One simple pseudo random number generator multiplies the current number by 25173, then adds 13849 to it. This value now becomes the new random number.
If you started from the system timer like you did (this is called seeding the random number generator), this series of numbers will be random enough for simple tasks!
MOV AH, 00h ; interrupt to get system timer in CX:DX
INT 1AH
mov [PRN], dx
call CalcNew ; -> AX is a random number
xor dx, dx
mov cx, 10
div cx ; here dx contains the remainder - from 0 to 9
add dl, '0' ; to ascii from '0' to '9'
mov ah, 02h ; call interrupt to display a value in DL
int 21h
call CalcNew ; -> AX is another random number
...
ret
; ----------------
; inputs: none (modifies PRN seed variable)
; clobbers: DX. returns: AX = next random number
CalcNew:
mov ax, 25173 ; LCG Multiplier
mul word ptr [PRN] ; DX:AX = LCG multiplier * seed
add ax, 13849 ; Add LCG increment value
; Modulo 65536, AX = (multiplier*seed+increment) mod 65536
mov [PRN], ax ; Update seed = return value
ret
This implements a Linear Congruential Generator (LCG) with a power-of-2 modulus. %65536 happens for free because the low 16 bits of the product + increment are in AX, and the higher bits aren’t.