The capacity of 2K x 16 PROM is to be expanded to 16K x 16. Find the number of PROM chips required and the number of address lines in the expanded memory.

Problem Statement:

We have a 2K x 16 PROM chip, and we want to expand its capacity to 16K x 16. Determine the number of PROM chips required and the number of address lines in the expanded memory.

Solution:

1. Number of PROM Chips Required:

a) The original 2K x 16 PROM has 2K = 2^11 memory locations, each with 16 bits of data.

b) The expanded memory should have 16K = 2^14 memory locations, each with 16 bits of data.

c) To achieve this expansion, we need to use multiple 2K x 16 PROM chips.

d) Let 'N' be the number of PROM chips required. Then, the total memory capacity (in bits) provided by 'N' chips is:

Total Memory Capacity = N x (2K x 16 bits) = N x (2^11 x 16 bits)

2. Equating Capacities:

a) We want the total memory capacity of the expanded memory to be equal to the desired capacity of 16K x 16 bits.

b) Equating the total memory capacity to the desired capacity, we get:

N x (2^11 x 16 bits) = 16K x 16 bits

3. Solving for 'N':

a) Dividing both sides of the equation by (2^11 x 16 bits), we get:

N = 16K / 2K

N = 2^4

N = 16

4. Number of Address Lines:

a) The original 2K x 16 PROM has 11 address lines (A0 to A10) to access its 2K memory locations.

b) The expanded memory with 16K memory locations will require more address lines to access all its locations.

c) The number of address lines (m) required for the expanded memory can be calculated using the formula:

m = log2(Number of Memory Locations)

5. Calculation of Address Lines:

m = log2(16K)

m = log2(2^14)

m = 14

Conclusion:

To expand the capacity of a 2K x 16 PROM to 16K x 16, we need 16 PROM chips. The expanded memory will have 14 address lines to access all its memory locations.