How Computers Store Information in Binary

To a person, a computer seems able to handle an astonishing variety of things: words, photographs, music, films and much more. Yet beneath this rich surface, every one of these different kinds of information is stored in exactly the same way. A computer does not really understand letters or pictures at all. Everything it holds, from a novel to a song, is reduced to long strings of just two symbols, usually written as the digits zero and one. This method of representing information using only two possible values is called the binary system, and grasping how it works reveals the simple foundation on which all digital technology is built.

The reason computers use only two symbols is a practical one, rooted in the machines themselves. A computer is built from vast numbers of tiny electronic switches. Like an ordinary light switch, each of these can be in one of two states: on or off. It is far easier and far more reliable to build a device that can tell the difference between just two clear states than one that must distinguish between many. A switch that is on can stand for a one, and a switch that is off can stand for a zero. Because the whole machine is made of such switches, a counting system with only two digits fits the hardware perfectly. A single one of these binary digits is called a bit, a name formed by shortening the phrase binary digit.

A single bit, on its own, can express very little; it can only say yes or no, on or off. The power of the system comes from combining bits into groups. With two bits there are four possible combinations, with three bits there are eight, and each extra bit doubles the number of patterns that can be represented. This doubling grows quickly, so that a modest number of bits can stand for a very large number of different things. Computer designers long ago settled on the practice of handling bits in groups of eight, and a group of eight bits is known as a byte. One byte can be arranged in well over two hundred distinct patterns, which turns out to be enough to cover a useful range of values.

Numbers are the most natural things to store in binary, because binary is simply another way of counting. In the everyday decimal system each position in a number is worth ten times the one to its right. Binary works on the same principle, except that each position is worth twice the one to its right rather than ten times. By adding together the values of the positions that contain a one, any whole number can be built up. This is why computers can perform arithmetic so readily: at bottom, calculation is just the manipulation of these patterns of ones and zeros according to fixed rules.

Letters and other characters are handled by agreement rather than by nature. Since a computer can only store numbers, each letter, digit and punctuation mark is assigned a number of its own, and it is that number, in binary, which is actually stored. As long as every machine follows the same code, a pattern of bits saved on one computer will be read as the same letter on another. Early computers used a widely adopted code in which each character fitted into a single byte, which was ample for the letters of the English alphabet and common symbols. Later systems extended this idea to cover the scripts of the world's many languages, so that text in almost any writing system can now be stored and exchanged.

Pictures are stored by dividing an image into a grid of tiny squares called pixels. Each pixel is a single dot of colour, and its colour is recorded as a set of numbers describing how much red, green and blue it contains. Those numbers are, once again, stored in binary. An image is therefore nothing more than a long list of colour values, one group for each pixel, and the finer the grid, the more detail the picture can hold and the more bits it takes to store. Sound is treated in a similar spirit: the smoothly changing pressure of a sound wave is measured many thousands of times a second, and each measurement is written down as a binary number.

What emerges from all this is a strikingly unified picture of the digital world. Text, images and sound look utterly different to us, but inside the machine they are all just numbers, and every number is just a pattern of ones and zeros held in a crowd of tiny switches. The same handful of ideas, repeated on an enormous scale and at tremendous speed, is enough to capture and reproduce almost any kind of information a person might wish to keep. The elegance of the binary system lies precisely in how much it achieves with how little.