Data with distinct values is called discrete data. Data with continuous values is called analog data. Discrete data stored in binary form is digital. Just think of "digital" as "numeric" and then "digital data" becomes "data stored as numbers." Digital data is stored as binary patterns, but from our level of abstraction, think of those patterns as numbers. With a set of distinct values, a binary encoding can be easily assigned to each one. With analog data, though, the data first has to be turned into discrete data.
This process is easiest to understand when there's only one value. Consider an ordinary mercury thermometer. To read the temperature, you compare the end of the line of mercury to a scale printed on the outside of the glass. This reading is an analog measurement. The mercury line can be any length and often doesn't line up with a mark on the temperature scale.
Consider a thermometer with a numeric display like a calculator. To display the temperature as a number, the thermometer has to convert the temperature from some kind of analog measurement to a discrete one. The process of converting an analog measurement to a number is called quantization.
This process loses some of the original data. Suppose you have a thermometer with a digital display hanging on your wall. It shows 72 degrees, but a minute later it changes to 73 degrees. You would not think that the temperature of the room changed one degree in an instant. Instead, the temperature was slowly rising, and at a point when it became closer to 73 than 72, the display changed. Analog data has a continuous range of values.
When they are replaced by a finite set of values, some rounding off must occur. The difference between analog data and its discrete representation is quantization error. Thus, if the temperature is actually 72.423 and the display reads 72, the 0.423 is the quantization error. This quantization error can be reduced by having more possible digital values. If the temperature could be displayed as 72.4, for example, then the quantization error would only be 0.023.
When a signal varies continuously over time, more sacrifices must be made to produce a digital version. Consider music that is changed into "digital audio." When music plays through a speaker, the speaker's cone moves in and out as the flow of current in the wire from the stereo goes up and down. A plotted line showing how strong the current is over time would be a continuous, if jagged, line.
The music example is a more complicated situation than the one dealing with temperature. The current has not only a continuous range of values (like the temperature), but also a changing value. To convert this kind of signal into discrete form requires a process called sampling. In statistics, sampling is used when an entire population cannot be queried. For instance, when 10,000 voters are asked who they will vote for in the presidential election, these 10,000 people represent, stand in, for the whole country.
In computer science, sampling means taking analog measurements at intervals and then quantizing each measurement. With the music example, rather than trying to capture the entire original signal, the audio is sampled many times per second, and whatever signal strength is recorded at that point is turned into a number.
Just as with quantization, the original signal is reproduced better when more samples are allotted per second. Whenever you see digital audio mentioned, it has two numbers that indicate its quality. One is the sample rate, which is the number of samples taken per second. The other is the number of bits per sample, which indicates how large a range is given to each quantized value. As these values increase, the reproduction becomes more accurate, but the resulting digital data also takes up more space.
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02122011
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