Find the minimum product of sums of the following expression
$$f = ABC + \overline A \,\overline B \,\overline C .$$

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

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

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.