1. Consider a multiplicative congruential generator for a 16-bit machine (that is b=16). What is the largest signed integer that can be stored in the machine (2b-1 -1)? Let the modulus equal the largest prime number less than the largest signed integer, and let the multiplier be a constant so that the generator has a full period (m-1). First, determine by hand the first three random numbers generated with this generator giving accuracy to four digits to the right of the decimal. Second, use Excel to verify your answers. Third, verify that the multiplier yields a generator with a period equal to one less than the modulus using Excel. (Note that the initial seed does not yield a random number.) PLEASE SHOW THE EXCEL FILE

Largest possible signed integer (2b-1 -1): ___________

Modulus (largest prime number) (m): _____ ___ (Use Google to find the appropriate prime.)

Multiplier (a): _661__

Initial random number seed (Z0): _121______

Z1: ___________ Random number_1 ___________

Z2: ____________ Random number_2: __________

Z3: _____________ Random number_3: __________