The Boolean logic function of interest can be specified in different manners:
- providing a well-formed formula of propositional calculus
- providing a binary number.
How to write a well-formed formula of propositional calculus
- Any type of letters can be used as variable.
- ! should be used as negation (negation): if A is a well-formed formula, !A is also well-formed.
- + as sum (logical disjunction): if A and B are well-formed formulas, so is A+B.
- . as product (logical conjunction): if A and B are well-formed formulas, so is A.B.
- ( and ) can be used to prioritize a sub-formula: if A is a well-formed formula, (A) is also well-formed.
The priority of the operators is !
The binary number (a list of 0 and 1 of length of 2n
with n the number of inputs) corresponds to the list of outputs of the different input states (it represents the last column of a truth table
of a well-formed formula).
For example, the two-input logic function XOR (exclusive or
) can be writen with the well-formed formula !a.b+!b.a
or with the binary number 0110
It is also possible to specify multiple functions simultaneously by writing the corresponding well-formed formulas in different lines.