1. IT Systems What Number? EN230-1 Justin Champion C208 – 3273 www.staffs.ac.uk/personel/engineering_and_technology/jjc1

2. IT Systems Contents What different number systems are there Why do we have them Conversion between

3. IT Systems We usually use the decimal system to represent numbers 0,1,2,3,4,5,6,7,8,9 Commonly referred to as Base 10 Machines as seen previously work on the basis of on or off These numbers are represented by 1 or 0 Commonly known as Binary or Base 2 This binary can be used to represent any of the decimal numbers

4. IT Systems Each bit in a binary number has a decimal value Below is a table for a 8-bit binary number Dec 1286432168421 Bin 11111111 2727 2626 2525 2424 23232 2121 2020

5. IT Systems There can be any number of bits/switches Each of those bits would be a switch 0 = off 1 = on 2020 21212 2323 1 248

6. IT Systems Each of the bits with are on (1) are added together This example is Value = 8 + 1 Value = 9 2020 21212 2323 1 248

7. IT Systems Another example What is this Value Value = 128 + 64 + 16 + 8 +1 Value = 217 2020 21212 2323 1 248 2424 16 2525 32 2626 64 2727 128

8. IT Systems Significant Bits Most significant bit This indicates if there was a change in the binary which part of the number would have the most effect. Least significant bit This indicates if there was a change in the binary which part of the number would have the least effect. Usually The most significant bit is the one furthest to the left Least significant bit is the one furthest to the right Changes This is however not the always the case and knowledge of the hardware and software being used is required Using encryption is an example where this may change 000000000101010 Most significant bit Least significant bit

9. IT Systems Significant Bits Conitnued Another term which is used for this is Big Endian The part of the sequence which has the most effect Little Endian The part of the sequence which has the least effect 000000000101010 Big Endian Little Endian

10. IT Systems Another example What is this value? Value = 1099511627775 1111111111111111111111111111111111111111 Take your time working it out !!!!!

11. IT Systems Why did it take so long to work out ??? There was too many digits you for you to work out The computer would have no problems at all with this Different number systems We use different number systems to keep it easier to understand for us Hexadecimal This number system is based upon base 16 Pub quiz question The term hexidecimal comes from the words Greek work Hexa meaning 6 Latin word Decimal meaning 10

12. IT Systems Hexadecimal lookup table 0 - 16 HexDecHexDec 0088 1199 22A10 33B11 44C12 55D13 66E14 77F15

13. IT Systems Hexadecimal Examples Decimal 16 = Hex F Decimal 11 = Hex B Decimal 27 = Hex 1B Decimal 64 = Hex 40

14. IT Systems Converting between types quickly Use a calculator ! Ruling that out Binary to Hexadecimal Break each part into 4 bits If you do not have multiples of 4 then add zeros at the beginning Calculate each part using the lookup table Put the Hex characters together You have the answer

15. IT Systems Worked Example Try this yourself with 11000011 00100110 in Hex Binary 0010 0110 Hex 2 6 Answer = 26 Hex

16. IT Systems Usually a symbol is used to indicate what number types is used Not a problems with binary, but with the others maybe a problem Hex is usually done by 34f2h A h at the end of the number A $ is used in the programming to indicate hex

17. IT Systems Conversion between Hex and Decimal 2F.4A to Decimal (2 * 16 1 ) + (15 * 16 0 ) + (4 * 16 -1 ) + (10 * 16 -2 ) = 47.74

18. IT Systems Character representation We have covered numbers One of the main uses of computers is the movement of text A standard format is used for text characters called ASCII ASCII = American Standard Code for Information Interchange This allows for the transfer of characters between computers and both understanding what was sent. Issues are common between sending characters between different operating systems, Panther (Apple), Unix and Windows

19. IT Systems ASCII Represented by a 7 bit binary value

20. IT Systems UNICODE Although ASCII is a worldwide standard UNICODE is a new standard Uses 8bits to represent the characters Supports a larger number of character sets Currently supports 34,168 characters Still being expanded Used in the new (Win2000 and above) windows operating systems. May become popular in the future if other OS’s accept the standard. Not that widely used at the moment

21. IT Systems Summary of what we have discussed Decimal Binary Hexadecimal Conversion ASCII