Question

Find the number of address lines required for (i) 4K RAM (ii) 8K ROM.

Answer 1

To determine the number of address lines required for a memory chip, you can use the formula:

\[
\text{Number of Address Lines} = \log_2(\text{Memory Size in Bytes})
\]

where the memory size is given in bytes.

### (I) 4K RAM

- **Memory Size:** 4K (where K = 1024)
- **Total Memory Size in Bytes:** \( 4 \times 1024 = 4096 \) bytes

\[
\text{Number of Address Lines} = \log_2(4096) = \log_2(2^{12}) = 12
\]

So, **12 address lines** are required for 4K RAM.

### (II) 8K ROM

- **Memory Size:** 8K (where K = 1024)
- **Total Memory Size in Bytes:** \( 8 \times 1024 = 8192 \) bytes

\[
\text{Number of Address Lines} = \log_2(8192) = \log_2(2^{13}) = 13
\]

So, **13 address lines** are required for 8K ROM.

### Summary:

- 4K RAM requires **12 address lines**.
- 8K ROM requires **13 address lines**.

Answer 2

The number of address lines required to access a memory depends on the total number of memory locations, which is a function of the size of the memory. The formula to calculate the number of address lines is:

\[
\text{Number of Address Lines} = \log_2(\text{Number of Memory Locations})
\]

(i) **For 4K RAM:**
- 4K means \( 4 \times 1024 = 4096 \) memory locations.
- Number of address lines required: \( \log_2(4096) = 12 \)

(ii) **For 8K ROM:**
- 8K means \( 8 \times 1024 = 8192 \) memory locations.
- Number of address lines required: \( \log_2(8192) = 13 \)

### Conclusion:
- For 4K RAM, 12 address lines are required.
- For 8K ROM, 13 address lines are required.