A-Level ComputingData 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 100 10 14 5 6 7

Data Representation•Binary representation is in the form of 2’s

as opposed to denary (base – 2)

128

64 32 16 8 4 2 1

1 0 0 0 0 0 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

•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

-128

64 32 16 8 4 2 1

1 0 0 0 0 0 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 RepresentationDenary 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