how does a 32 bit arm processor access all memory addresses in 2 GB of ram

Question

most processors now are 32-bits or 64-bits

if a system had 2 GB of ram ,and the machine was byte-addressable that would end up having 2147483648 memory addresses if the processor was to access the address 1000000000 which is 30bits .

now how there will be space for that address in the instruction since the instruction is limited to 32-bits and there must be space for the opcode and the operand which is the register to store the loaded number then there would be no space for the memory address if I am not wrong

I also read that some old machines had a processor of 16 bits and address bus width of 32-bits which allowed them to access up to 2^32 bytes of memory which is the same case how would an instruction limited to 16 bits access a 32-bit address in memory in an instruction ? thanks