An old English saying goes, "What's the point in having a dog & barking yourself!"
In other words, why manually split your integers when you've got a compiler to do it for you!

Note that many (most? all?) compilers will evaluate constant expressions at compile time; they don't put in all the code to do the calculation every time at runtime!

eg, here is the source & resulting assembler produced by Keil C51:

#define AAFF 0xaaff    
unsigned char aa;      
unsigned char ff;      
                       
aa = AAFF >> 8;        
R     MOV     aa,#0AAH 
ff = AAFF;             
R     MOV     ff,#0FFH 

Note that, in general, it's safer to include a Mask, to ensure that you don't get any unexpected effects from sign-extension, etc; eg,

aa = (AAFF & 0xff00) >> 8;
R     MOV     aa,#0AAH    
ff =  AAFF & 0x00ff;      
R     MOV     ff,#0FFH    

Note that the generated assembler is the same.