Consider a multiplexer with $$X$$ and $$Y$$ as data inputs and $$Z$$ as control input. If $$z=0$$ select input $$x,$$ and $$z=1$$ selects input $$Y$$. what are the connections required to realize the $$2-$$variable Boolean function $$f=T+R$$ without using any additional Hardware?

$$SR.$$ latch made by cross coupling two $$NAND$$ gates if $$S=R=0,$$ Then it will result in

Consider the partial implementation of a $$2$$-bit counter using $$T$$ flip-flops following the sequence $$0$$-$$2$$-$$3$$-$$1$$-$$0,$$ as shown below.

To complete the circuit, the input $$X$$ should be

Identify the correct translation into logical notation of the following assertion.

$$Some\,boys\,in\,the\,class\,are\,taller\,than\,all\,the\,girls$$
Note: taller$$\left( {x,\,y} \right)$$ is true if $$x$$ is taller than $$y$$.