The same remarks and recommended references presented in the previous chapter also applies to this chapter. The reader is urged to review that material before continuing onward. Almost all electrical engineers are well acquainted with the Boolean algebra and it will not be reviewed except to remind the reader of a few theorems and operations. Most of the following review will concentrate on digital logic operations including a short review of Karnough maps.

Boolean Algebra and Gate Operation:

The basic concepts of Boolean algebra will be assumed except to remind the reader of DeMorgan's theorem and duality. DeMorgan's theorem may be defined by equations 8.1a,b as,

(8.1ab)

These two theorems may easily be proved to one's self with a truth tables. Of course these relationships can easily be expanded to larger relationships as follows,

For example, for a more complex function, such as f = (A+B) + CD, one could complement F to get the complement as,

Another concept worth recalling is duality. The dual of a an expression is obtained by interchanging AND with OR, OR with AND, and interchange the 0's with 1's, and 1's with 0's; the variables are left unchanged. For example, for the following expression for f, the dual of f is found by the above operation,

For the dual, if it is known that a function is true, then the dual will be true, but f ? f _DUAL.

(For convenience, the dot --meaning the AND function-- will...