Computer Basics

Step 1: Understanding cache parameters.
Cache size = 32 KB = bytes
Block size = 32 bytes = bytes
Step 2: Calculating number of cache blocks.

Step 3: Calculating block offset bits.
Block size is bytes, so block offset requires bits.
Step 4: Calculating index bits.
Number of cache blocks is , so index bits required are .
Step 5: Total cache addressing bits.
Cache addressing bits = Index bits + Block offset bits

Step 6: Final conclusion.
Thus, the number of bits needed for cache addressing is 15.

Step 1: Understanding inputs and outputs.
A 4-bit multiplier has two 4-bit inputs. Therefore, total input bits = bits.
Step 2: Calculating number of input combinations.
Number of possible input combinations = .
Step 3: Determining output size.
Multiplying two 4-bit numbers produces an 8-bit result.
Step 4: Calculating ROM size.
Each of the 256 input combinations stores an 8-bit output.
Total ROM size = bits = Kbits.
Step 5: Final conclusion.
Therefore, the amount of ROM needed to implement a 4-bit multiplier is 2 Kbits.