1 + 1 = 1, LOGIC PUZZLE - IchigoJam

We have 0 and 1 only (in logic world), now let's do calculations. First we start with addition. "|" (vertical bar).
There is no increase in digit with 1 adding by 1, still remains to be 1, that's the "logical sum".
Next is the multiplication, use "&". (Use comma to separate and calculate collectively)
If number multiplied by 1, answer is that same number, and it becomes zero when it is multiplied by 0, that's the "logical multiplication".
To perform unusual addition use "^". Even when both numbers are 1, the answer is zero
It is only for 1^1, but the rest remain same as "logic sum". That's "XOR" (exclusive OR)
Logic calculations can be put collectively up to maximum of 16!
Addition of binary numbers with 4 digits. You can calculate 1|0, 0|0, 1|1, 0|1 all at once!
Try it!
1. What is the answer for 3|1?
2. Use hint: ?BIN$(1),BIN$(2),BIN$(3), solve the puzzle 3|1
3. Lets do calculations of ?8323^35 and ?8323^35^35
4. Change to different numbers, let's play with secret numbers using logic
5. Let's do various calculations, let's make logic puzzles

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