In networking, there are three important number systems:

• Base 2 – binary
• Base 10 – decimal
• Base 16 – hexadecimal

Recall that the base of a number system refers to the number of different symbols that can occupy one position. For example, binary numbers have only two different placeholders, 0 and 1. Decimal numbers have 10 different placeholders, the numbers 0-9. Hexadecimal numbers have 16 different placeholders, the numbers 0-9 and the letters A-F.

Remember that 10x10 can be written as 10². 10² means ten squared or ten raised to the second power. When written this way, it is said that 10 is the base of the number and 2 is the exponent of the number. 10x10x10 can be written as 10³. 10³ means ten cubed or ten raised to the third power. The base is still 10, but the exponent is now 3. Use the Media Activity below to practice calculating exponents. Enter x, and y is calculated, or enter y, and x is calculated.  

The base of a number system also refers to the value of each digit. The least significant digit has a value of base⁰, or one. The next digit has a value of base¹. This is equal to 2 for binary numbers, 10 for decimal numbers, and 16 for hexadecimal numbers. 

Numbers with exponents are used to easily represent very large or very small numbers. It is much easier and less error-prone to represent one billion numerically as 10⁹ than as 1000000000. Many calculations involved in cable testing involve numbers that are very large, so exponents are the preferred format. Exponents can be explored in the flash activity.

One way to work with the very large and very small numbers that occur in networking is to transform the numbers according to the rule, or mathematical function, known as the logarithm. Logarithms are referenced to the base of the number system being used. For example, base 10 logarithms are often abbreviated log.

To take the “log” of a number use a calculator or the flash activity. For example, log (10⁹) equals 9, log (10^-3) = -3. You can also take the logarithm of numbers that are not powers of 10, but you cannot take the logarithm of a negative number. While the study of logarithms is beyond the scope of this course, the terminology is used commonly in calculating decibels, a way of measuring signals on copper, optical, and wireless media.

Interactive Media Activity Interactivity: Logarithms This activity calculates log base 10 according to values entered for x and y.

   

Interactive Media Activity Interactivity: Powers of Ten This activity calculates the powers of ten.

   

Web Links A Review of Logarithms http://www.sosmath.com/algebra/logs/ log1/ log1.html