A-Level Computing Data representation

Objectives Know how data can be represented in a computer system Understand the need for various forms of representation Be able to explain and convert from one form to another

Data Representation Data on a computer system is stored in electrical signals These represent binary data Can be one of two states Here they are represented as a 0 or 1 Cannot be anything else

Data Representation A 0 or 1 is known as a BIT BITS are grouped into…….BYTES (8 BITS) A group of BYTES is a WORD The size of a word depends on the computer, a 64 bit machine has a word size of 8 bits.

Data Representation 4567 Denary Notation – grouped into values of 10s

Data Representation Binary representation is in the form of 2’s as opposed to denary (base – 2)

Data Representation Binary addition similar to denary addition, when a result is greater than 9 we ‘pass one over’ = = = 10 (carry 1 over) = 11 (carry 1 over)

Data Representation Binary multiplication works in the same way as denary (7 x 10 = 70) Move decimal point along by number of 0s 0 X 0 = 0 0 X 1 = 0 1 X 1 = 1 1 X 10 = 10

Data Representation Negative numbers are represented using two’s compliment form Significant bit is Negative

Data Representation Converting negative denary to binary Basic rule is to (invert the digits and add 1) Convert = Add 1 =

Hexadecimal Binary can be complex for humans to understand Hexadecimal is a ‘halfway house’ Used as a shorthand form of binary In base 16

Data Representation DenaryHexadecimal A 11B 12C 13D 14E 15F 16G

Data Representation Grouped into 4 bits Each group represents one number E.g = = 13 = D 0011 = 3 = 3 = D3