Bytes and Hex Computer memory

Bytes and Hex
CS 1428 Fall 2011 Jill Seaman Lecture 16
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Computer memory
 Memory is a sequence of bits:
 bit is on or off  represent with 0 or 1
• 1 byte = 8 bits • char is stored in 1 byte • sizeof(x) returns the size of data in bytes
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Measuring computer memory

 Memory is measured in bytes  using powers of 2

1 Kilobyte = 210 =

1,024 bytes

1 Megabyte = 220 =

1,048,576 bytes

1 Gigabyte = 230 =

1,073,741,824 bytes

1 Terabyte = 240 = 1,099,511,627,776 bytes

about a thousand about a million about a billion about a trillion

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How big are files?
 Some typical sizes of files containing certain data:
pdf file: about 200KB (Lecture15.pdf=193KB) photo: about 500KB - 1.4MB song: about 3.5MB to 8MB video: 5 min: 92 MB
full length movie 600-700MB up to around 2GB
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How much memory is in ...?
 Some typical sizes of storage in various devices
ipod: 2GB (shuffle) 160GB (classic) iphone: 8/16/32/64 GB RAM in a computer: 1 to 4GB (depending on age) Hard drive in laptop: 120GB, 500GB, 750GB Hard drive in desktop: 500GB, 1TB External hard drive: 320GB, 3TB 5
How many songs can I store?
 If one MP3 song is 20MB, how many songs will fit on a 4.7GB DVD?
How many times 20MB fits into 4700MB: x * 20MB = 4.7GB 1GB = 1000MB, so multiply rhs by 1000: x * 20MB = 4700MB x = 4700/20 = 235
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Memory Addresses
 Every byte in Main Memory (Ram) has an “address”.
 The address is a number  The locations (bytes) are numbered in
sequential order:
0, 1, 2, 3, 4, 5, 6, . . . several million or billion
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Memory Addresses

 You can use the “address of” operator to find the address of any variable in your program:

int main () {
int x; cout << &x << endl;
}

Output: 0xf79c14

 What is “0xf79c14”?

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Hexadecimal

 
!
 !






  


      






























   ,A,B,C,D,E,F

• In C++, hexadecimal values have “0x” in front of them (that is “zero x”).

• Not enough digits: Use A for 10, B for 11, C for

12, D for 13, E for 14, and F for 15.

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Counting in various systems

Decimal

Binary

Hexadecimal

 ----------------------------------------------

0

0

0

1

1

1

2

10

2

3

11

3

4

100

4

5

101

5

6

110

6

7

111

7

8

1000

8

9

1001

9

10

1010

A

11

1011

B

12

1100

C

13

1101

D

14

1110

E

15

1111

F

16

10000

10

17

10001

11 ...

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Converting from hex to binary
 Hex to binary:  Replace each hex digit with its 4-bit binary
equivalent (pad 1,2,3, bit values with zeros).
A3 = 1010 0011
2E9A = 0010 1110 1001 1010
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Converting from binary to hex
 Binary to hex:  break the binary up into 4 bit segments (start
from the right).  Replace each 4-bit segment with the
corresponding hex digit from table: 0110110000 => 0001 1011 0000 (pad the left with zeros) => 1 B 0
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Back to the memory address:
 What is “0xf79c14”?  f79c14 is in hexadecimal
F79C14 = 1111 0111 1001 1100 0001 0100
15x165 + 7x164 + 9x163 + 12x162 + 1x161 + 4x160 = 16,227,348
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