Boolean Algebra

Logical Operation

• The three basic logical operations are:

• AND

• OR

• NOT

• AND is denoted by a dot ( · )

• OR is denoted by a plus ( + )

• NOT is denoted by an overbar, a single quote mark ( ' ), or ( ~ ) before the variable

Logical Gate

Universal Gates

Duality rules

• The dual of an algebraic expression is obtained by interchanging + and ⋅ interchanging 0's and 1's, while variables don't inverted

• Seek the dual of a function, the operation order kept as same as the origin function

• The identities appear in dual pairs. When there is only one identity on a line the identity is self-dual. i.e., the dual expression = the original expression.

• Unless it happens to be self-dual, the dual of an expression does not equal the expression itself.

Duality rules (Cont.)¶

• If the function G is the dual of F, then F is also G of duality. G and F are mutually duality formula.

• 👩🏼‍💼If the two logical functions F and G are equal, then the duality formula F' and G' are the same.

• Example:

Complementing Functions¶

• For logic function F, interchange + and ⋅ operators and complement each constant value and literal, then obtained the new function is the inverse function of the original function, referred to as F`

• 求出反函数的形式

• Example：

Useful Theroms