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 $${Q_2}\,{Q_1}\,{Q_0} = 000$$

Two $$NAND$$ gates having open collector outputs are tied together as shown in fig. The logic function $$Y,$$ implemented by the circuit is.