Binary Arithmetic / Representing Characters & Images GapFill

In addition to representing data in binary, it is also important to be able to perform  binary arithmeticmathematicscalculationsbinary codes, including addition, multiplication and division. Addition is very straightforward and uses the carry forward method used in denary arithmetic:

Denary: Adding 84 and 163

When the column 6 + 8 = 14 , the 1 is ‘carried’ to the next column

Binary: Adding 100101 and 10001100

In exactly the same way, if a column is greater than 1, the extra 1 is ‘carried’ to the next column

Multiplication
Example: 24 is 0001 1000 in binary, moving the number to the left equals 48, moving again equals 96 i.e. 48 x 2

Division
Example: using the same number 0001 1000, moving this to the right divides the number by 2 equals 12, moving again equals 6

When data is entered into a computer via the keyboard, it does not transmit that the B key or the 8 key has been pressed; the keyboard sends a  binarydenaryhexadecimalcomputer signal which has to be translated using the character set used by the keyboard. For example, character sets for French and English use 26 characters and 10 digits but many languages use more than this, e.g. Japanese. 

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  ASCIIelectronicsystemdigital character set uses  16 bits7 bits8 bits1 bit 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). The  ManycodeAllcodeAutocodeUnicode character set uses  more 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 charactersmore bits than ASCII to store each character, and can represent more charactersfewer bits than ASCII to store each character, and can represent more characters.

Since all data and instructions on a computer are stored and processed using binary, this includes text, images and sound. 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  lower the image qualityhigher the image qualityhigher the bit depthlower the bit depth. 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) = number of pixels ÷ bit depth size (bits) = bit depth * number of pixelssize (bits) = bit depth ÷ number of pixels.