How these timer values are derived?

Question

I have a 8051 micro controller ,it has timer0,1,2,3 with different modes.

in timer0,mode0, i got a sample code (as shown below).

datasheet 8051

from that code

TH0_INIT=0xFC //5.0ms@XTAL=12MHz, Period = (10.85/2) ms@XTAL=22.1184MHz
TL0_INIT=0x0F

both TH0,TL0 load with hex values..but could not derive these values from equation below . (website) Could you please tell me, how these hex values derive?

tick = (1/(Fosc/12)
tick = 12/Fosc$$ For Fosc == 11.0592Mhz, the tick time will be
tick = 12/11.0592M = 1.085069444us = 1.085us
Delay = TimerCount * tick
 Count = (Delay/tick)
 RegValue = TimerMax- Count RegValue = TimerMax-(Delay/tick) = TimerMax - (Delay/1.085us)
 RegValue = TimerMax-((Delay/1.085) * 10^6)$$

source code for timer0,mode0

#include "N76E003.h"
#include "Common.h"
#include "Delay.h"
#include "Function_define.h"
#include "SFR_Macro.h"
#define TH0_INIT \
 0xFC // 5.0ms@XTAL=12MHz, Period = (10.85/2) ms @XTAL = 22.1184MHz
#define TL0_INIT 0x0F
void Timer0_ISR(void) interrupt 1 // interrupt address is 0x000B
{
 TH0 = TH0_INIT;
 TL0 = TL0_INIT;
 P12 = ~P12; // GPIO
 toggle when interrupt
}
void main(void) {
 TMOD = 0XFF;
 Set_All_GPIO_Quasi_Mode;
 TIMER0_MODE0_ENABLE;
 clr_T0M;
 clr_T1M;
 TH0 = TH0_INIT;
 TL0 = TL0_INIT;
 // set_ET0; //enable Timer0 interrupt
 // enable Timer1 interrupt
 set_EA; // enable interrupts
 set_TR0; // Timer0 run
 while (1) {
 TH0 = TH0_INIT;
 TL0 = TL0_INIT;
 set_TR0;
 while (!TF0)
 ;
 clr_TR0;
 P12 = ~P12;
 TF0 = 0;
 }
}

• User323693: What is the delay you are looking for? What value of register are you getting? Mode 0 is only 13 bit mode which means counts of only upto 0x1FFF possible

Answer 1

For mode 0:

1. 8192 is the number of ticks available before the timer overflows (13 bit mode).
2. Assuming 12MHz clock, the timer will be clicking at 1 MHz.
3. One tick is equal to 1 us
4. Let us compute counters for 5 ms
5. Register value is 8192 - 0.005/1u.
6. So the counters should have value of 3192.
7. Timer higher byte = 0x0C
8. Timer lower byte = 0x78

• RAVI: But...why ..TH0_INIT=0xFC TL0_INIT=0x0F?
• User323693: @RAVI that nearly comes to about 1 ms.. since mode 0 only supports 13bit, there is no way the counter valid values can be higher than 0x2000. Does the code run? Can you check once and validate