Digital design is based on the processing of binary variables. In this chapter, we will review the principles of Boolean algebra and the minimization of Boolean expressions. Hazards and basic numbering systems will also be discussed.

Digital design uses a two-value algebra. Variables can take one of two values that can be represented by

ON and OFF,

TRUE and FALSE,

1 and 0.

The algebra of two values, known as Boolean algebra, after George Boole (1815–1864), has five basic operators. In decreasing order of precedence (i.e., in the absence of parentheses, operations at the top of the list should be evaluated first) these are:

1. NOT

2. AND

3. OR

4. IMPLIES

5. EQUIVALENCE ...

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