GATE CS 2009 Q7 — Combinational Circuits

To find the number of RAM chips required, we divide the total target memory capacity by the capacity of a single RAM chip.

1. Target Memory Capacity:
$$\text{Total Capacity} = 256\text{ K bytes} = 256\text{ K} \times 8\text{ bits}$$

2. Capacity of a Single RAM Chip:
$$\text{Chip Capacity} = 32\text{ K} \times 1\text{ bit}$$

3. Number of Chips Required:
$$\text{Number of Chips} = \frac{\text{Total Capacity}}{\text{Chip Capacity}} = \frac{256\text{ K} \times 8\text{ bits}}{32\text{ K} \times 1\text{ bit}}$$

Simplifying the expression:
$$\text{Number of Chips} = \frac{256}{32} \times 8 = 8 \times 8 = 64$$

Thus, $64$ chips of size $32\text{K} \times 1$ are required to construct a $256\text{K}$ bytes memory.