1. Bits & Bytes How Computers Represent Data

2. Data Representation How do computers represent data?
Computers are digital and use electricity:
Recognize only two discrete states: on or off
Use binary system with two unique digits: 0(off) and 1(on), called bits (binary digits)

3. Data Representation What is a byte? 8 bits grouped together as a unit
Provides 256 different combinations of 0s and 1s
Allows representation of 256 individual characters
Numbers, uppercase/lowercase letters and punctuation marks

4. Data Representation Decimal – base 10 Binary – base 2
Each position can have 10 values:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Binary – base 2
Each position can have 2 values:
0, 1
Hexadecimal – base 16
Each position can have 16 values:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Decimal
Hex
Binary
000 00
001 01  
002 02  
003 03  
004 04  
005 05  
006 06  
007 07  
008 08  
009 09  
010 0A  
011 0B  
012 0C  
013 0D  
014 0E  
015 0F  
016 10  
017 11  
018 12  
019 13  
020 14  
10^3 10^2 10^1 10^0

5. Data Representation 16^0 1 01 16^1 16 10 16^2 256 FF 00 = 0 01 02 … 0E
Decimal / Place Value
2^0 1
2^26
67,108,864
2^1 2
2^27
134,217,728
2^2 4
2^28
268,435,456
2^3 8
2^29
536,870,912
2^4 16
2^30
1,073,741,824
2^5 32
2^31
2,147,483,648
2^6 64
2^32
4,294,967,296
2^7
128
2^33
8,589,934,592
2^8
256
2^34
17,179,869,184
2^9
512
2^35
34,359,738,368
2^10
1,024
2^36
68,719,476,736
2^11
2,048
2^37
137,438,953,472
2^12
4,096
2^38
274,877,906,944
2^13
8,192
2^39
549,755,813,888
2^14
16,384
2^40
1,099,511,627,776
2^15
32,768
2^41
2,199,023,255,552
2^16
65,536
2^42
4,398,046,511,104
2^17
131,072
2^43
8,796,093,022,208
2^18
262,144
2^44
17,592,186,044,416
2^19
524,288
2^45
35,184,372,088,832
2^20
1,048,576
2^46
70,368,744,177,664
2^21
2,097,152
2^47
140,737,488,355,328
2^22
4,194,304
2^48
281,474,976,710,656
2^23
8,388,608
2^49
562,949,953,421,312
2^24
16,777,216
2^50
1,125,899,906,842,620
2^25
33,554,432
2^51
2,251,799,813,685,250
16^
16^
16^ FF
00 = 0 01 02 … 0E 0F 10 11
FF = 255

6. Kilo, Mega, Giga, Tera …
Storage of data (bits & bytes) is often categorized as:
Kilo (KB)
Roughly 1,000; actually 210 (1,024)
Mega (MB)
Roughly 1,000,000; actually 220 (1,048,576)
Giga (GB)
Roughly 1,000,000,000; actually 230 (1,073,741,824)
Tera (TB)
Roughly 1,000,000,000,000; actually 240 (1,099,511,627,776)
Peta (PB)
Roughly 1,000,000,000,000,000; actually 250 (1,125,899,900,000,000)
Exa, Zetta, Yotta…

7. Text Representation
What are the popular coding systems to represent text?
ASCII (8 bit) - American Standard Code for Information Interchange - most common today (typically only uses 7 bits)
EBCDIC (8 bit) - Extended Binary Coded Decimal Interchange Code – IBM mainframes
Unicode (16 bit) – newer coding scheme capable of representing all world’s languages

8. Text Representation - ASCII
Decimal | Hexadecimal | Character | Binary

9. Text Representation – ASCII Extended
Decimal | Hexadecimal | Character | Binary

10. Text Representation – Unicode
Unicode includes same codes as ASCII with either a prefixed or suffixed null character as well as many others

11. Representing Images Pixels - picture element
Grid of small points (dots) that make up an image
More pixels results in clearer /more precise image
Two Methods
Bit-mapped graphics
Use bytes – each pixel represented by an array of bits
Vector graphics
Image comprised of points, lines, curves, and shapes
Use mathematical formulas to define and represent image