// Author: ***
// Date:   ***
// Tabs:   ***  (indicate the separation between tab stops)

//==============================================================
// These functions work on arrays that represent binary numbers.
// Each value in the arrays is either 0 or 1, and the low order
// bit is at index 0.  For example, if array A contains binary
// number 14 (1110 in standard binary notation), then it might be
// that
//    A[0] = 0
//    A[1] = 1
//    A[2] = 1
//    A[3] = 1
//
// Say that a binary number is *normalized* if its highest order
// bit is 1.  (As a special case, 0 is normalized if it is
// represented by an array of length 0.)
//
// All results of these functions are normalized.  But the
// parameters are not required to be normalized.  For example,
// if array A holds
//    A[0] = 0
//    A[1] = 1
//    A[2] = 1
//    A[3] = 1
//    A[4] = 0
//    A[5] = 0
// then A is a non-normalized representation of 14.
//==============================================================


public class Arithmetic
{
  //=================================================================
  // inc(A) returns an array of bits representing A+1.
  //=================================================================

  public static byte[] inc(byte[] A)
  {
    ...
  }

  //=================================================================
  // sum(A,B) returns an array of bits representing A+B.
  //=================================================================

  public static byte[] sum(byte[] A, byte[] B)
  {
    ...
  }

  //=================================================================
  // product(A,B) returns an array of bits representing A*B.
  //=================================================================

  public static byte[] product(byte[] A, byte[] B)
  {
    ...
  }
}