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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 1000 4 100 5 10 6 1 7 Data Representation • Binary representation is in the form of 2’s as opposed to denary (base – 2) 128 64 1 0 32 0 16 0 8 0 4 0 2 1 1 1 Data Representation • Binary addition similar to denary addition, when a result is greater than 9 we ‘pass one over’ • 0+0=0 • 0+1=1 • 1 + 1 = 10 (carry 1 over) • 1 + 1 + 1 = 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 • 0X0=0 • 0X1=0 • 1X1=1 • 1 X 10 = 10 Data Representation • Negative numbers are represented using two’s compliment form • Significant bit is Negative -128 64 1 0 32 0 16 0 8 0 4 0 2 1 1 1 Data Representation • Converting negative denary to binary • Basic rule is to (invert the digits and add 1) •3 • 00000011 • Convert = 11111100 • Add 1 = 11111101 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 Denary Hexadecimal 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 A 11 B 12 C 13 D 14 E 15 F 16 G Data Representation • Grouped into 4 bits • Each group represents one number • E.g. 11010011 = 211 • 1101 = 13 = D • 0011 = 3 = 3 • = D3