Data Representation

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Binary Basics

Advantages of Binary:

less rules of arithmatic - less operations to be programmed

0s and 1s are easier to represent digitally

if the voltage changes, it won't affect the data - it's either on or off

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Negative Numbers

Two's Complement:

You need to convert the number into it's positive version

Then invert it, so all the 0s are 1a and all the 1s are 0s

Add one starting at the right

EXAMPLE:

The largest negative number that can be represented is -128

In Two's Compliment, the MSB (the one on the far left) is a sign bit. If it's a 1, then the number will be negative, if it's a 0, it'll be positive

Another way to convert negatives is to:

first convert the positive version into binary

then invert everything after the first 1, going from right to left

Min & Max Limits:

Calculate the 2 to the power of the total number of bits

The negative value is half of that number

Then you take away 1 to get the positive value

EXAMPLE: The range of positive and negative numbers that can be stored with 16 bits

2^16 = 65536

65536 / 2 = 32768 (This is the negative value)

32768 - 1 = 32767 (This is the positive value)

The range of numbers that can be stored is -32768 to 32767

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ASCII & Unicode

ASCII

in extended ASCII, you use 8 bits to store each character

a character set is the name given to the whole set of characters a keyboard can produce

control characters are the ones that aren't printed on screen (non-printable characters like ctrl and delete)

each character has a number that is converted and stored as binary

Extended ASCII can store more characters than standard ASCII, like the copyright symbol.

Unicode

AKA Universal Character Set

it can store far more languages and characters

it uses 16 bits, so it uses more memory

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Bitmap & Vector Graphics

Bitmaps:

each pixel stores the colour of said pixel

the more bits used to store each pixel, the more colours can be represented

this uses up more memory to store

Vectors;

store picture by each objects attributes

doesn't store the picture, rather, how to draw it

Comparison:

Vectors don't lose quality when scaled but can't be edited at pixel level like bitmaps

Vectors use less storage, but can't show photo realistic scenes

Vectors are easily manipulated

you need special software to open vectors