= 1020
]

✅ Address of A[2][1] = 1020

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✅ 5. Difference Between Row-Major and Column-Major

Feature	Row-Major Order	Column-Major Order
Storage Order	Row wise	Column wise
Used In	C, C++	FORTRAN, MATLAB
Formula Uses	Columns (N)	Rows (M)
First Stored	First row	First column

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✅ 6. Conclusion

A two-dimensional array is stored in contiguous memory, but because memory is linear, it is stored using either:

✅ Row-Major Order (row by row – C/C++)
✅ Column-Major Order (column by column – FORTRAN)

Address of any element can be calculated using standard formulas.

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