3. [25 marks] Fractional Numbers and Blackboard Notation. Infinite binary expansions of rational numbers are either pure recurring or mixed recurring depending on whether the cycle starts immediately after the point (pure recurring), or somewhat later (mixed recurring). a) [math] Show the infinite binary expansion of 37.8 without normalization. b) [math] Show the infinite hexadecimal expansion of 37.8 without normalization. c) [math] Show the infinite binary expansion of 37.8 with normalization. Include the scale factor, with a decimal exponent. (This is a _scaled_ binary expansion). d) [math] Show the infinite hexadecimal expansion of 37.8 with normalization. Include the scale factor, with a decimal exponent. Write the scale factor as a power of 2. Note: normalization = 1.xxx in both cases (bin and hex). e) Show, in normalized binary blackboard notation, the approximation to 37.8 for a fixed-size fractional field that is 20 bits long. Show these 20 bits. Now, show these same 20 bits in hexadecimal (5 hexits).