Consider a multiplicative congruential generator for a 16-bit machine. What is t

Question

Consider a multiplicative congruential generator for a 16-bit machine. What is the largest signed integer that can be stored in the machine? Let the modulus equal the largest prime less than the largest integer, and let the multiplier be a constant so that the generator has a full period. 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, verily 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.)

Explanation / Answer

The first bit is the signed bit, 0 represents the positive number and 1 represents a negative number

Largest Possible Integer Value: 2^(15) - 1 = 32767

Largest Prime Number less than the largest possible integer value = 32749

32749 mod 661 = 360

661 mod 360 = 301

360 mod 301 = 59

Hence the first three random numbers will be equal to 360, 301 and 59

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