Using MIPS,

If PC is at 0x1FFFf000 what would be the range possible by using a single branch instruction?

ANS:

the branch address range is 0x1FFDF004 ~ 0x2001F000,

PC + 4 + 0x1FFFC = 0x2001 F000 PC + 4 - 0x20000 = 0x1FFD F004

As I understand, the maximum we can add is 0x1FFFC since it's the biggest number we obtain after shifting by two the biggest 16 bit number ( ( 2^15 - 1 )*4 )

but why is 0x20000 the biggest number we can substract? How did we obtain this number