Converting from base-2 to base-16

  • Context: High School 
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Discussion Overview

The discussion revolves around the conversion of binary fractions to hexadecimal, specifically focusing on the number 0.01011001012. Participants explore the methodology for converting both integer and fractional binary numbers to base-16.

Discussion Character

  • Technical explanation, Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant inquires about converting the binary fraction 0.01011001012 to base-16, expressing confusion over the binary point.
  • Another participant explains the conversion process for binary fractions, noting that each group of four binary digits corresponds to a power of 1/16, and provides an example with the first four digits representing 5 in hex.
  • Several participants suggest numerical values, with one proposing that the next number in the conversion sequence is 9, while another suggests 0.594.
  • A participant questions the relationship between 0.01011001012 in base-2 and 0.1 in base-2, asking whether it is greater or less than 0.1.
  • There is a claim that 0.01011001012 equals 0.59416, which is affirmed by another participant.

Areas of Agreement / Disagreement

Participants express differing views on the conversion process and the resulting values, with some uncertainty regarding the correctness of the numerical equivalences presented.

Contextual Notes

Some assumptions about the conversion process may be missing, and there is a lack of clarity on the steps taken to arrive at the proposed numerical values.

Who May Find This Useful

Individuals interested in number systems, particularly those studying binary and hexadecimal conversions, may find this discussion relevant.

johann1301
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How does one convert a number like 0.01011001012 to a base-16 system?

I know how to do for ex. 100011102, but the comma (or period confuses me)...
 
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johann1301 said:
How does one convert a number like 0.01011001012 to a base-16 system?

I know how to do for ex. 100011102, but the comma (or period confuses me)...
Conversion between binary and hex integers is pretty easy - each group of four binary digits, starting from the left, can be written as a single hex digit.

Converting binary fractions is almost as easy. Starting at the "binary" point, each group of four binary digits represents a power of 1/16. The first four digits to the right of the point are 0101, or 5 in hex, and continue in the same pattern. The first hex digit represents sixteenths, the next represents 256th-s (1/(162), and so on.
 
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next number is 9?
 
0.594?
 
0.1 - base 2 would be 1/2 = 0.5

Is 0.0101100101 - base 2 greater than or less than 0.1 - base 2?
 
i meant 0.59416

0.01011001012 = 0.59416 ?
 
Last edited:
johann1301 said:
i meant 0.59416

0.01011001012 = 0.59416 ?
Looks good.
 
Thanks!
 

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