GATE CS 2014 Set 2 Q34 — Intermediate Code Generation

In C, multi-dimensional arrays are stored in row-major order. For a 3D array declared as type X[D1][D2][D3], the byte offset of the element $X[i][j][k]$ from the base address is calculated as:

where $w$ is the size (in bytes) of each element of the array.

Let us compare this formula with the given intermediate code:

• t0 = i * 1024 $\implies D_2 \times D_3 \times w = 1024$
• t1 = j * 32 $\implies D_3 \times w = 32$
• t2 = k * 4 $\implies w = 4$

Step 1: Determine the data type

Since $w = 4$ bytes, and the question specifies that an integer is $32$ bits ($4$ bytes) and a character is $8$ bits ($1$ byte), the array $X$ must be of type int. This eliminates options C and D.

Step 2: Determine the dimensions

• Using $D_3 \times w = 32$ and $w = 4$: $$D_3 \times 4 = 32 \implies D_3 = 8$$
• Using $D_2 \times D_3 \times w = 1024$: $$D_2 \times 8 \times 4 = 1024 \implies D_2 \times 32 = 1024 \implies D_2 = 32$$

Thus, the array must be declared with dimensions $D_2 = 32$ and $D_3 = 8$, which matches int X[D1][32][8].

Looking at the options, Option A (int X[32][32][8]) is the only correct match.