Purpose
How to represent a fraction in binary format

> GetBinaryRep <- function(x, n = 52) {
+     result <- vector()
+     for (i in 1:n) {
+         x <- 2 * x
+         result <- c(result, x)
+         if (x > 1)
+             x <- x - 1
+     }
+     return(ifelse(result > 1, 1, 0))
+ }
> x <- 0.274
> print(GetBinaryRep(x, 100))
  [1] 0 1 0 0 0 1 1 0 0 0 1 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1
 [38] 0 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
> plot(GetBinaryRep(x, 100), pch = 19)

Lect_13_1-002.jpg

As you can any decimal ends up with a recurring pattern OR
gets rounded off based on the mantissa allowed in the floating point arithmetic