Converting 1/7 to Base 2: A Scientific Approach

[zeebo17]

What is 1/7 in base 2? How would you solve for this?

Thanks!

 

[Hurkyl]

The same as it is in any other base.

I assume you meant to ask how to compute its infinite binary expansion? Use long division.

 

[sjb-2812]

As perhaps a hint, what is 1/2 in binary?

 

[dmtr]

http://www.wolframalpha.com/input/?i=1/7+in+binary

 

[DoctorBinary]

Just multiply your fraction by 2 repeatedly, writing a 0 for products less than 1, and a 1 for products greater than 1 (for the latter, subtract out 1 before continuing with the multiplication). For example:

1/7 * 2 = 2/7
2/7 * 2 = 4/7
4/7 * 2 = 1 1/7
1/7 * 2 = ... (repeats)

The binary value is 0.(001), where () indicates the repeating part.

For a little more detailed explanation, see heading "dec2bin_f()" in my article "http://www.exploringbinary.com/base-conversion-in-php-using-bcmath/".

 

[Steve.pf]

What is 1/7 in base 2? How would you solve for this?

Thanks!

wouldn't it be:

1/111

But in decimal form it would be:

0.100010111000001001

I'm not sure if it's the correct answer though. My logic was to take the result of 1/7:

0.142857

remove the decimal (by multiplying it by 1,000,000) then converting that number to binary and then re-placing the decimal.

Is my method correct?

 

[Integral]

wouldn't it be:

1/111

sure but not real interesting.

But in decimal form it would be:

0.100010111000001001

I'm not sure if it's the correct answer though. My logic was to take the result of 1/7:

0.142857

remove the decimal (by multiplying it by 1,000,000) then converting that number to binary and then re-placing the decimal.

Is my method correct?

No your method is not correct nor is your result. See the post by DoctorBinary for the correct algorithm. Following his process the integer part of each computation yields a digit of the binary number.

 

[sjb-2812]

wouldn't it be:

1/111

Perhaps another way to look at it, what is 0.537 as a decimal fraction? 5/10 + 3/10² + 7/10³, so what is 0.111 as a binary fraction? 1/2 + 1/2² + 1/2³ = 0.875₁₀

 

[HallsofIvy]

But .111 is NOT the same as 1/111 in decimal or binary.