Memory Addressing: 48-bit vs 64-bit (Transcript Notes)

48-bit Address Space

Our systems currently use a 48-bit address. This means each memory location is identified by a unique 48-digit binary number. It allows access to a maximum of $2^{48}$ bytes of memory.

• To simplify $2^{48} \text{ bytes}$: We break it down as $2^8 \times 2^{40} \text{ bytes}$.

• Since $2^{40} \text{ bytes}$ is 1 Tebibyte (TiB) and $2^8 = 256$, this means $256 \times 1 \text{ TiB} = 256 \text{ TiB}$.

• So, $2^{48} \text{ bytes} \approx 256 \text{ TB}$.

64-bit Address Space

Newer architecture supports a larger 64-bit addressing space. This means each memory location is identified by a unique 64-digit binary number, allowing access to a much greater amount of memory.

• Maximum addressable memory: $2^{64} \text{ bytes}$.

• To simplify $2^{64} \text{ bytes}$: We write it as $2^4 \times 2^{60} \text{ bytes}$.

• Since $2^{60} \text{ bytes}$ is 1 Exbibyte (EiB) and $2^4 = 16$, this means $16 \times 1 \text{ EiB} = 16 \text{ EiB}$.

• So, $2^{64} \text{ bytes} \approx 16 \text{ EiB}$ (or $16 \text{ EB}$ in decimal).

Clarifications on Units:

• EiB (Exbibyte): A binary unit, equal to $2^{60} \text{ bytes}$.

• EB (Exabyte): A decimal unit, equal to $10^{18} \text{ bytes}$.

Comparing 32-bit vs. 30-bit Addressing

• 32-bit addressing: Each memory location uses a 32-digit binary number. Total memory is $2^{32} \text{ bytes}$.

  • This is $2^2 \times 2^{30} \text{ bytes}$. Since $2^{30} \text{ bytes}$ is 1 Gibibyte (GiB) and $2^2 = 4$, this results in $4 \text{ GiB}$.

• 30-bit addressing: Each memory location uses a 30-digit binary number. Total memory is $2^{30} \text{ bytes}$, which directly equals $1 \text{ GiB}$.

Each additional address bit doubles the addressable memory. While systems use techniques like PAE, the addressing width defines the theoretical limit.

Practical Implications & Study Strategy

• Study Tip: Note specific memory sizes; they are often tested.

• Exam Preparation: Be ready to convert between address bits (n) and total memory using the formula $2^n \text{ bytes}$. Differentiate between binary (KiB, MiB, GiB, TiB, EiB) and decimal (KB, MB, GB, TB, EB) units.

Quick Recap for Exam-Ready Understanding

• 48-bit address space: Max memory $2^{48} \text{ bytes} \approx 256 \text{ TB}$.

• 64-bit address space: Max memory $2^{64} \text{ bytes} \approx 16 \text{ EiB}$.

• 32-bit addressing: Max memory $2^{32} \text{ bytes} = 4 \text{ GiB}$.

• 30-bit addressing: Max memory $2^{30} \text{ bytes} = 1 \text{ GiB}$.