For efficiency we use a half-dozen signals, but we could actually represent all logical relationships with just a single signal. There are two such signals we can work with--one that represents the negation of a conjunction (X) and another that represents the negation of a disjunction (Y). A key point is that negation is represented by the duplication of a string.

.............PN..........PQA......PN...........PQO
P Q || PPX | PQXPQXX | PPY | PQYPQYY
1..1........0....................1........0...................1
1..0........0....................0........0...................1
0..1........1....................0........1...................1
0..0........1....................0........1...................0

There are a number of equivalence rules that allow us to see how we can work with just one signal. A few are given below:
PQA=PNQNON=PQXPQXX=PPYQQYYPPYQQYYY
PQO=PNQNAN=PPXQQXXPPXQQXXX=PQYPQYY
PQAN=PNQNO=PQX=PQYPQYYPQYPQYYY
PQON=PNQNA=PPXQQXXPPXQQXXX=PQY
PQC=PNQO=PQNAN=PQQXX=PPYQYPPYQYY

Experiment with the program PLN2VAL.

In algebraic notation PQX becomes PQ+1 and PQY becomes PQ+P+Q+1.

Return to truth-functional relationships.