Given a function F that accepts two pairs of 2 bit integers (from 0 to 3), that returns the integer division of the two integers as a two bit integer. Is said function a universal operator? (Assume division by 0 is not possible).
(1,0) / (1,0) = (1,0)
We've never really been taught the proper way to prove such things, only to insert values and check if it's possible to implement NOT+OR / NOT+AND / NAND / NOR.
However, with this function, I don't understand:
- How it's possible to have two outputs?
- What values to insert?
Here's how far I got:
F(1,0,1,0) = (0)(1) <---- Means we can now use 0 and 1 + made 1 (right?)
F(0, 0,1,0) = (0)(0) <---- Means we made 0.
F(1,0, 1, 0) = (0)(1) <---- we can change 0 to 1. (How does that help?)
For clarity, consider the following (partial) truth table:
1,0,1,0 1,0
0 0 0 0 = x x
0 0 0 1 = 0 0
0 0 1 0 = 0 0
0 0 1 1 = 0 0
0 1 0 0 = x x
0 1 0 1 = 0 1
0 1 1 0 = 0 0
0 1 1 1 = 0 0
1 0 0 0 = x x
1 0 0 1 = 1 0