Cross-Switch.
We don't care about the stuations:
A=0 B=0 X=0
A=0 B=0 X=1
A=1 B=1 X=0
A=1 B=1 X=1
because they never occur, so:
A B X QA QB
0 0 0 x x
0 0 1 x x
0 1 0 0 1
0 1 1 1 0
1 0 0 1 0
1 0 1 0 1
1 1 0 x x
1 1 1 x x
Cross as Left veksel (connect A and B): We only care about
A=B=1
situations, because A and B are always under voltage:
A B X QA QB
0 0 0 x x
0 0 1 x x
0 1 0 x x
0 1 1 x x
1 0 0 x x
1 0 1 x x
1 1 0 1 0
1 1 1 0 1
This (A=B=1) situations were "don't care" for the Cross-Switch, so we may combine them into the new ComboCross:
A B X QA QB
0 0 0 x x
0 0 1 x x
0 1 0 0 1
0 1 1 1 0
1 0 0 1 0
1 0 1 0 1
1 1 0 1 0
1 1 1 0 1
Autogenerated circuit: Logisim -> Combinational Analysis -> Table
[ Build Circuit ]
Circuit name: X
[v] Use 2 Inputs Gates Only,
[ ] Use NAND Gates Only
[ OK ]
ComboCross as Right veksel (use only QA or QB):
The ComboCross truth table perfectly satisfies our needs for the "Right veksel".
Logisim simulation for 6 nodes "Hallway lighting":
download solution here. Use "Project -> Analyze circuit" to recover the Truth Table (don't cares would be lost and replaced with actual values for auto-generated subcircuit X)