(return of the…) Data blast 2.1.4 Digital Representation
Go… 1 2 3
Candidates should be able to: define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte 1 bit = 1 binary digit – represents an electrical signal being on or off. 12/01/2019 Horbury Academy ICT and Business Studies
Candidates should be able to: define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte 4 bits = 1 nibble. 12/01/2019 Horbury Academy ICT and Business Studies
Candidates should be able to: define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte 8 bits = 1 byte Stands for "by eight"? 12/01/2019 Horbury Academy ICT and Business Studies
Candidates should be able to: define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte (kilo = 1000) 1024 bytes = 1 kilobyte (mega = million) 1024 kilobytes = 1 megabyte 1024 megabytes = 1 gigabyte (giga = billion) 1024 gigabytes = 1 terabyte (tera = trillion) 12/01/2019 Horbury Academy ICT and Business Studies
Candidates should be able to: understand that data needs to be converted into a binary format to be processed by a computer. Computers work by processing electrical signals. Electrical signals can be either on or off Text, images, sound and instructions all need to be converted into binary so that computers can understand the information 12/01/2019 Horbury Academy ICT and Business Studies
Candidates should be able to: convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa 1 Convert the following binary number to denary. 12/01/2019 Horbury Academy ICT and Business Studies
Candidates should be able to: convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa 128 64 32 16 8 4 2 1 Write the column headings above each number Start with “1” and double each time. 12/01/2019 Horbury Academy ICT and Business Studies
Candidates should be able to: convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa 128 64 32 16 8 4 2 1 Write down all the numbers with a “1” below them 128 + 32 + 16 + 2 12/01/2019 Horbury Academy ICT and Business Studies
Candidates should be able to: convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa Add them up… 178 12/01/2019 Horbury Academy ICT and Business Studies
Converting from denary to binary Convert the following denary number to binary. 178
Horbury Academy ICT and Business Studies Step 1 Write out the column headings… 178 128 64 32 16 8 4 2 1 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Step 2 Find the biggest number that will fit… 178 128 64 32 16 8 4 2 1 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Step 3 Write a “1” below that number… 178 128 64 32 16 8 4 2 1 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Step 4 Take away the column heading from our number 50 is now our target number 178 – 128 = 50 128 64 32 16 8 4 2 1 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Step 5 Work through the columns. 50 128 64 32 16 8 4 2 1 Is the column heading (64) Bigger than our target number (50) Yes? – write a zero 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Step 6 Work through the columns. 50 128 64 32 16 8 4 2 1 Is the column heading (32) Bigger than our target number (50) No? – write a one 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Step 7 Work out the next target… 50 – 32 = 18 128 64 32 16 8 4 2 1 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Step 7 Continue! 128 64 32 16 8 4 2 1 18 18 is bigger than 16 128 64 32 16 8 4 2 1 2 2 is not bigger than 8 128 64 32 16 8 4 2 1 2 2 is not bigger than 4 128 64 32 16 8 4 2 1 2 2 is equal to 2 128 64 32 16 8 4 2 1 Write a 0! 12/01/2019 Horbury Academy ICT and Business Studies
Adding two binary numbers 0110 1100 1111 0011 + 1 1 1 1 Just like normal, start on the right… …for the exam, the first nibble will probably not have any "carries" 12/01/2019 Horbury Academy ICT and Business Studies
Adding two binary numbers 0110 1100 1111 0011 + 0 + 1 = 1 (no carries) 1 1 1 1 1 The second nibble may have some carries 12/01/2019 Horbury Academy ICT and Business Studies
Adding two binary numbers 0110 1100 1111 0011 + 1 + 1 = 10 (so write 0, and carry 1) 1 1 1 1 1 1 The second nibble may have some carries 12/01/2019 Horbury Academy ICT and Business Studies
Adding two binary numbers 0110 1100 1111 0011 + 1 + 1 (+ carry) = 11 (so write 1, and carry 1) 1 1 1 1 1 1 1 1 The second nibble may have some carries 12/01/2019 Horbury Academy ICT and Business Studies
Adding two binary numbers 0110 1100 1111 0011 + 0 + 1 (+ carry) = 10 (so write 0, and carry 1) 1 1 1 1 1 1 1 1 1 The second nibble may have some carries 12/01/2019 Horbury Academy ICT and Business Studies
Adding two binary numbers 0110 1100 1111 0011 + 1 1 1 1 1 1 1 1 1 1 This leaves the carried 1, which goes into the 9th column 12/01/2019 Horbury Academy ICT and Business Studies
Adding two binary numbers 0110 1100 1111 0011 + 1 1 1 1 1 1 1 1 1 1 This would produce an error as we can only store 8 bits in a byte. You will usually be asked to explain this. 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Hex As well as binary, we often use Hexadecimal in computing. Hexadecimal use the numbers 0 to 9 and then the letter A to F 1 2 3 4 5 6 7 8 9 A B C D E F 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Convert denary to hex… 165 (denary) = A5 (hex) Divide by 16 165/16 = 10 remainder 5 A in hex 5 in hex 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Convert hex to denary… CD (hex) = 205 (denary) Convert to denary CD C = 12 D = 13 Multiply by 16 12 x 16 = 192 …add 13 192 + 13 = 205 12/01/2019 Horbury Academy ICT and Business Studies
How to convert binary to hex… Step 1 – write down the binary numbers 1 to 16… 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 12/01/2019 Horbury Academy ICT and Business Studies
How to convert binary to hex… Step 2 – Write the Hex numbers next to them… 0000 0001 0010 0011 1 2 3 0100 0101 0110 0111 4 5 6 7 1000 1001 1010 1011 8 9 A B 1100 1101 1110 1111 C D E F 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Convert binary to hex Split your number in two nibbles… 0110 1011 12/01/2019 Horbury Academy ICT and Business Studies
Horbury Academy ICT and Business Studies Convert binary to hex Convert each nibble into hex… 0110 1011 6 B 12/01/2019 Horbury Academy ICT and Business Studies
Why do we use Hexadecimal? Binary numbers get very long very quickly – for example 1023 is 1111111111 This means that they are difficult to remember and it is easy to make mistakes when you enter them This is why we use hex: 1111111111 = 3FF 12/01/2019 Horbury Academy ICT and Business Studies