Units, data storage and compression (1.2.3–5) GapFill

Computers use electrical circuits to transfer and process data. Because an electrical component can only be in one of two states (on or off), data on a computer must be stored as binary values, where each digit can be either 0 or 1. A single binary digit is known as a  characterBooleanbitbyte and is the smallest amount of information that a computer can store.

As file sizes and computer storage capacities have increased significantly since the first computers, it is not practical to refer to all data in bits (a modern PC can easily have over 8,000,000,000,000 bits of storage). For this reason, there are a few units of data that are useful to know, including a byte (which is made up of 8 bits), a kilobyte (which is made up of  1,000 bits8 bytes2,000 bits1,000 bytes) and a  petabytegigabyteterabytemegabyte (which is made up of 1,000 kilobytes).

Because each bit can have one of two values, the number of values that can be stored by n bits is 2ⁿ, so 8 bits can be used to store  25664128512 different values. When a group of bits is used to represent a number, the rightmost digit is worth 1, the digit to the left of that is worth 2, the next 4, and so on (every digit is worth twice as much as the digit to the right of it). This means that if every digit is moved two places to the left, the value of the number  becomes twice as largebecomes four times largerbecomes four times smallerbecomes half as large.

Binary numbers are often converted to hexadecimal numbers  to make them easier to readto make logical operations easier for the computerto reduce the number of bits needed to store themto make mathematical operations easier for the computer as each hexadecimal digit represents four binary digits (e.g. 82 in hexadecimal is the equivalent of  01010010010100111000000110000010 in binary). Binary is not just used to represent numbers, but to represent all forms of data, including text, images and sound. To represent text, each character is stored as a binary value of a fixed number of bits, depending on the character set used (e.g. the ASCII character set uses  1 bit7 bits16 bits8 bits to represent each character). Each binary value represents a different character (so 'A' is represented in ASCII as 1000001, while 'a' is represented as 1100001). Unicode is a character set that uses  more bits than ASCII to store each character, and can represent more charactersmore bits than ASCII to store each character, and cannot represent all ASCII charactersfewer bits than ASCII to store each character, and cannot represent all ASCII charactersfewer bits than ASCII to store each character, and can represent more characters. 

Images on a computer can be displayed as a grid of pixels, where each pixel is assigned a value that specifies its colour. The more pixels an image uses, the  higher the potential image qualityhigher the bit depthless storage the image will needlarger the image will be. The bit depth on an image is the number of bits used to store each individual pixel, with a larger bit depth allowing the image to use more colours. The file size of the image can be calculated as  size (bits) = bit depth ÷ number of pixelssize (bits) = bit depth * number of pixelssize (bits) = bit depth ^ number of pixelssize (bits) = bit depth ÷ number of pixels.

Sounds are created by continuous waves, which cannot be directly represented as binary values. To store a sound on a computer, the sound wave must first be converted into discrete values. This is done by sampling the sound wave at set intervals, which produces a sequence of discrete values that approximates the wave. The size of a sound file can be calculated as  size (bits) = sample rate * duration of sound ÷ bit depthsize (bits) = bit depth * sample rate * duration of soundsize (bits) = bit depth * duration of sound ÷ sample ratesize (bits) = bit depth * sample rate ÷ duration of sound.