1. Behind the scenes in your computer
Bits and Bytes
Behind the scenes in your computer

2. All computer storage is organized into bytes
Think of each byte as a little storage bin
Each byte is made up of 8 bits
Each bit is an electronic circuit that is either on or off (off = 0, on = 1)
A specific sequence of 0’s and 1’s in a byte is called a bit pattern

3. So, how many bytes are in your computer?
Common Prefixes
Kilo
103
1,000
Thousand
Mega
106
1,000,000
Million
Giga
109
1,000,000,000
Billion
Tera
1012
1,000,000,000,000
Trillion
Typical Capacities:
RAM: 1, 2, 4, 6 or 8 GB
Diskette: MB
Flash drive: 2, 4, 8, 16, 32, 64, 128 GB
CD: 800 MB
DVD: 4.7 GB
Hard Drive: 500 GB – 2 TB

4. Converting Between Units
To Convert …
From To
Action KB
Bytes
Multiply by 1,000 (move decimal point 3 places right) MB
Multiply by 1,000,000 (move decimal point 6 places right) GB
Multiply by 1,000,000,000 (move decimal point 9 places right)
Divide by 1,000 (move decimal point 3 places left)
Divide by 1,000,000 (move decimal point 6 places left)
Divide by 1,000,000,000 (move decimal point 9 places left)
Example 1: KB = ? MB
5200 × 1000 = 5,200,000 bytes
5,200,000 /1,000,000 = 5.2 MB
Example 2: 7.5 GB = ? KB
7.5 × 1,000,000,000 = 7,500,000,000 bytes
7,500,000,000 / 1000 = 7,500,000 KB

5. You Try:
3.2 MB = ? Bytes 6.4 GB = ? MB 57,000 Bytes = ? KB 25,000 KB = ? MB

6. What kinds of information do you store on your computer?
numerical values (binary number system)
text/character data (ASCII or Unicode)
program instructions (machine language)
images (jpg, gif, tiff, bmp, wmf, etc.)
video (mp4, mov, avi, wmv, etc.)
music (mp3, wav, wma, au, etc.)

7. “Kathy Ames” is text It would be stored like this using ASCII codes
It would be stored like this using ASCII codes

8. Numerical values needed for arithmetic are stored using a different scheme
The numerical value 40 would be stored like this using the binary number system.
(note that “bit” stands for “binary digit”)

9. How do binary numbers work?
Decimal Number System
Binary Number System
Base 10
Base 2
10 digits (0,1,2,3,4,5,6,7,8,9)
2 digits (0,1)
Positional values based on powers of 10
Positional values based on powers of 2
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
8-bit binary number

10. Converting from Binary to Decimal
What is the decimal value of the bit pattern ?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Simple! Just add up the positional values where the 1’s appear:
= 106
So, we say that = 106 decimal

11. Converting from Decimal to Binary
How can we represent the decimal value 151 in binary?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Simple! Just think about money and consider positional values
as bills and 151 “dollars” as the amount we must make.
Then “count change” from largest “denomination” to smallest until total value of change is accumulated.

12. Converting from Decimal to Binary
How can we represent the decimal value 151 in binary?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Running Total: 128

13. Converting from Decimal to Binary
How can we represent the decimal value 151 in binary?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Running Total: 128

14. Converting from Decimal to Binary
How can we represent the decimal value 151 in binary?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Running Total: 128

15. Converting from Decimal to Binary
How can we represent the decimal value 151 in binary?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Running Total: = 144

16. Converting from Decimal to Binary
How can we represent the decimal value 151 in binary?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Running Total: = 144

17. Converting from Decimal to Binary
How can we represent the decimal value 151 in binary?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Running Total: = 148

18. Converting from Decimal to Binary
How can we represent the decimal value 151 in binary?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Running Total: = 150

19. Converting from Decimal to Binary
How can we represent the decimal value 151 in binary?
Positional Values
128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20
Binary Number
Running Total: = 151
So, 151 decimal =

20. So What is Hexadecimal? (often called “hex”)
A base 16 number system
16 possible digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
Positional values are powers of 16
Mainly used is as “short hand” for binary
1 hex digit = 4 binary digits

21. Hex Digits Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 00011 2 3 4 5 6 7
Hex Digit
4-bit binary
0000
0001
0010
0011
0100
0101
0110
0111
Dec Value 8 9 10 11 12 13 14 15
Hex Digit A B C D E F
4-bit binary
1000
1001
1010
1011
1100
1101
1110
1111

22. Converting from Hex to Decimal
What is the decimal value of hex 3B?
Positional Values 16 1
161
160
Hex Number 3 B
Simple! 3 × 16 + B × 1 = 3 × × 1 = = 59
So, we say that 3B hex = 59 decimal

23. Converting from Hex to Decimal
What is the decimal value of hex E4?
Positional Values 16 1
161
160
Hex Number E 4
Simple! E × × 1 = 14 × × 1 = = 228
So, we say that E4 hex = 228 decimal

24. Let’s take another look at Hex 3B
Dec Value 1 2 3 4 5 6 7
Hex Digit
4-bit binary
0000
0001
0010
0011
0100
0101
0110
0111
Dec Value 8 9 10 11 12 13 14 15
Hex Digit A B C D E F
4-bit binary
1000
1001
1010
1011
1100
1101
1110
1111
So Hex 3B = Binary
First Digit
Second Digit 3 B
0011
1011
(And note that Binary
= = 59 Decimal)

25. Let’s take another look at Hex E4
Dec Value 1 2 3 4 5 6 7
Hex Digit
4-bit binary
0000
0001
0010
0011
0100
0101
0110
0111
Dec Value 8 9 10 11 12 13 14 15
Hex Digit A B C D E F
4-bit binary
1000
1001
1010
1011
1100
1101
1110
1111
So Hex E4 = Binary
First Digit
Second Digit E 4
1110
0100
(And note that Binary
= = 228 Decimal)

26. What about converting Binary 10100010 to Hex?
Dec Value 1 2 3 4 5 6 7
Hex Digit
4-bit binary
0000
0001
0010
0011
0100
0101
0110
0111
Dec Value 8 9 10 11 12 13 14 15
Hex Digit A B C D E F
4-bit binary
1000
1001
1010
1011
1100
1101
1110
1111
First Digit
Second Digit
1010
0010

27. What about converting Binary 10100010 to Hex?
Dec Value 1 2 3 4 5 6 7
Hex Digit
4-bit binary
0000
0001
0010
0011
0100
0101
0110
0111
Dec Value 8 9 10 11 12 13 14 15
Hex Digit A B C D E F
4-bit binary
1000
1001
1010
1011
1100
1101
1110
1111
First Digit
Second Digit
1010
0010 A 2
So Binary = A2 Hex

28. Verify that Binary 10100010 and Hex A2 have the same Decimal values
Binary = = 162 Hex A2 = A × × 1 = 10 × × 1 = = 162

29. You try:
Convert 210 Decimal to: Binary: Hex: Convert 2D Hex to: Decimal: Convert Binary to: