1. A-Level Computing Data representation

2. 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

3. 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

4. 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.

5. Data Representation 4567 Denary Notation – grouped into values of 10s 1000100101 4567

6. Data Representation Binary representation is in the form of 2’s as opposed to denary (base – 2) 1286432168421 10000011

7. 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)

8. 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

9. Data Representation Negative numbers are represented using two’s compliment form Significant bit is Negative -1286432168421 10000011

10. Data Representation Converting negative denary to binary Basic rule is to (invert the digits and add 1) 3 00000011 Convert = 11111100 Add 1 = 11111101

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

12. Data Representation DenaryHexadecimal 11 22 33 44 55 66 77 88 99 10A 11B 12C 13D 14E 15F 16G

13. Data Representation Grouped into 4 bits Each group represents one number E.g. 11010011 = 211 1101 = 13 = D 0011 = 3 = 3 = D3