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The problem of random values observed on inputs are generally caused by floating inputs. An input is considered in floating state if it's not driven by an output or a some kind of source. In this case, a floating input behaves like an antenna, it can get any voltage level randomly and the logic connected to it switches between 1 & 0 randomly.

It seems most of the time, electronics and uC beginners learn about them for the first time when they experiment with buttons. My experience was similar. The input was triggering when I get my finger close to the button, but before I actually press or even touch it. Later, I observed that they can also be triggered by the changes of adjacent output pins of the uC.

Fortunately, the solution is simple. Just add a pull-up or pull-down resistor, so that the output is driven by VDD or GND even when the button is not pressed. Pull-ups seem to be more popular (I'm not sure why), so you generally connect the button in such a way that it pulls the input pin to the ground when the button is pressed and provide a pull-up resistor between the pin and VDD. In this case, your program logic reads the input as 0 when the button is pressed.

BTW, you could connect the pin directly to the VDD to prevent it from floating. But in this case, a button press would short circuit VDD to GND, collapse the VDD and reset the uC. This can also damage the power regulator (actually most of them have thermal shutdown to protect themselves), the button itself or the wires (or traces on the PCB). This is why you need a resistor.

Most uCs also provide internal weak pull-ups which can be activated by software. Here, weak means that these resistors have high values (like 100k ohms) and they don't pull the pin strongly. In cases where you need stronger ones (like pulling up communication lines) you may need to use external ones.

Some more recent uCs may provide internal weak pull-down resistors too. STM32 uCs have this capability. Your PIC12F1822 has only pull-up resistors, but fortunately they can be controlled individually. In some older PIC models, you have single switch to activate pull-ups on all pins of PORTB.

To activate internal weak pull-up on RA4:

Fixed it - RB0 doesn't accept CCP2. Needed to change the pin to RC1

Isolate the problem first:

• Connect the input to 3.3 V power bus, maybe better via 2K resistor, and check if the circuit gets triggered.
• Measure the voltages in our 2.5 v output and verify if they are within the ranges that a 3.3 V input would respect. If not, you need a level converter.

This should give the answer is it a voltage level problem, is it a software problem, or is it a hardware problem somewhere else.

I rewrite your code and tested it in MPLAB simulation. It works as expected. It changes modes in ascending order, then runs in the selected mode until the change button pressed again, then it changes to the next mode. You can add more working modes if you want or you can modify the way the how GPIOs blinking. There is no __delay_ms(), that's why the delays run without consuming the CPU. Please test it in a real circuit and give me a feedback.

In your configuration is TX pin RC6 so switch:

The answer to your question is that you need to study a working example of what the "new" method that Microchip supports for assembly language programming using the pic-as(v2.20) tool chain.

This tool chain only works with MPLABX v5.40 and later.

I want to point out that my only affiliation with Microchip is as a customer. At present I am cursed with porting several legacy MPASM project to build with this "new" method. The documentation available from Microchip is sketchy at best.

Just for you I have created an MPLABX v5.40 assembly language project for the PIC10F200 you can access here on git hub.

Warning: The XC8 v2.20 installer does not always install the pic-as(v2.20) tool chain automatically. You may need to use the manual method to add tool chains to MPLABX v5.40, I leave this as an exercise for the student.

Ok, so here is a solution for your homework:

Your digits are BCD coded(BinaryCodedDecimal), each digit 0-9 is coded in four bits 0000-1001.

DisplayLED toggles between 0 and 1, to select which digit to display, you must ensure you don't update the random value until it have been displayed, actually you should probably update it even more seldom as the display relays on the after glow in the LED and our slow eyes to display an image.