Converting numbers (binary and so on)

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In summary: Once you're done reading that, for Octal and Hex its exactly the same process except you multiply and divide by 8 and 16 instead of by 2.Anyone can help me to solve the problem?how to convert 0.65 (decimal numbers) to binary,octal and hexadecimal numbers?thx..=)I would first convert 0.65 into a proper fraction of the lowest common denominator in base 10, convert the numerator and denominator to the new base, then do long division. But only use that to check your answer.http://www.Newton.dep.anl.gov/Newton/askasci/1995/math/M
  • #1
soonsoon88
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Anyone can help me to solve the problem?

how to convert 0.65 (decimal numbers) to binary,octal and hexadecimal numbers?
thx..=)
 
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  • #3
soonsoon88 said:
Anyone can help me to solve the problem?

how to convert 0.65 (decimal numbers) to binary,octal and hexadecimal numbers?
thx..=)

I would first convert 0.65 into a proper fraction of the lowest common denominator in base 10, convert the numerator and denominator to the new base, then do long division.

0.65 = 65/100 = 13/20 ----> 1101/101002 = 15/248 = D/1416

Of course, you have to know how to do long division in the different bases.
 
  • #4
eugenius said:
Here is a website that does it for you. http://www.easysurf.cc/cnver17.htm#b10tob2

Once you are done reading that, for Octal and Hex its exactly the same process except you multiply and divide by 8 and 16 instead of by 2.

After you've converted 0.65 to binary, there's a shortcut to convert it to octal and hex. Just group the bits into 3s (for octal) and 4s (for hex). For example, 0.101 would be 0.5 in octal and 0.A in hex.

By the way, you can also check your binary answer with the decimal/binary converter I wrote: http://www.exploringbinary.com/binary-converter/ . It is arbitrary precision, which means you can convert very large and very small numbers.
 
  • #5
OmCheeto said:
I would first convert 0.65 into a proper fraction of the lowest common denominator in base 10, convert the numerator and denominator to the new base, then do long division.

0.65 = 65/100 = 13/20 ----> 1101/101002 = 15/248 = D/1416

Of course, you have to know how to do long division in the different bases.

That would be the best way to do it in a computer, but I'd say the "repeated multiplication by new base" method works best for humans!
 

1. What is binary and how does it differ from other number systems?

Binary is a number system that uses only two digits, 0 and 1, to represent numbers. It differs from other number systems, such as decimal, which uses 10 digits, in that it is a base 2 system. This means that each digit in a binary number represents a power of 2 instead of a power of 10.

2. How do you convert a decimal number to binary?

To convert a decimal number to binary, you can use the repeated division method. Start by dividing the decimal number by 2 and writing down the remainder. Then, continue dividing the quotient by 2 until you reach 0. The remainders, read from bottom to top, will give you the binary equivalent of the decimal number.

3. What is the purpose of using hexadecimal numbers?

Hexadecimal numbers are often used in computing because they provide a more compact way of representing binary numbers. Each hex digit represents a group of 4 binary digits, making it easier to read and write long binary numbers. Additionally, hexadecimal numbers are commonly used for representing memory addresses in computer systems.

4. Can you convert a binary number to a decimal number?

Yes, you can convert a binary number to a decimal number by using the positional notation method. Each digit in a binary number represents a power of 2, starting from the rightmost digit. Simply multiply each digit by its corresponding power of 2 and add up the results to get the decimal equivalent.

5. How do you convert a binary number to a different base?

To convert a binary number to a different base, such as octal or hexadecimal, you can use a similar method as converting to decimal. Divide the binary number into groups of the corresponding number of digits for the new base, and then use the positional notation method to convert each group to the new base. Finally, combine the results to get the converted number.

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