The address of the first location of a 256 kilo byte (KB) memory is (2500)H. Choose the correct address ...

 

Q. The address of the first location of a 256 kilo byte (KB) memory is (2500)H. Choose the correct address of the last location of the memory.

(A) (2FFF)H (B) (124FF)H (C) (424FF)H (D) (324FF)H

The address of the first location of a 256 KB memory is (2500)H. Choose the correct address of the last location of the memory.

Starting Address

(2500)H

Memory Size

256 KB

Step-by-Step Solution

Step 1: Convert Memory Size into Bytes

We know that:

\[ 1 KB = 1024 \text{ bytes} \]

Given memory size = 256 KB.

\[ 256 KB = 256 \times 1024 \] \[ = 262144 \text{ bytes} \]

Step 2: Convert Bytes into Hexadecimal

Convert 262144 into hexadecimal notation.

\[ 262144_{10}=40000_{16} \]

Therefore, 256 KB = 40000H bytes.

Step 3: Calculate the Last Memory Address

Use the following formula:

\[ \boxed{ \text{Last Address} = \text{Starting Address} + \text{Memory Size} -1 } \]

Substitute the given values:

\[ =2500_H+40000_H-1 \] \[ =42500_H-1 \] \[ =424FF_H \]

Correct Answer

Last Memory Address

\[ \boxed{(424FF)_H} \]

The last location of the 256 KB memory is 424FFH.

Shortcut Method for GATE Exams

Remember this formula to solve memory address calculation problems quickly:

\[ \boxed{ \text{Last Address} = \text{Starting Address} + \text{Size} -1 } \]

Why subtract 1? Because the starting address itself is counted as the first memory location.

For example, if memory starts at address 100 and contains 10 bytes, the last address is 109, not 110.

Important Points for GATE Preparation

• ✓ 1 KB = 1024 bytes in the conventional binary memory-size convention used in this question.
• ✓ 1 MB = 1024 KB.
• ✓ Always subtract 1 when calculating the last address from the starting address and size.
• ✓ Hexadecimal numbers use digits from 0 to 9 and A to F.
• ✓ Check whether the memory is byte-addressable or word-addressable before calculating addresses.

Frequently Asked Questions

How do you calculate the last address of memory?

Use Last Address = Starting Address + Memory Size - 1. Ensure the memory size is expressed in addressable units, such as bytes for byte-addressable memory.

How many bytes are there in 256 KB?

Using the binary convention, 256 KB = 256 × 1024 = 262144 bytes.

Why is 1 subtracted while calculating the last address?

Because the starting address represents the first location. Therefore, a memory containing N bytes occupies N consecutive addresses, from the starting address through starting address + N - 1.

What is the last address of 256 KB memory starting at 2500H?

The last address is 424FFH, assuming byte-addressable memory and 1 KB = 1024 bytes.

Conclusion

Memory address calculation is an important topic in Computer Organization and Architecture. For a memory of 256 KB starting at 2500H, the last address is 424FFH. Remember the starting address + memory size - 1 formula to solve similar GATE examination problems.