Electronic – How does the BRGE instruction work in assembly? Why is this code not functioning properly

The answer is in avr/interrupt.h line 228 which decides to use jmp on ATMEGA and rjmp on other micros. Presumably you could override it back to rjmp as long as you make sure your ISR's address is within the allowable range for rjmp.

The documentation for avr/interrupt.h as mentioned in another answer explains how to mark the ISR as naked to avoid any function setup/teardown overhead. You could even write the function using inline assembly, but you can probably get exactly the instructions you want from C, too.

The hex number is a convenience based on the hardware of the processor and memory. A 4 digit hex number like FA3B represents 16 digits in binary (1111 1010 0011 1011), which are the 16 address lines of the system memory. There is a physical 1 to 1 relationship between the binary numbers and the hardware "wires". They are 1 or 0 which is on or off. There are a little over 65,000 possible combinations of those 16 digits ( 2 to the 16th power which everyone calls 64K).

Decoding this to get to a single set of memory bits is done in parallel. In your idea of distance (or some norm that measures how hard it is to reach a memory location) from the ALU, they are all the same distance and take the same amount of time to find. The address lines go to decoding circuits and the outputs are all 0 except the one combination that matches the address bits. Split this into a matrix of 256 rows and 256 columns for each bit of data. If you are fetching a byte, like in an AVR, there are 8 sets. This fits on the flat plane of a silicon slice. The decoders do simple things. They can have 4 inputs and 16 outputs like the 7400 series logic chips. They can be kept that simple and use a bunch of them or on modern chips, more likely one big decoder circuit. You can see how they branch out like a tree along the side of a memory block in some microscopic pictures of memory chips.

Check some wiki type info on how RAM works or easier to picture, ROM - because you don't have to write to it. Looking at a simple example, like a 16 byte ROM should make it clear. -- A quick search did not turn up any good diagrams! Check a data sheet for the 74HC138 to see a simple decoder stage circuit.

For a mental picture that is logically valid, view each memory bit as having sixteen comparators that compare the values on the address bus with its particular address out of the 64K possible values. They all do the comparison simultaneously and only one answers.

If that sounds like it would use a lot of power, it would. In reality it is a divide and conquer strategy. Take the highest digit. In the case or FA3B the most significant binary bit is 1. That means the location is in the upper 32K of memory, so the lower 32K does not even need to be turned on. The next bit is a 1 so it is in the upper 16K of the upper 32 K. Then the upper 8K and the upper 4K and the upper 2K. Finally a 0! So it is in the lower 1K of that last 2K then the upper 512 of that and the lower 256 of that and the lower 128 of that and lower 64 then upper 32 upper 16 upper 8 lower 4 upper 2 and finally it is the upper one of the final two possibilities. I think I counted right.

As you can see, if you arrange the memory in small blocks you don't even have to turn on most if it for any particular access. You can use the address logic to also power up the part of the chip that is needed on the fly, so to speak.

All this to emulate the linear address model of the ALU (or the tape of a Turing Machine).