A memory chip has a capacity of 4 kB. How many address lines are required?

Explanation:

A memory chip has a capacity of 4 kB. To determine the number of address lines required, we need to understand the relationship between memory capacity and address lines. The capacity of a memory chip is the product of the number of addressable memory locations and the size of each memory location.

Firstly, 4 kB (kilobytes) needs to be converted into bytes. Since 1 kB = 1024 bytes, we have:

4 kB = 4 × 1024 bytes = 4096 bytes

Each memory location in a typical memory chip stores 1 byte of data. Therefore, the memory chip with a capacity of 4096 bytes has 4096 addressable memory locations.

The number of address lines required (n) can be determined using the formula:

Number of addressable memory locations = 2ⁿ

Setting this equal to the number of memory locations we have:

2ⁿ = 4096

To solve for n, we take the logarithm base 2 of both sides:

n = log₂(4096)

Since 4096 is a power of 2 (specifically, 2¹²), we have:

n = 12

Therefore, 12 address lines are required to address 4096 memory locations.

Hence, the correct answer is option 2, which is 12.