The TCP/IP Guide  9  Networking Fundamentals       9  Backgrounder: Data Representation and the Mathematics of Computing

Binary, Octal and Hexadecimal Arithmetic 1 2 3 Bit Masking (Setting, Clearing and Inverting) Using Boolean Logical Functions

Combining Boolean Functions to Create Boolean Expressions

The functions described above can also be combined in arbitrary ways to produce more complex logical conditions. Boolean logic expressions are used in many different contexts in the computing field. A common place that most people use them is in a World Wide Web search engine. For example, if you enter “cheese AND (cheddar OR swiss) NOT wisconsin” into a search engine, the program will return pages that contain the word “cheese” that also contain the word “cheddar” or “swiss” (or both), but that do not contain the word “wisconsin”.

(Sorry, Wisconsinite cheese lovers—but I live in Vermont! J)

Boolean functions are the building blocks of much of the circuitry within computer hardware. The functions are implemented as tiny gates that are designed to allow electrical energy to flow to the output only based on certain combinations of inputs as described by the truth tables for functions like NOT, AND, OR and others. In networking, boolean logic is important for describing certain conditions and functions in the operation of networks. Boolean functions are also very important because they are used to set, clear and mask strings of binary digits, which we will explore in the next topic.

Binary, Octal and Hexadecimal Arithmetic 1 2 3 Bit Masking (Setting, Clearing and Inverting) Using Boolean Logical Functions