Memory Mapping Formula Cheatsheet

1. Physical Address (in bits):

$$ Physical Address Bits=log⁡2(Main Memory Size in Bytes)\text{Physical Address Bits} = \log_2(\text{Main Memory Size in Bytes}) $$

2. Number of Blocks:

• Main Memory Blocks:

  $$ Number of Blocks in Main Memory=Main Memory Size Block Size\text{Number of Blocks in Main Memory} = \frac{\text{Main Memory Size}}{\text{Block Size}} $$

• Cache Memory Blocks:

  $$ Number of Blocks in Cache Memory=Cache Memory SizeBlock Size\text{Number of Blocks in Cache Memory} = \frac{\text{Cache Memory Size}}{\text{Block Size}} $$

3. Block Offset (Word Offset):

$$ Block Offset Bits=log⁡2(Block Size in Bytes)\text{Block Offset Bits} = \log_2(\text{Block Size in Bytes}) $$

4. Cache Index (Direct Mapping Only):

$$ Cache Block Index Bits=log⁡2(Number of Blocks in Cache)\text{Cache Block Index Bits} = \log_2(\text{Number of Blocks in Cache}) $$

5. Tag Bits:

• Direct Mapping:

  $$ Tag Bits=Physical Address Bits−Cache Block Index Bits−Block Offset Bits\text{Tag Bits} = \text{Physical Address Bits} - \text{Cache Block Index Bits} - \text{Block Offset Bits} $$

• Associative Mapping:

  $$ Tag Bits=Physical Address Bits−Block Offset Bits\text{Tag Bits} = \text{Physical Address Bits} - \text{Block Offset Bits} $$

• Set Associative Mapping:

  $$ Tag Bits=Physical Address Bits−Set Offset Bits−Block Offset Bits\text{Tag Bits} = \text{Physical Address Bits} - \text{Set Offset Bits} - \text{Block Offset Bits} $$

6. Set Offset (Set Associative Mapping Only):