State the Both's algorithm for multiplication of two numbers, Draw a block diagram for the implementation of the Booth's algorithm for determining the product of two $$8-$$bit signed numbers.

A block -set associative cache memory consists of $$128$$ blocks divided into four block sets. The main memory consists of $$16,384$$ blocks and each blocks contains $$256$$ eight bit words.

(i) How many bits are required for addressing the main memory?

(ii) How many bits are needed to represent the TAG, SET and WORD fields?

Consider the number given by the decimal expression.
$${16^3} \times 9 + {16^2} \times 7 + 16 \times 5 + 3$$

The number of $$1's$$ in the unsigned binary representation of the number is _______.

Show with the help of a block diagram represent Boolean function:
$$f=AB+BC+CA$$ can be realized using only $$4:1$$ multiplexer.