A way to organize the results of combining logical Boolean variables for a single Boolean operation.
Since there are 22=4 possible combinations of two Boolean variables, there are 24 = 16 possible Boolean operations on two variables (If we had three variables, there would be 23=8 possible outcomes and thus 28=256 possible operations). If we combine all of the possible truth tables into a single table, we can order the truth tables by the number that results from interpreting the four results as a binary representation:
P = 0 1 0 1
Q = 0 0 1 1 Dec Hex Interpretation
------- --- --- ----------------
0 0 0 0 0 0 Zero
0 0 0 1 1 1 P AND Q
0 0 1 0 2 2 Q AND (NOT P)
0 0 1 1 3 3 Q
0 1 0 0 4 4 P AND (NOT Q)
0 1 0 1 5 5 P
0 1 1 0 6 6 (P != Q) aka (P XOR Q)
0 1 1 1 7 7 P OR Q
1 0 0 0 8 8 NOT (P OR Q)
1 0 0 1 9 9 (P = Q) aka (P iff Q)
1 0 1 0 10 A NOT P
1 0 1 1 11 B P -> Q aka (P implies Q)
1 1 0 0 12 C NOT Q
1 1 0 1 13 D P <- Q aka (P if Q)
1 1 1 0 14 E NOT (P AND Q)
1 1 1 1 15 F One
Each four-digit binary representation can also be interpreted as a hexadecimal digit; This will be familiar to old-time GUI (Windows and X) programmers as the list of raster operators when performing something like a bitblt.