3 ms·
An easier easier way: 1/3 = 0.3333... = 0.????...b *2 = 0.6666... 0 -> 0.0???...b *2 = 1.3333... 1 -> 0.01??...b -1 =
by jonsen 7y ago
An easier easier way:
1/3 = 0.3333... = 0.????...b
*2 = 0.6666... 0 -> 0.0???...b
*2 = 1.3333... 1 -> 0.01??...b
-1 = 0.3333...
*2 = 0.6666... 0 -> 0.010?...b
etc.
- dTal 7y agoThis is insightful, but hard to read. Essentially: 1/3 * 4 = 4/3 4/3 = 1 + 1/3 So, working backwards, our number can be more and more closely approximated by repeatedly adding 1 and dividing by 4 - or in binary, prepending a 1 and shifting two places right: 0.01010101...
- air7 7y agoNice. Maybe an easier^3 could be: 1/3 = 0.xyz 4/3 = 1.xyz Meaning (shl,2) leaves the same digits after the decimal point. So it must be 0.010101...