Consider a computing system that uses DNA to store information. Given that DNA is formed from the 4 nucleobases adenine, cytosine, guanine, and thymine (uracil is only found in RNA) let us assume that our storage of numbers will be base 4. Assume that we have p=3 for the mantissa and the exponent E[2,2].

a. Calculate how many numbers can we represent with this system? What are the underflow and overflow limits?

b. Graphically show how the numbers on the decimal real line are distributed. (write in python)

c. How many more numbers can we store in N base-pairs versus N bits where the mantissa and exponent are the same relative length