Nested Radicals and Gray Code

This example shows how these equations are treated. If the first sign of the radical expression is positive then the function sin() is replaced by the function cos(). Here the conversion of an integer to Gray code differs from the standard method, as you do not need to convert the number to binary first (both methods are equivalent).

To make it clearer, my method for converting an integer to Gray code (binary) uses successive divisions by powers of 2 and looks at the parity of the rounded quotient.

Example

29/2 = 14.5 ≈ 15 ⇒ 1
29/4 = 7.25 ≈ 7 ⇒ 1
29/8 = 3.625 ≈ 4 ⇒ 0
29/16 = 1.8125 ≈ 2 ⇒ 0
29/32 = 0.90625 ≈ 1 ⇒ 1

The decimal value 29 has the binary value 10011 in Gray code.