Que. $2$ a$)\backslash ($ A $\backslash )$ continuous signal has any value between $0$ to $5$ V and is to be quantized using an ADC of appropriate bit resolution

i$)$ How many binary bits are required for the mean square quantization error to be less than $0\mathrm{.}01.$

$\backslash ((3\backslash$mathrm$\{$CO$\}2)\backslash )$

ii$)$ What is actual mean square quantization error of an Sbit ADC for the above input signal?

b$)$ Two binary symbols and dot periods $($nothing transmitted$)$ are received successively over four channels independently and simultaneously. The symbol is marked $\text{'}\backslash (\backslash$mathrm$\{$S$\}=1\backslash )\text{'}$ and dot is marked $\text{'}\backslash (\backslash$mathrm$\{$D$\}=0\backslash )\text{'}.$ The numbers in each reception of the four channels S$+$D of the four channels generates a random variable. $($For eg$.$ Say three symbols and one dot received in one trial $\backslash (\backslash$mathrm$\{$S$\}+\backslash$mathrm$\{$D$\}=3+0=3\backslash )$; the sum can vary between $4$ to $0).\backslash ($ S $\backslash )$ and D are equiprobable.

i$)$ Find mean value of this random variable following delta distribution

$(3$ CO$5)$

ii$)$ Find variasce of this random variable.

$(3$ CO$5)$