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

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.

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