Step by Step solution about How to resolve the algorithm Gray code step by step in the Ruby programming language

The provided Ruby code defines two methods (to_gray and from_gray) for the Integer class to convert between a regular integer and its Gray code representation.

• to_gray method:

  • It converts a regular integer (e.g., 10) to its Gray code representation (e.g., 1101).
  • It first checks if the input integer is negative. If it is, it raises a Math::DomainError with the message "integer is negative".
  • If the input integer is non-negative, it performs bitwise XOR (^) between the input integer and the result of shifting the input integer right by one bit (>> 1). This operation converts the input integer into its Gray code representation.

• from_gray method:

  • It converts a Gray code (e.g., 1101) back to its regular integer representation (e.g., 10).
  • Similar to to_gray, it first checks if the input integer (Gray code) is negative. If it is, it raises a Math::DomainError with the message "integer is negative".
  • If the input integer is non-negative, it defines a recursive block named recurse.
  • The recurse block takes an input integer as an argument and performs the following operations:
    • If the input integer is 0, it returns 0.
    • Otherwise, it recursively calls recurse on the input integer shifted right by one bit (>> 1), multiplies the result by 2 (<< 1), and bitwise ORs (|) it with the result of XORing the first and second bits of the input integer.
  • The recurse block is initially called with the input integer (Gray code), and the result is assigned to the variable decoded.
  • Finally, the decoded variable is returned as the regular integer representation of the input Gray code.

After defining these two methods, the code iterates through the integers from 0 to 31, converts each integer to Gray code using to_gray, converts the Gray code back to a regular integer using from_gray, and prints out the results.

This code is useful for understanding the conversion between regular integers and Gray codes, which have various applications in computer science, such as error detection and correction, computer graphics, and digital circuits.

class Integer
  # Converts a normal integer to a Gray code.
  def to_gray
    raise Math::DomainError, "integer is negative" if self < 0
    self ^ (self >> 1)
  end
  
  # Converts a Gray code to a normal integer.
  def from_gray
    raise Math::DomainError, "integer is negative" if self < 0
    recurse = proc do |i|
      next 0 if i == 0
      o = recurse[i >> 1] << 1
      o | (i[0] ^ o[1])
    end
    recurse[self]
  end
end

(0..31).each do |number|
  encoded = number.to_gray
  decoded = encoded.from_gray
  printf "%2d : %5b => %5b => %5b : %2d\n",
         number, number, encoded, decoded, decoded
end