Question

2. There are a large number of algorithms for generating random numbers. The Linear Congruential Method is one of them, and it has the following form: In+1 = modm(a In + c) This generates the next number in the sequence by multiplying the previous number In by a, adding c, and taking modulo m. Write an assembly code for a subroutine which generates 8 bit random numbers with m=256, a=5, and c=67.

Answer 1

Solution: Subroutine random 8-bit random number generator. : in order for this routine to work, there are 2 things to consider ; a) some type of non-zero value 'seed' must first be loaded into ml b) the sequence will repeat after calls to the routine RANDOMM: MOV A, RN4 RRC MOV RN4,RN3 MOV RN3,RN2 MOV RN2,RN1 : 8-bit to carry ; shift all bytes left MOV A, RN-4 RRC MOV TEMP1. A MOV A. RN1 :was RNS : get bit-8 (in carry) into old RN3 ; save it for later RLC MOV RN1, A MOV A. TEMP1 XRL MOV TEMP1, A bit 1 to 7 in positiorn put back : restore A A, RN1 mod 2 sum of all bits in ml and the carry bit : save it

MOV A, RN4 RRC MOV RN4. A MOV A. RN3 RRC ; rotate RN4 MOV RN3. A MOV A. RN72 RRC MOV RN2, A MOV A, TEMP1 RLC MOV RN1. A MOV RANNUM, A ; rotate RN3 ; rotate RN2 restore A xor over-writes all 8 bits, but doesn't matter ; random number!! RET stop RANDOM end

This generates the next number in the sequence by multiplying the previous number in bv a, adding c. and taking modulo m m-256, a-5 and c-67 For this generator is defined by the recurrence relation: Where is the sequence of pseudorandom values And m: 0 < m : the modulus a, 0 <a <m the multiplier c, 0 cSm , the increment A0,0 <m, the "seed" or start value. a = 2, the generator is often called a multiplicative congruential generator (M or Lehmer RNG. If c-67, the method is called a mixed congruential generator. The period of a general LCG is at most m=256, and for some choices of factor a much less than that. Provided that the offset cis nonzero, the LCG will have a full period for all seed values if and only if 1. c and m are relatively prime. 2. 2-1 is divisible bv all prime factors ofm 3. α-l is a multiple of 4 if m is a multiple of 4.