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?

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.

Fill in the blanks:
In the two bit full-adder/sub tractor unit shown in Fig., when the switch is in position $$2.$$ $$.....$$ using $$.....$$ arithmetic.

For the synchronous counter shown in fig. write the truth table of $${Q_0},\,\,{Q_1}$$ and $${Q_2}$$ after each pulse starting from $${Q_0} = {Q_1} = {Q_2} = 0$$ and determine the counting sequenced also the modulus of the counter

What is the modules of the counter with initial state $${Q_2}\,{Q_1}\,{Q_0} = 000$$