On the Subject of A>N<D

I see fancy names are in the vogue now.

On the module there are three screens and a keypad with numbers from 0-9. On the middle screen there are two 5-digit binary numbers. On the top-left screen there will be a symbol and on the top-right screen there will be a stage number.

This module can only be solved if all other non boss modules are solved. With each solved module* you’ll have to note down the information displayed on the module and work out the correct answer to submit at the end.

Solving module:

The two binary numbers are considered as an input. Take each bit of the displayed inputs maintaining their order (top is the 1st, bottom is the last) and perform the correct logic gate on it to get the new binary number. The symbol displayed on the top screen shows the logic gate that must be used. However, if the displayed symbol is ¬ (NOT) invert every bit in the top binary number (1 becomes 0 and vice versa) then convert it to decimal as normal.

For example if the showed binary numbers are 10101 and 00110 and the gate is OR then the new binary number should be 10111.

Then convert the worked out binary number back into base 10. If the stage number is even, take the number and modulo it by 10. Otherwise if it’s odd then take the digital root of the number. This is your answer for this stage.

If you strike, module will display the symbol and binary numbers for this stage. Press the correct digit to continue the submission.

*Some modules are ignored by A>N<D.

Logic gates used by A>N<D:

Symbol and name Meaning
∧ (AND) Returns true if all inputs are true. Else returns false.
∨ (OR) Returns true if any input is true. Else returns false.
⊻ (XOR) Returns true if exactly one input is true. Else returns false.
| (NAND) Returns false if all inputs are true. Else returns true.
↓ (NOR) Returns false if any input is true. Else returns true.
↔ (XNOR) Returns false if exactly one input is true. Else returns true.
→ (Implication Left) Returns false when the 1st input is true and the 2nd input is false. Else returns true.
← (Implication Right) Returns false when 1st input is false and 2nd input is true. Else returns true.