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The principle of Semiconductor Great Wisdom Crystallized in Tiny Devices

What Are Binary Numbers?


What is a Binary Number

A binary number is any number expressed using 0s and 1s. Computers, in particular, perform operations using just these two numerical values.

Advantages of digital processing

Analog processing is a method of processing numbers and data as a continuous stream of values. Vinyl records, clocks with moving hands, and mercury thermometers are the examples that readily come to mind. In digital processing, in contrast, numbers and data are processed as discrete (or non-continuous) values. Surprisingly enough, the abacus—a mechanical calculator that has been used by the Japanese for centuries—is a kind of digital processing device.
Digital processing is highly resistant to the signal decay and noise, and digital data do not deteriorate easily. For this reason, even inherently analog signals such as sounds and visual images are mostly recorded digitally today. And there is another reason that works strongly in favor of digital processing: it's that all computers we use perform logical operations digitally, based on just two numerical values—0 and 1.

Logical operations based on 1 and 0

In computer science, calculations are referred to as operations. Computers can perform several types of operations, including mathematical operations (addition, subtraction, multiplication, and division) and logical operations. The latter is the kind of operations that are uniquely suited to computers.
There are three basic logical operators (AND, OR, NOT), and even the most complex logic can be stated by a combination of these operators. Popular magazines often carry aptitude tests of all kinds to entertain the readers: by answering yes or no to a series of questions, readers can find their aptitude for a given subject. This process is not unlike a logical operation. Questions in aptitude tests are similar to statements that are either true or false, which are called propositions in logic. Computers evaluate if each proposition is true or false, and return the value 1 if true and 0 if false, moving on to subsequent propositions until the final evaluation is reached.

The necessity and potential of the binary system

Why do computers use the binary system? The main reason is that computers perform logical operations using the rules of algebra, similar to those used in mathematical operations such as addition, subtraction, multiplication, and division. The rules of symbolic logic, also known as Boolean algebra, provide formulas for mathematically expressing logical operations that are descendants of Aristotelian methods. Because the values of the variables used in Boolean algebra are usually 1 and 0, it was natural that a binary numeral system was adopted in computers.
Computers are much more than simple calculators, because they can perform logical as well as mathematical operations. This capability has led their evolution into "thinking machines." Equipped with microcomputer chips, many cars today automatically apply brakes to avoid imminent danger, and advanced microwave ovens optimally adjust cooking time and temperature. These feats are enabled because computers perform huge amounts of logical operations at lightening speeds.