4. (??, 22 pts) We saw in lecture methods to store integers (both negative and non-negative) and real numbers as sequences of 0s and 1s. Integers can be stored exactly (using binary numbers and/or 2’s complement), but real numbers must be approximated by rational numbers. In decimal (base 10), a rational number can be expanded as, for example, 11 8 = 1.375. That is, 11 8 = 1 × 100 + 3 × 10−1 + 7 × 10−2 + 5 × 10−3 . In a similar fashion, we can expand a rational number in binary, 11 8 = · · · # × 2 0 + # × 2 −1 + # × 2 −2 + # × 2 −3 + · · · = 1 × 2 0 + 0 × 2 −1 + 1 × 2 −2 + 1 × 2 −3 . Thus, we can write 11/8 as 1.011 in binary; thereby converting it to a sequence of 0s and 1s (and a decimal—binary?—point). (a) Is 0.1 the binary expansion of 1/2? Explain why or why not. (b) Determine the binary expansion of 45/16. Remember that a rational number is a number that can be written as a ratio of integers, such as 1/2, 3/4, and 5/1.