Boolean  algebra

BY using the Boolean representations for logic operations, some of the mathematical properties of addition, multiplication, and negation can be applied to form Boolean equations. The logical combinations on any side of any equation are equivalent.In some ways, Boolean algebra differs from the conventional algebra. You should use logic rules instead of “regular” rules for addition, additive inverse (negation), and multiplication.  By using these rules, certain facts, called as theorems, can be obtained. Boolean theorems all take the form of equations. Some of the common Boolean theorems are listed in the Table given below.

Boolean algebra is much less messy than the truth tables for designing and evaluating the logic circuits. Some of the engineers prefer truth tables because the various logic operations are easier to envision, and all the values are shown for all the logic states in all parts of the digital circuit. Other engineers would not deal with all those ls and 0s, nor cover the whole tabletops with gigantic printouts. Boolean algebra gets around that.

For the extremely complex logical circuits, computers are used as assistance in design. They are good at combinatorial derivations and optimization problems which would be uneconomical if done by a salaried engineer.