Transcript Document
COSC1078 Introduction to
Information Technology
Lecture 10
Binary Representation
James Harland
[email protected]
Lecture 10: Binary Representation
Intro to IT
Introduction to IT
1 Introduction
2 Images
3 Audio
4 Video
5 Binary Representation
WebTest 1, Assignment 1
6 Data Storage
7 Machine Processing
8 Operating Systems
WebLearn Test 2
9 Processes
Assignment 2
10 Internet
11 Internet Security
WebLearn Test 3
12 Future of IT
Assignment 3, Peer and Self Assessment
Lecture 10: Binary Representation
Intro to IT
Overview
Questions?
WebLearn Test 1
Binary Representation
Questions?
Lecture 10: Binary Representation
Intro to IT
Web Test 1
Week 5
Quizzes (practice tests) up now
Due by 11.59pm Sunday 22nd August
Content will be on weeks 2-4
Images
Audio
Video
Lecture 10: Binary Representation
Intro to IT
Assignment 1
JUST
DO
IT!
Use GIMP (or a similar tool) to perform some
manipulations on an image
Address six issues in relation to this
Main emphasis is on process, not result!
SUBMIT VIA WEBLEARN
Due by 11.59pm Sunday 3rd April
Lecture 10: Binary Representation
Intro to IT
Introduction
Lecture 10: Binary Representation
Intro to IT
Overview
01010100001010101010100110100010101001101001010010
100011100010101010100101111001001010…
Lecture 10: Binary Representation
Intro to IT
What do computers do?
Compute!
Input/Output
Processing
Memory
Lecture 10: Binary Representation
Intro to IT
History
…
Babbage’s Difference Engine (1849)
Babbage’s Analytical Engine (1837-1871, never built)
Turing’s Universal Machine (1936, mathematical model)
Turing digital Boolean-logic multiplier (1937)
Colossus (1943, destroyed 1945)
ENIAC (1946)
Von Neumann architecture (c. 1945)
EDVAC (1949)
CSIRAC (1949)
Lecture 10: Binary Representation
Intro to IT
Computer Memory
Cells of 8 bits each (one byte)
…
Most
significant
bit
address
Lecture 10: Binary Representation
…
Least
significant
bit
Intro to IT
Random Access Memory (RAM)
Random access means any cell can be accessed at any
time (and in any order)
Volatile – contents cleared when machine is switched off
Very fast compared to other forms of memory
DRAM: dynamic RAM (replenishes charges constantly)
SDRAM: synchronous DRAM – faster still
Often have small very fast caches and registers
Lecture 10: Binary Representation
Intro to IT
Magnetic Disk
Thin spinning metal disk with magnetic coating
Each disk contains a number of circular tracks
Often several disks stacked on top of each other
Cylinders made up of tracks made up of sectors
Can have very large storage this way
Slow access time!
Lecture 9: Data Storage Devices
Intro to IT
Magnetic Disk (Hard Disk)
Seek time: move heads from one track to another
Latency time: half time for complete disk rotation
Access time: seek time + latency time
Transfer rate: rate data can be read from disk
`Typical’ Hard disk
Seek time: 2ms to 15ms
Latency time: 8ms to 20ms
Transfer rate: 0.5 GB per second
Sounds fast, but is actually quite slow …
Lecture 9: Data Storage Devices
Intro to IT
Optical Disks (CDs, DVDs)
Laser readers rather than magnetic ones
Disks more error-tolerant than magnetic ones
Type
Features
Date
Storage
CD
“compact disk”
1984
800MB
DVD
Multiple layers
1995
15GB
Blu-ray
`blue laser’
2004
100GB
(405 vs 650 nm)
Lecture 9: Data Storage Devices
Intro to IT
Flash Drives
Disks of all sorts are slow compared to other circuits
Flash drives ‘write’ small electronic circuits
Eventually decay after many changes of data
Suitable for slow-changing data, not main memory
Portable and much more resilient than disks
Lecture 9: Data Storage Devices
Intro to IT
Older Storage Types
Magnetic tape
`Floppy’ disk
(5.25’’ disk)
3.5’’ disk
Lecture 9: Data Storage Devices
Intro to IT
Binary Codes
“Meet me at Fred’s”
234
12.43434343
-620
0
Lecture 10: Binary Representation
1
1
0
0
Intro to IT
1
1
0
ASCII
American Standard Code for Information
Interchange
7-bit patterns to represent
letters (upper and lower case)
numbers
,.,;“$%@*&!?<>…
Total of 128 different characters
Lecture 10: Binary Representation
Intro to IT
ASCII
01001000
01100101
01101100
01101100
01101111
00101110
H
e
l
l
o
.
Hello!
Unicode: uses 16 bits, can do Chinese,
Japanese & Hebrew characters
Lecture 10: Binary Representation
Intro to IT
Numbers
Represented in binary notation
25 in ASCII is 00110010 00110101
8 bits per digit seems too much!
Can represent 256 different numbers in 8 bits …
Don’t want to add, multiply etc. in ASCII …
Remember that 1 + 1 = 10 …
Lecture 10: Binary Representation
Intro to IT
Two’s Complement
Bit pattern
Value
011
3
010
2
001
1
000
0
111
-1
110
-2
101
-3
100
-4
Lecture 10: Binary Representation
How do you store
negative numbers?
Intro to IT
Two’s Complement
0 first means +ve (sign bit)
1 first means –ve
+ve: Count from 0 up to 01n-1
-ve: Start from
1n
down to
3 is 011, -3 is 101
2 is 010, -2 is 110
1 is 001, -1 is 111
Lecture 10: Binary Representation
10n-1
Bit pattern
Value
011
3
010
2
001
1
000
0
111
-1
110
-2
101
-3
100
-4
Intro to IT
Two’s Complement
Bit pattern
Value
011
3
010
2
011 + 111 = 1010
001
1
Answer is 010, ie 2.
000
0
111
-1
110
-2
101
-3
100
-4
1 + 2: add in obvious way
3 – 1: calculate as 3 + (-1)
Can add and subtract with
the same circuits
Lecture 10: Binary Representation
Intro to IT
Excess Notation
A different encoding of the
numbers
“naive” bit pattern encodes 4
more than actual value
100 (looks like 4) encodes 0
101 (looks like 5) encodes 1
110 (looks like 6) encodes 2
Lecture 10: Binary Representation
Bit pattern
Value
111
3
110
2
101
1
100
0
011
-1
010
-2
001
-3
000
-4
Intro to IT
Floating Point
exponent
sign bit
Mantissa
100.101
1 bit for sign
3 bits for exponent
4 bits for mantissa
Lecture 10: Binary Representation
Intro to IT
Floating Point
Mantissa: digit sequence (1st digit always 1)
Exponent: where to put the .
This is generally given in ‘excess’ notation
Binary form of 2.423 x 104
01011001 means +ve 0.1001 shifted 101 place
= 1.001
Lecture 10: Binary Representation
Intro to IT
Truncation Errors
Beware adding small numbers to large ones!
Finite length of encoding means that
sometimes digits are lost
Not often a problem, but can be …
Lecture 10: Binary Representation
Intro to IT
Parity Bits
Add a ‘parity bit’ to each byte
Odd parity: make total of 1s in all 9 bits odd
Even parity: make total of 1s in all 9 bits even
If parity is wrong, then an error has occurred
Lecture 10: Binary Representation
Intro to IT
Conclusion
Get Assignment and WebTest done this week
Do online quizzes later this week
Keep reading! (book particularly)
Lecture 10: Binary Representation
Intro to IT