CX 103: Introduction to Computers

Lecture 11
 
 

Announcements

Exam 1: Tuesday, March 13


Today:

Bits, Bytes, and Binary II

What is a Bit?

0 and 1 are called Binary Digits (or Bits)
 
 

View a bit as the fundamental unit of storage on a computer.
 
 

Binary Number System: elements are 0,1

Decimal Number System: elements are 0,1,2,3,4,5,6,7,8,9
 


What is a Byte?

A single bit has limited usefulness: it can represent only two values (0 or 1) and hence can distinguish only between two states.

A Byte is an ordered string of 8 bits:

Examples:
 
1
0
0
1
0
0
0
1

 
 
0
0
0
0
0
0
0
0

 
 
1
1
1
0
0
1
0
1

 
 
1
1
1
1
1
1
1
1

 
 
 

How many different Bytes are there?

How many different states can a byte represent?
 
 

Two Bits: 22 = 4 possibilities


 
0
0
0
1
1
0
1
1

With 2 bits, we can represent 22 = 4 states
 
 
 
 
 
 

Three Bits: 23 = 8 possibilities


 
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1

number of bits number of states Power of 2
1
2
21
2
4
22
3
8
23
4
16
24
5
32
25
6
64
26
7
128
27
8
256
28
9
512
29
10
1024
210
15
32768
215
16
65536
216

Typical Computer Keyboard: ~ 105 keys

Each key has 2 positions -> ~ 210 different messages can be sent to the computer.

Now 27 = 128 and 28 = 256

7 bits would not suffice, but 8 will.

Thus there are enough bytes to distinguish 256 distinct objects.

One such set: the whole numbers from 0 to 255:

0,1,2,3,4,....,254,255

Is there an easy to do this?

Place Holder Notation!

Decimal Notation:

467 = 400 + 60 + 7

= 4 * 100 + 6 * 10 + 7 * 1

= 4 * 102 + 6 *101 + 7 * 100

1101 = 1 *103+ 1 * 102 + 0 * 101 + 1 * 100

Binary Notation

11012 = 1 * 23+ 1 * 22 + 0 * 21 + 1 * 20

= 8 + 4 +1 = 13

1         00000001

2         00000010

3         00000011

4         00000100

5         00000101

6         00000110

7         00000111

8         00001000

etc.

Going from Decimal to Binary

Powers of Two
 
1 2 3 4 5 6 7 8 9 10 11 12
2 4 8 16 32 64 128 256 512 1024 2048 4096

Find highest power of two less than the number

Subract that power

Repeat

1492 = 1024 + 468

= 1024 + 256 + 212

= 1024 + 256 + 128 + 84

= 1024 + 256 + 128 + 64 + 20

= 1024 + 256 + 128 + 64 + 16 + 4
 
1024 512 256 128 64 32 16 8 4 2 1
1 0 1 1 1 0 1 0 1 0 0

1 0 1 1 1 0 1 0 1 0 0



ASCII

Which binary patterns should represet which keyboard elements?

American Standard Code for Information Interchange

(1963)

Windows, Macs and UNIX machines all use ASCII to store characters.

Larger IBM mainframes and minicomputers use the EBCDIC standard

(AS/400 stores your student records this way)

http://tronweb.super-nova.co.jp/characcodehist.html

A Brief History of Character Codes
in
North America, Europe, and East Asia

Steven J. Searle



Although the ASCII character code was adopted by manufacturers of minicomputers, workstations, and personal computers in the U.S., and later turned into an international standard by the ISO, in the field of mainframe computers, IBM--the dominant force in the world of computing in the 1960s and 1970s--decided to go its own way.

This was most likely decided on the basis of concern for compatibility with past technology, but many people viewed it as primarily a marketing strategy to keep IBM customers locked into IBM hardware and software.

In any event, the company created a proprietary 8-bit character code (2^8 = 256 code points) called EBCDIC [pronounced eb-see-dick ], which stands for "Extended Binary Coded Decimal Interchange Code." It was used on the successful IBM System/360 mainframe computer series, which hit the market in April 1964. EBCDIC is an extension to 8 bits of BCDIC (Binary Coded Decimal Interchange Code), an earlier 6-bit binary code (2^6 = 64 code points) for IBM computers. (It should be noted that some sources refer to this previous 6-bit character code simply as BCD, or "Binary Coded Decimal," but BCD is also used to refer to a 4-bit character code [2^4 = 16 code points] for encoding Arabic numerals.)

ASCII/EBCDIC Comparsion: http://www.flash.net/~gwstern/ascii_ebcdic.html


 
 

Printable Characters



 
decimal Character   decimal Character   decimal Character
032 (Space)   064 @   096 `
033 !   065 A   097 a
034 "   066 B   098 b
035 #   067 C   099 c
036 $   068 D   100 d
037 %   069 E   101 e
038 &   070 F   102 f
039 '   071 G   103 g
040 (   072 H   104 h
041 )   073 I   105 i
042 *   074 J   106 j
043 +   075 K   107 k
044 ,   076 L   108 l
045 -   077 M   109 m
046 .   078 N   110 n
047 /   079 O   111 o
048 0   080 P   112 p
049 1   081 Q   113 q
050 2   082 R   114 r
051 3   083 S   115 s
052 4   084 T   116 t
053 5   085 U   117 u
054 6   086 V   118 v
055 7   087 W   119 w
056 8   088 X   120 x
057 9   089 Y   121 y
058 :   090 Z   122 z
059 ;   091 [   123 {
060 <   092 \   124 |
061 =   093 ]   125 }
062 >   094 ^   126 ~
063 ?   095 _   127 DEL

 

Patterns



 
065 A   097 a
066 B   098 b
067 C   099 c
068 D   100 d
069 E   101 e
070 F   102 f
...        
088 X   120 x
089 Y   121 y
090 Z   122 z

 

Upper and lower case version of the same letter are 32 apart.
 
F ->  70 = 64 + 4 + 2  0 1 0 0 0 1 1 1
f  ->  92 = 64 + 32 + 4 + 2  0 1 1 0 0 1 1 1

 
 
 

Nonprintable Characters
Decinal Value          
000 NUL (Null char.)   016 DLE (Data Link Escape)
001 SOH (Start of Header)   017 DC1 (XON)  (Device Control 1)
002 STX (Start of Text)   018 DC2 (Device Control 2)
003 ETX (End of Text)   019 DC3 (XOFF) (Device Control 3)
004 EOT (End of Transmission)   020 DC4 (Device Control 4)
005 ENQ (Enquiry)   021 NAK (Negative Acknowledgement)
006 ACK (Acknowledgment)   022 SYN (Synchronous Idle)
007 BEL (Bell)   023 ETB (End of Trans. Block)
008 BS (Backspace)   024 CAN (Cancel)
009 HT (Horizontal Tab)   025 EM (End of Medium)
010 LF (Line Feed)   026 SUB (Substitute)
011 VT (Vertical Tab)   027 ESC (Escape)
012 FF (Form Feed)   028 FS (File Separator)
013 CR (Carriage Return)   029 GS (Group Separator)
014 SO (Serial In)(Shift Out)   030 RS (Request to Send)(Record Separator)
015 SI (Serial Out)(Shift Out)   031 US (Unit Separator)

 

Designers of PCs, Macs and UNIX machines chose

different ways to represent "carriage return"

PCs: 13 and 10 (Carriage return and line feed)

Macs: 13

UNIX: 10

Makes it tricky to exchange files.

What is a KB?

A kilobyte (1 KB) is defined as 210 = 1024 bytes.

1 KB = 210  bytes= 1024 ~ 1000 bytes

A megabyte (1 MB) is 210 kilobytes:

1 MB = 210  KB = 210  210 bytes

= 220 bytes = 1,048,576 bytes

~ 1,000,000 bytes.

Rough Conversion: 210 ~ 103

Example: 220 = 210 210 ~ 103 103 = 106

Computer Memory: 64 MB

Floppy Disk: 1.44 MB

Zip Disk: 100 MB

A gigabyte (1 GB) is 210  megabytes:

1 GB = 210  MB = 210 220 bytes

= 230 bytes = 1,073,741,824 bytes

~ 1,000,000,000 bytes. (1 billion bytes)

Storage Space on Hard Drive: 20GB

CD-ROM : 650 MB


 

Human Terms:

A densely packed single spaced typed sheet of paper = 60 lines @ 80 characters

= 4800 characters ~ 5 KB
 
 
 
 

Alice in Wonderland:

27,808 words

148,491 characters ~ 150 KB

Number Systems

Question: What does 100 mean?
 
 

Answer: The meaning depends on the base
 
 

Base 10:

(100)10 = 1 * 102 + 0 * 101 + 0 * 100
 
 
 
 

Base 2

(100)2 = 1 * 22 + 0 * 21 + 0 * 20
 
 

Base 5

(100)5 = 1 * 52 + 0 * 51 + 0 * 50

Available Digits:

Base 2: 0,1

Base 5: 0,1,2,3,4

Base 10: 0,1,2,3,4,5,6,7,8,9

Base 16: 0,1,2,3,5,6,7,8,9,?,?,?,?,?,?

Hexadecimal (Base 16)

0,1,2,3,5,6,7,8,9,A,B,C,D,E,F

Counting to 20


 
Base 10 Base 2 Base 5 Base 16
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 10 5
6 110 11 6
7 111 12 7
8 1000 13 8
9 1001 14 9
10 1010 20 A
11 1011 21 B
12 1100 22 C
13 1101 23 D
14 1110 24 E
15 1111 30 F
16 10000 31 10
17 10001 32 11
18 10010 33 12
19 10011 34 13
20 10100 40 14

 
 
 

What is the decimal equivalent of the hexadecimal 2F?

2F = 2 * 161 + F * 160

= 32 + 15 = 47
 
 

Find Hexadecimal representation of 1492

Powers of 16: 16 256 4096 65536

1492 = 5 * 256 + 212

= 5 * 256 + 13 * 16 + 4

= 5 * 162 + D* 161 + 4 * 160

= 5D4