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I was given this question as homework but unfortunately amid this COVID time schools are down and so prof is not too clear in his explanation and the book does not mention anything regarding rounding, only how to convert.

Books: "Fundamentals of Discrete Math for Computer Science" - Tom Jenkyns, Ben Stephenson

Convert 1203.201 from base 10 to base 2, but round your answer: (a) To 6 significant figures and to 12 significant figures. (b) To 3 places after the base point. (c) What is the rounding rule for base 2?

From my calculation, it comes out to be

(1203.201)base10 = (100|1011|0011|.0011|0011|0111)base2

a. 6 sig figures: 100|1100|0000 => since the 7th figure is '1' we round up but it looks to me like it only has 5 sig figures now.

12 sig figures: 100|1011|0011|.0 => this look simple since the 13rd figure is '0'

b. 3 digits after base point: 100|1011|0011|.000 => the 4th digit after the base point is 1 so we round up but once again it doesn't look like 3 digits anymore.

c. I am tempted to put it like for decimal whereas if the digit after is '1' then we round up

Thank you for checking in.

Intern
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  • You are right about the rounding rule but you did the calculations wrong in part b: the digits after the point should be .010. I think you are saying you have fewer significant figures or digits after the point than you expect because the rounding results in a trailing 0. That's OK. To three decimal places 0.9999 (decimal) is 1.000 (which makes sense because 0.999 is a worse three place approximation than 1.000). – Rob Arthan Mar 24 '20 at 22:38
  • @RobArthan Google will tell you the rounding rules for binary numbers. Have I misunderstood?

    "I was given this question as homework but unfortunately amid this COVID time schools are down and so prof is not too clear in his explanation and the book does not mention anything regarding rounding, only how to convert."

     – John Douma Mar 25 '20 at 01:14
  • @JohnDouma trust me I have googled everything from how to round binaries to youtube videos but the way they explain it when it comes to "tie break situation" kinda not so clear. – Intern Mar 25 '20 at 06:32
  • @RobArthan thank you for pointing that out, it does make sense what you're saying. – Intern Mar 25 '20 at 06:33

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