$1.$ How many bits do you need to represent the binary equivalent of a decimal number in the range $\backslash ([0,255]\backslash )?$ in the range $\backslash ([0,1024]\backslash )?$

$2.$ What does the binary string $01100101$ mean if it is

$-$ a binary number? Find its decimal equivalent using the double and add method.

$-$ a binary$-$coded$-$decimal $($BCD$)?$ Find its decimal equivalent.

$-$ an ASCII code? Find the character equivalent.

$3.$ Use the method presented by The Organic Chemistry Tutor to convert

$-$ the binary number $10101101$ to its equivalent Gray code

$-$ the Gray code $01110100$ to its equivalent binary number

$4.$ How would you display the real time clock value of $\backslash (\backslash$mathrm$\{$HH$\}$: $\backslash$mathrm$\{$MM$\}$: $\backslash$mathrm$\{$SS$\}=\backslash )13$:$29$:$50$ in BCD$?$

$5.$ In multiplexers, the number $\backslash ($ m $\backslash )$ of data inputs and the number $\backslash ($ n $\backslash )$ of select inputs are related by $\backslash ($ m$=2^\{$n$\}\backslash ).$ What would you do if $\backslash ($ m $\backslash )$ is not a power of $2$ of $\backslash ($ n $\backslash ),$ such as a $3$:$1$ mux?

$6.$ Decoders are often used as demultiplexers. What does a decoder need to have in order to function as a demultiplexer?

$7.$ In a binary encoder, how do we differentiate the cases where there is no active input and where only the least weighted input is active?

$8.$ What is the limitation of the error detecting code presented in the video by All About Electronics?