A numerical code connects language and visual objects with calculation. But strings of binary digits are hard for humans to read, so it is common to rewrite binary numerals in four$-$digit blocks. Since four binary digits can represent the numbers from $0$ to $16,$ we can use the digits $0$ to $9$ with their usual meanings and then let A$,$ B$,...,$ F stand for $10,11,...,15.$ In effect, this means we are representing numbers in base $16,$ so this representation is known as hexadecimal. a$.$ Translate the hexadecimals $37,5$A$,$ B$9,$ and ED into ordinary decimal numerals. How many different numbers can be written as two$-$digit hexadecimals? What are they? b$.$ A byte is a block of eight binary digits. If we separate an eight$-$digit byte into two four$-$digit halves, each half can be converted to a single hexadecimal digit. Illustrate this process using the binary numerals $00010001,00111000,10011001.$ Is the resulting two$-$digit hexadecimal always the correct translation of the byte? Explain.