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1.5 | Math for a Digital Age |
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1.5.2 | Analog and digital systems |
As time goes on, the world is becoming
more and more digital. The world used to depend entirely on analog
processes, machinery, and communications for its functions.
The
variables that characterize an analog system may have an infinite
number of values. For example, the hands on an analog clock face may
show an infinite number of times of the day. In digital systems, the
variables that characterize them only occupy a fixed number of
discrete values. In binary arithmetic, as used on modern computers,
only two values are allowed. They are 0 and 1. Computers and cable modems are
examples of digital devices.
Digital devices are gradually
replacing analog devices. Thirty years ago, digital watches, home
computers, cable modems, electronic games, electronic car parts, and
flat-screen monitors did not exist.
Can a world without computers even be imagined? Twenty years ago it was rare for someone to have a home computer. Now computers are embedded in toys, watches, Personal Digital Assistants (PDAs), pets (for identification), and "smart" cards (credit cards with embedded microchips). In twenty years, it may be commonplace for doctors to treat medical conditions using digital devices embedded in the skin, swallowed by the patient, or injected into the bloodstream. Traditional telephones transmit voice over copper wire using analog signals. When using a microphone connected to a computer and the accompanying software to talk "long distance" to someone for free, the analog phone system between the user and the Telco (Phone Company) is being circumvented with a digital transmission over a data network connecting the user to the Internet Service Provider (ISP). In other words, the user effectively bypasses the toll system (long distance charges), as the ISP links on both ends are local. This is an example of how digital systems are changing lives. The changes that happen from year to year do not seem to be very dramatic. However, if someone were to live in isolation for five years and then return to the modern world, they would be shocked at the drastic changes that had taken place due to digital technology. Digital devices make it easier to do everyday tasks, but they also make it harder for individuals to appreciate the effort that people used to endure to complete those same tasks. The only constant is change, and the digital age will continue to progress independently of how people feel about its impact on their lives. The more digital the world becomes, the more important it is to understand the basic function of digital systems. How do computers work at the most fundamental level? What is going on at the core of a computer that makes it perform a certain way? The answer is that it all comes down to zeros and ones. This chapter will explore how a computer thinks. The math of the digital age, arithmetic with "binary" and "hexadecimal" numbers, will be explored. It is important to have this foundation in math in order to continue in IT.
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