Representation Of Data
- 1. The Software Developers View of Hardware Representation of Data within a Computer System
- 2. Syllabus Representation of data within a computer system: Character representation: Hexadecimal ASCII Conversion between binary and decimal.
- 3. Why does this mean? Basically, software cannot run without hardware. Therefore, this chapter we will concentrate on the following: How inputs (data) are represented by the computer? – Binary & ASCII How inputs are stored? – Logic Gates The processing of data. – Calculations & Understanding Data Streams
- 4. How does a computer work? INPUT DECODE PROCESS OUTPUT 001010010100101001101010101010101001010000101010111111100101
- 5. Representation of Data Binary is the BASE 2 number system which is represented as electronic voltage (on/off) or importantly as (0 or 1). Decimal Input Binary Control Binary Processing Decimal Output Hexadecimal Storage
- 6. Representation of Data The processor of computer system is required to convert between binary and decimal which are inputted and outputted from the system. Computers and programs are required to have a comprehensive knowledge regarding these conversions.
- 7. Understanding Binary Numbers Imagine you need to illuminate a room with a variable amount of light. You need to be able to set the lighting level from total darkness (0 watts of light) right up to a maximum of 255 watts of light. You have 2 options...
- 8. One 255 watt bulb and a dimmer With the dimmer set at 0, there is no light, and set at full you would have 255 watts. Varying the position of the dimmer would give varying light output.
- 9. But there is a problem... How do you set an EXACT light level? The dimmer is difficult to accurately set the light level.
- 10. Too much guesswork! So to set the light level at say, 37 watts, you would have to turn the dimmer till it is putting out about 37 watts. Trouble is, no matter how accurate you try to be, it will always be an close estimation, not an exact amount!
- 11. So what about this? Imagine a set of 8 lightbulbs of varying outputs, from 1 watt right up to 128 watts, with each bulb twice as strong as the one next to it...
- 12. So what about this? To set exactly 37 watts of light, you could turn on the 32 watt bulb
- 13. So what about this? … then add in the 4 watt bulb… (so now you have 36 watts)
- 14. So what about this? … and finally the 1 watt bulb. You now have EXACTLY 37 watts of light!
- 15. So what about this? If you read the bulbs from left to right, they go off, off, on, off, off, on, off, on, or in computer terms...
- 16. In other words... 00100101 = 37
- 17. Converting Binary To Decimal Binary is referred to as BASE-2 arithmetic. This is because it uses two states, on or off (0 and 1). The bits 0 and 1 are representative of the on/off circuits within a computer system. Computers work in binary, but humans use decimal numbers.
- 18. Converting Binary To Decimal To convert the following binary number: 11010011 2 It is best to draw up the following table. 1 2 4 8 16 32 64 128
- 19. Converting Binary To Decimal To convert the following binary number: 11010011 2 It is best to draw up the following table. Then insert the binary number below. 1 1 0 0 1 0 1 1 1 2 4 8 16 32 64 128
- 20. Converting Binary To Decimal Every time there is a 1 in the column the corresponding number is added to a total. 128 + 64 + 16 + 2 + 1 = 211 10 1 1 0 0 1 0 1 1 1 2 4 8 16 32 64 128
- 21. Converting Decimal To Binary To convert the following decimal number: 110 10 It is best to draw up the following table again. 1 2 4 8 16 32 64 128
- 22. Converting Decimal To Binary But this time find the largest number that will go into 110 10 In this case 128 doesn’t go into 110 but 64 does go into 110. So we place a 0 under 128 and a 1 under 64. 1 2 4 8 16 32 64 128
- 23. Converting Decimal To Binary But this time find the largest number that will go into 110 10 In this case 128 10 doesn’t go into 110 10 but 64 10 does go into 110 10 . So we place a 0 under 128 and a 1 under 64. 1 0 1 2 4 8 16 32 64 128
- 24. Converting Decimal To Binary The next step is to subtract 64 10 from 110 10 110 10 – 64 10 = 46 10 Our new number is 46 10 so we must find out what number goes into 46 10 1 0 1 2 4 8 16 32 64 128
- 25. Converting Decimal To Binary 32 10 goes into 46 10 So we place a 1 under the 32 column. And 46 10 – 32 10 = 14 10 1 0 1 2 4 8 16 32 64 128
- 26. Converting Decimal To Binary 32 10 goes into 46 10 So we place a 1 under the 32 column. And 46 10 – 32 10 = 14 10 1 1 0 1 2 4 8 16 32 64 128
- 27. Converting Decimal To Binary The process continues: 16 10 doesn’t go into 14 10 However, 8 10 goes into 14 10 14 10 – 8 10 = 6 10 1 1 0 1 2 4 8 16 32 64 128
- 28. Converting Decimal To Binary The process continues: 16 10 doesn’t go into 14 10 However, 8 10 goes into 14 10 14 10 – 8 10 = 6 10 1 0 1 1 0 1 2 4 8 16 32 64 128
- 29. Converting Decimal To Binary 4 10 goes into 6 10 6 10 – 4 10 = 2 10 And 2 10 goes into 2 10 Which leaves no remainder. 1 0 1 1 0 1 2 4 8 16 32 64 128
- 30. Converting Decimal To Binary 4 10 goes into 6 10 6 10 – 4 10 = 2 10 And 2 10 goes into 2 10 Which leaves no remainder. 0 1 1 1 0 1 1 0 1 2 4 8 16 32 64 128
- 31. ACTIVITY 1 Convert the following binary numbers to decimal. (Show working) 1001 2 10110110 2 Convert the following decimal numbers to binary. (Show working) 68 10 288 10
- 32. ACTIVITY 2 Identify why hexadecimal is used as a numbering system. Convert the following hexadecimal numbers to binary. (Show working) A45 16 28F 16 1001011101 2
- 33. Character Representation It is very important for the development of a key for the translation between the English (Human) and the Binary (Computer) so interaction could be initiated. So there were THREE different methods developed with most commonly used being ASCII.
- 34. Character Representation 1. BCD (Binary Coded Decimal Represents decimal values as a 4-bit binary format called nibbles. Very good for numbers, but not for other characters. i.e. only 16 characters can be represented.
- 35. Character Representation 2. EBCDIC Stands for: Extended Binary Coded Decimal Interchange. Represents an 8-bit code which gives 256 possible characters. Used primarily for IBM mainframe computers.
- 36. Character Representation 3. ASCII Stands for: American Standard Code for Information Interchange. In 1963 it first was used as a 7-bit code that would represent 128 characters. However has been changed to an 8-bit system known as Extended ASCII.