The state of Washington uses a twelve character identification number system to for its drivers licenses. 1) The first five characters are the first five letters of the individuals surname (last name). If an individuals last name contains 4 or fewer letters, the symbol * is used to fill in the remaining spaces. 2) The sixth character is the individuals first initial. 3) The seventh character is the individuals middle initial. The symbol * is used if an individual does not have a middle name. 4) The next two characters are obtained by computing subtracting the individuals year-of-birth (YOB) from 100. In other words, 100 - YOB. 5) The tenth character is the check digit. 6) The eleventh character is the month-of-birth code. It assigns a character according to the code presented in the table below. The alternate codes are used to avoid collisions. 7) The last character is the code for the day of the month on which the individaul was born. The day-of-month-born code is presented in the table below. Examples: Driver Information License Number Joseph Marshall Pollan  POLLAJM304PR Born: October 19, 1970 Tracy Holland  HOLLAT*554J5 Born: April 25, 1945 Alexander William Moe MOE**AW240MD Born: July 4, 1976   The Check Digit Scheme:     Consider the twelve character Washington State/Manitoba Province driver's license number a1a2a3a4a5a6a7a8a9a10a11a12.  The check digit a10 is created by first assigning digits to the non-digit characters in the identification number using the table below and then performing the following calculation: a10 = |a1-a2+a3-a4+a5-a6+a7-a8+a9-a11+a12| (mod 10) This scheme does not catch all single digit errors.  It also does not catch all transposition of adjacent digit errors. Examples:  A valid number: POLLAJM304PR Digit Assignments: POLLAJM304PR = 763311430479 Calculation: |a1-a2+a3-a4+a5-a6+a7-a8+a9-a11+a12| (mod 10)            = |7-6+3-3+1-1+4-3+0-7+9| (mod 10)            = |4| (mod 10)            = 4 (mod 10)            = 4 Since 4 is the check digit, this is a valid number. An invalid number: MOE**AZ240MD Digit Assignments: MOE**AZ247MD = 465001924044 Calculation: |a1-a2+a3-a4+a5-a6+a7-a8+a9-a11+a12| (mod 10)                      = |4-6+5-0+0-1+9-2+4-4+4| (mod 10)            = |13| (mod 10)            = 13 (mod 10)            = 3 Since the check digit is 0, not 3, this number is invalid.         Paper Assignment: You are employed by the New York State Department of Motor Vehicles. You have been asked to develop a new drivers' license identification number system for the state. The new identification numbers must encode a person's first and last name, the person's date of birth, and the county in which that person resides. In addition, the identification number must be only ten-characters long, one of which must be the check digit. Consequently, in addition to creating a hashing function, you also need to develop a check digit scheme for this identification number system. Write a paper, in the form of a report, that presents the new driver's license identification number systems (with check digit scheme) to the head of the Department of Motor Vehicles. Make a strong case for the adoption of your system by doing the following: Give a step-by-step description, with sufficient examples, on how driver's personal information would be used. Include a detailed description of the hashing function and the check digit scheme. Argue that your system avoids most, if not all, types of collisions, using examples as needed.