On February $25,1991,$ a Patriot missile battery operating in Saudi Arabia failed to identify an incoming scud missile, resulting in the deaths of $28$ American soldiers and injuries to around $100$ others. This was due to a simple numerical error: the internal clock in the radar system counted in $1/10$ths of a second using a $24-$bit binary number representation. a$)$ What is the error $($expressed as a decimal number in seconds$)$ associated with each $$tick$$ of the system$$s clock? Assume the first bit indicates units $(20),$ the second bit halves $(21),$ etc. For example, a four$-$bit number might be $0\mathrm{.}110($decimal $0\mathrm{.}75).$ b$)$ What is the cumulative time error after $100$ hrs $($the time the missile battery had been operating$)?$ How far will a Scud missile