I can most of the time successfully convert between base 10 and another base or another base and base 10 or between 2 bases where one of them is a power of the other(like base 2 and base 4 or base 3 and base 9).(adsbygoogle = window.adsbygoogle || []).push({});

With negative bases I sometimes don't get what I want in that negative base and with fractional bases there are 2 expansions for every rational number greater than or equal to 1, They are an infinite sequence of digits to the left and a terminating or repeating decimal to the right. But how will I know if it is a repeating decimal and what repeats in that repeating decimal?

Like what if I wanted to represent 2/3 in base 1/2?

Also I don't know of an easy way to convert between 2 bases that are not powers of each other or base 10 and another base.

Here is how I convert between base 10 and another base:

1) ##log_n(x) = y## Here n is the base I want to convert to and x is the base 10 number I want to convert.

2) ##y =## some irrational number ##y' =## Just the integer and not the whole irrational

3) ##\frac{x}{n^{y'}}##

4) Write down the integer part(which is equal to ##z##) as the digit in the ##n^{y'}## place

5) ##z*n^{y'}##

6)##x-(z*n^{y'})##

7) repeat until you reach the ##n^0## place

8) If needed extend it to decimals in base ##n##.

When I convert between 2 bases that are powers of each other I start from the right and make n groups of ##log_x(y)## digits where ##x## is the current base and ##y## is a power of that base. I then take those groups as if they were individual numbers themselves, add up their values and write down their values from right to left

But how can I convert directly between 1 base and another base when it is neither one of these 2 previous scenarios like for example converting directly from base 2 to base 3?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Converting between bases

Tags:

Loading...

Similar Threads - Converting between bases | Date |
---|---|

I Convert from rectangular to Spherical Coordinates | Oct 5, 2017 |

I How to find the nth binary permutation? | Jan 16, 2017 |

I Convert 2 variables into 1 representative variable | Nov 9, 2016 |

Between -180 and 180 degrees (convert a larger angle) | Mar 27, 2015 |

**Physics Forums - The Fusion of Science and Community**