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Sine and Square waves (Core) / Exponents and logarithms (Optional)


Sine waves and square waves (Core)
4.1.2 Sine waves, or sinusoids, are graphs of mathematical functions. Sine waves are periodic, which means that they repeat the same pattern at regular intervals. Sine waves vary continuously, which means that no adjacent points on the graph have the same value.


Sine waves are graphical representations of many natural occurrences that change regularly over time. Some examples of these occurrences are the distance from the earth to the sun, the distance from the ground while riding a Ferris wheel, and the time of day that the sun rises. Since sine waves vary continuously, they are examples of analog waves.

Square waves, like sine waves, are periodic. However, square wave graphs do not continuously vary with time. The wave maintains one value and then suddenly changes to a different value. After a short amount of time it changes back to the original value. Square waves represent digital signals, or pulses. Like all waves, square waves can be described in terms of amplitude, period, and frequency.

The next page reviews exponents and logarithms.

Exponents and logarithms (Optional)
4.1.3 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 placeholders, which are zero and one. Decimal numbers have ten different placeholders, the numbers 0 to 9. Hexadecimal numbers have 16 different placeholders, the numbers 0 to 9 and the letters A to F.

Remember that 10 x 10 can be written as 102. 102 means ten squared or ten raised to the second power. 10 is the base of the number and 2 is the exponent of the number. 10 x 10 x 10 can be written as 103. 103 means ten cubed or ten raised to the third power. The base is ten and the exponent is three. Use the Interactive Media Activity to calculate exponents. Enter a value for x to calculate y or a value for y to calculate x.

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 cable-testing calculations involve numbers that are very large and require exponents. Use the Interactive Media Activity to learn more about exponents.

One way to work with the very large and very small numbers is to transform the numbers based on the mathematical rule known as a logarithm. Logarithm is abbreviated as "log". Any number may be used as a base for a system of logarithms. However, base 10 has many advantages not obtainable in ordinary calculations with other bases. Base 10 is used almost exclusively for ordinary calculations. Logarithms with 10 as a base are called common logarithms. It is not possible to obtain the logarithm of a negative number.

To take the log of a number use a calculator or the Interactive Media Activity. For example, the log of (109) = 9. It is possible to take the logarithm of numbers that are not powers of ten. It is not possible to determine the logarithm of a negative number. The study of logarithms is beyond the scope of this course. However, the terminology is often used to calculate decibels and measure signal intensity on copper, optical, and wireless media.

The next page will explain how to calculate decibels.

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