Fibonacci was a commonly known sequence on numbers. Its sequence behaves recursively as F(n) = F(n-1) + F(n-2). In addition fibonacci number grows massively as its index increments, therefore we need such large binary representation in order to compute high order fibonacci number. Below are examples of some fibonacci numbers.
Example : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765,…
Here, i wrote a code that able to generate any fibonacci numbers that fit into 128-bit binary system. So far, i found that the largest fibonacci number that fit on 128-bit binary representation was 3.328511 x 1038 which actually the 186-th fibonacci number. The code here was developed and simulated using MPLAB v8.0 and it works well. Next time, i’ll try to develop 2048-bits or perhaps 4096-bits fibonacci number generator hopefully🙂 .
For more detail explanation, please consider Fibonacci Number article on Wikipedia.
You may freely use this code under the GNU Public License v3.0. Cheers .