Lesson Objectives Aims You should be able to: Explain why data is represented in binary form Define some basic binary storage terms Understand that data needs to be converted to binary to be processed by a computer

Quick recap Computers are binary devices This means they are DIGITAL The real world is ANALOGUE This means computers can’t understand our world (data) without conversion

Digital V Analogue Digital information is binary, that means it can be either off or on 1 or 0 Like a light switch.

Analogue Analogue or real world data is, generally, constantly changing Analogue values do not tend to jump from one to the other, there is a small, incremental movement

Therefore Computers CANNOT understand analogue information There is always a need for conversion Most input and output devices do ADC or DAC This enables to computer to process data in a form it understands – binary.

Useful On its own, Binary doesn’t seem that useful But we can combine strings of binary digits and interpret them as sound, images, text etc We will investigate this in coming lessons

Learn to count You should know this, but lets do it anyway. How do you count to 10? What happens we get to 9? This point is pivotal…

It’s all about the BASE. Geddit? See what I did there? Our number system Our number system is called Denary It is BASE 10 Which means… we have 10 digits 0..9 It’s all about the BASE. Geddit? See what I did there?

Lets go through on the board: Denary Lets go through on the board: How we count What happens when we run out of digits How we arrive at a value for each column What a number really is

Denary Notes Number system rules Any number system has a set of digits (in denary this is 0..9, 10 in total) The number of available digits is the BASE of the number system When all digits have been used and a higher number is required, simply reset the current column to 0 and start again at 1 in the next column The first (units) column in any number system has a value of 1x the digit Subsequent columns have a value of the base x previous column A number is actually the sum of each digit, multiplied by it’s column value = (4x1000) + (3x100) + (2x10) + (4x1) = 4324 Thousands (x1000) Hundreds (x100) Tens (x10) Units (x1) 4 3 2

Binary The binary number system works in the same way The ONLY difference is we only have 2 digits – 0 and 1

Lets go through on the board: Binary Lets go through on the board: How we count What happens when we run out of digits How we arrive at a value for each column How to work out the value of a binary number

Copy the example… 128 64 32 16 8 4 2 1 Binary numbers are simple to work out – they use the same rules as denary! 1 means ON so add up its value 0 means OFF so ignore it So this number is: (128x1) + (64x0) + (32x0) + (16x0) + (8x1) + (4x0) + (2x1) + (1x1) Anything x0 = 0 and anything x1 is itself so… 128+8+2+1 = 139

Binary Quantities The smallest piece of information a computer can understand is a 1 or a 0 This single digit is called a BIT. Obviously, this isn’t too useful on its own. If we group 4 BITS together, we have 16 possible combinations – a NYBBLE

Copy this in to your notes Binary Quantities 1 or 0 = Bit 4 bits = Nybble 8 bits = Byte (most common grouping) 1024 bytes = 1 Kilobyte (Kb) (2^10) 1024Kb = 1 Megabyte (Mb) (2^20) 1024Mb = 1 Gigabyte (Gb) (2^30) 1024Gb = 1 Terabyte (Tb) (2^40) 1024Tb = 1 Petabyte (Pb) (2^50) All are powers of 2

June 2015, Q8 (b)