### a$.$ Difference between Digital and Analog Electronics$**$Analog Electronics:$**-**$Definition$**$: Analog electronics deals with continuous signals that vary in time and can take on any value within a given range. These signals are often represented by waveforms.$-**$Characteristics$**$: Analog signals can be affected by noise, and their performance can degrade over distance. They are typically represented in a linear fashion.$-**$Examples$**$: $-**$Audio Signals$**$: Sound waves captured by a microphone are analog signals. They can be amplified using analog amplifiers. $-**$Temperature Sensors$**$: Devices like thermocouples produce a continuous voltage that varies with temperature. $-**$Radio Transmitters$**$: AM $($Amplitude Modulation$)$ and FM $($Frequency Modulation$)$ radio signals are analog.$**$Digital Electronics:$**-**$Definition$**$: Digital electronics deals with discrete signals that have two states, often represented as binary values $(0$ and $1).$ These signals are processed in a non$-$linear fashion.$-**$Characteristics$**$: Digital signals are less susceptible to noise, making them more reliable for long$-$distance transmission. They can be easily stored and manipulated using digital circuits.$-**$Examples$**$: $-**$Microcontrollers$**$: Devices that operate using binary logic to perform tasks and control other devices. $-**$Digital Audio$**$: Music files stored in formats like MP$3$ or WAV, which are represented as a series of digital samples. $-**$Computers$**$: All computing devices operate on digital logic, processing information in binary form.### b$.$ Operational Amplifier AnalysisGiven: $-\backslash ($ R$\_1=4\backslash ,$ k$\backslash$Omega $\backslash )-\backslash ($ R$\_2=8\backslash ,$ k$\backslash$Omega $\backslash )$#### $($i$)$ Derivation of Voltage Gain and Output VoltageFor a non$-$inverting operational amplifier configuration, the voltage gain $\backslash ($ A$\_$v $\backslash )$ is given by the formula:$\backslash [$A$\_$v $=1+\backslash$frac$\{$R$\_2\}\{$R$\_1\}\backslash ]$Substituting the given values:$\backslash [$A$\_$v $=1+\backslash$frac$\{8\backslash ,$ k$\backslash$Omega$\}\{4\backslash ,$ k$\backslash$Omega$\}=1+2=3\backslash ]$The output voltage $\backslash ($ V$\_\{$out$\}\backslash )$ can be calculated using the formula:$\backslash [$V$\_\{$out$\}=$ A$\_$v $\backslash$times V$\_\{$in$\}\backslash ]$Where $\backslash ($ V$\_\{$in$\}\backslash )$ is the input voltage.#### $($ii$)$ Determine the Voltage Gain and Output Voltage for $\backslash ($ V$\_\{$in$\}=-0\mathrm{.}3$V $\backslash )$Using the voltage gain derived:$\backslash [$A$\_$v $=3\backslash ]$Now$,$ substituting $\backslash ($ V$\_\{$in$\}=-0\mathrm{.}3$V $\backslash )$ into the output voltage formula:$\backslash [$V$\_\{$out$\}=3\backslash$times $(-0\mathrm{.}3$V$)=-0\mathrm{.}9$V$\backslash ]$### Summary$-$ The voltage gain $\backslash ($ A$\_$v $\backslash )$ of the operational amplifier is $**3**.-$ The output voltage $\backslash ($ V$\_\{$out$\}\backslash )$ for an input voltage of $\backslash (-0\mathrm{.}3$V $\backslash )$ is $**-0\mathrm{.}9$V$**.$