Consider the unsigned $$8$$-bit fixed point binary number representation below $$${b_7}\,\,{b_6}\,\,{b_5}\,\,{b_4}\,\,{b_3}\,\,.\,\,{b_2}\,\,{b_1}\,\,{b_0}$$$
where the position of the binary point is between $${b_3}$$ and $${b_2}$$. Assume $${b_7}$$ is the most significant bit. Some of the decimal numbers listed below cannot be represented exactly in the above representation:
$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(i)$$ $$31.500$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(ii)$$ $$0.875$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(iii)$$ $$12.100$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ (iv) $$3.001$$

Which one of the following statements is true?

Consider the minterm list form of a Boolean function 𝐹 given below. $$F\left( {P,Q,R,S} \right) = $$ $$\sum {m\left( {0,2,5,7,9,11} \right)} $$ $$ + \,\,d\left( {3,8,10,12,14} \right)$$

Here, $$m$$ denotes a minterm and $$d$$ denotes a don’t care term. The number of essential prime implicants of the function $$F$$ is ______.

Let $$ \oplus $$ and $$ \odot $$ denote the Exclusive OR and Exclusive NOR operations, respectively.

Which one of the following is NOT CORRECT?

Let $$G$$ be a finite group on $$84$$ elements. The size of a largest possible proper subgroup of $$G$$ is ________.