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Binary

Computers use binary because they contain trillions of tiny transistors that can only be on or off. On is represented by the number 1, and off is represented by the number 0.

Binary can also be known as 'base 2'.

Converting to Decimal

Write in the column values

Add together the column values that have a 1

01001110=78

Converting from Decimal

Write in the column values

Start with the biggest value. If it can be taken away insert a 1, else, insert a 0.

Subtract the column value from the original number and repeat step 2 & 3 until the new value = 0.

78=01001110

Hexadecimal

Hexadecimal uses 16 symbols and is also known as 'base 16'.

0=0, 1=1, 2=2, 3=3, 4=4, 5=5, 6=6, 7=7, 8=8, 9=9, A=10, B=11, C=12, D=13, E=14, F=15.

0101 1100

5 C 01011100=5C

Binary Arithmetic

00110110

01101100 A LEFT shift DOUBLES a number.

00110110

00011011 A RIGHT shift HALVES a number.

Adding binary

0+0=0 00110110

0+1=1 00001001

1+1=10 00111111

Overflow = The answer is too large to fit into the register (it is 9 bits in length). Where this happens, an overflow is said to have occurred.

Storage of Characters

ASCII - The method computers use to convert text to numbers is very simple.

Certain numbers would represent certain letters and symbols.

This agreement was called the American Standard Code for Information Interchange, or ASCII.

Extended ASCII - The extended ASCII table uses 8 bits instead of 7.

The first 127 characters are the same as ASCII.

Numbers 128 – 255 are used for characters missing from the ASCII table.

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Unicode

Unicode is a 16-bit character set. This means it has room for around 65000 possible characters.

This is enough for all characters from all languages (including emojis).

The disadvantage is that it takes up A LOT of storage.

Representation of graphics and sound

Bitmap is the most common way of storing graphics on a computer.

Bitmaps split the image up into millions of tiny segments called pixels.

Each of these segments is then assigned a colour, so that when all the coloured squares are viewed together, a whole image is seen.

Indexed colour

A table of numbers to colours is used to look up which number to use for each pixel.

RGB

RGB is the most common system.

Each pixel is given an amount of Red, Green and Blue. By mixing these 3 primary colours, all other colours can be created.

Vectors

Vector graphics don’t use pixels, they use mathematical functions to describe shapes.

Vectors consist of lines, circles, squares and Bezier curves.

Sound

Sound is caused by vibrations – these vibrations cause air molecules to group together then spread apart very quickly.

You can save space by removing samples, but this means that high frequency sounds would be lost.