Converting from base-2 to base-16

  • Thread starter johann1301
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In summary, converting between binary and hex integers involves grouping binary digits into sets of four and writing them as a single hex digit. Converting binary fractions involves using powers of 1/16, with the first four digits to the right of the binary point representing sixteenths and continuing in the same pattern. When comparing numbers in different bases, it is important to pay attention to the base used for each number.
  • #1
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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  • #2
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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  • #3
next number is 9?
 
  • #4
0.594?
 
  • #5
0.1 - base 2 would be 1/2 = 0.5

Is 0.0101100101 - base 2 greater than or less than 0.1 - base 2?
 
  • #6
i meant 0.59416

0.01011001012 = 0.59416 ?
 
Last edited:
  • #7
johann1301 said:
i meant 0.59416

0.01011001012 = 0.59416 ?
Looks good.
 
  • #8
Thanks!
 

1. How do you convert binary numbers to hexadecimal numbers?

To convert from base-2 to base-16, you can use the shortcut method of grouping the binary digits into sets of four and replacing them with their corresponding hexadecimal value. For example, the binary number 1001 would be grouped as 0010 0001 and then converted to 21 in hexadecimal.

2. Why is it useful to convert between base-2 and base-16?

Converting between base-2 and base-16 can be useful for various reasons, such as representing large binary numbers in a more concise form or for easier understanding and comparison of binary data. Additionally, many modern computer systems use hexadecimal as a shorthand notation for binary values, making the conversion necessary for programming and debugging purposes.

3. What is the difference between base-2 and base-16 number systems?

Base-2, also known as the binary number system, uses only two digits (0 and 1) to represent all numbers. Base-16, also known as the hexadecimal number system, uses 16 digits (0-9 and A-F) to represent all numbers. This makes base-16 a more compact number system than base-2, as it can represent larger numbers with fewer digits.

4. Can you convert any binary number to hexadecimal?

Yes, any binary number can be converted to hexadecimal using the grouping method mentioned earlier. However, some binary numbers may result in a longer hexadecimal representation due to the need for leading zeros.

5. Are there any other methods for converting between base-2 and base-16?

Yes, there are other methods for converting between base-2 and base-16, such as using a binary-to-hexadecimal conversion table or using mathematical formulas. However, the grouping method is the most commonly used and efficient method.

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