3.8. (NUMERICAL METHODS) Suppose you have only 3 bits to represent as closely as

Question

3.8. (NUMERICAL METHODS) Suppose you have only 3 bits to represent as closely as possible the decimal system number 0.10. Assume that none of the bits are needed to represent the binary point or 0’s to the left of the binary point. What is the binary number that would come closest to this decimal system number?
3.9. Repeat 3.8, but assume that you have 5 bits instead of only 3. How does your answer compare with that of Problem 3.8.
3.8. (NUMERICAL METHODS) Suppose you have only 3 bits to represent as closely as possible the decimal system number 0.10. Assume that none of the bits are needed to represent the binary point or 0’s to the left of the binary point. What is the binary number that would come closest to this decimal system number?
3.9. Repeat 3.8, but assume that you have 5 bits instead of only 3. How does your answer compare with that of Problem 3.8.

3.9. Repeat 3.8, but assume that you have 5 bits instead of only 3. How does your answer compare with that of Problem 3.8. 3.9. Repeat 3.8, but assume that you have 5 bits instead of only 3. How does your answer compare with that of Problem 3.8.

Explanation / Answer

Mathematically, the binary representation of the decimal fraction 1/10 is, in fact, infinite.

.1 (decimal) = .00011001100110011 . . . (base 2) .

The above conversion can be obtained by multiplying the part left to the decimal point with 2 and appending the whole number part of the number obtained in sequence so to obtain .000110011...(base2)

Therefore for 3 bits, we can store only 011 while for 5 bits we can store 10011

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