Chapter 8

Fluency with Information Technology4th edition

by Lawrence Snyder(slides by Deborah Woodall : woodall@mc.edu)

1

Computer Circuits

Computer circuits can be in one of two stateslow or high

Also known as:0 and 1off and onfalse and trueno and yesabsence and presence

2

Discrete Values

These two states of a circuit are said to be

discrete or distinct

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Two States

• Low voltage in RAM, VRAM, or the CPU corresponds to– Demagnetized spot – Hard drive– Bump – CD or DVD

• High voltage in RAM, VRAM, or the CPU corresponds to– Magnetized spot – Hard drive– Land – CD or DVD

• Everything must be encoded into a representation using these two states (written as 0's and 1's).

4

Bits

• Each circuit is more commonly called a bit where bit is short for binary digit

• Why? The only digits in the binary number system are

0 and 1 which fit in perfectly with the two state

nature of a computer.

5

Number Systems

• Decimal number system– We know this!– base 10– 10 symbols 0 - 9– e.g. 1375, also written

(1 * 103) + (3 * 102) + (7 * 101) + (5 * 100)

• Binary number system– What is this?– base 2– 2 symbols 0 – 1– e.g. 1001, also written

(1 * 23) + ( 0 * 22) + (0 * 21) + ( 1 * 20)

6

Number Systems

• Decimal number system– We know this!– base 10– 10 symbols 0 - 9– e.g. 1375, also written

(1 * 103) + (3 * 102) + (7 * 101) + (5 * 100)

• Binary number system– What is this?– base 2– 2 symbols 0 – 1– e.g. 1001, also written

(1 * 23) + ( 0 * 22) + (0 * 21) + ( 1 * 20)

7

Encoding Text

• How many bits, minimum, would it take to encode…?

26 lowercase letters and 10 digits 36 total characters

8

Powers of 2This many bits Will encode this many

items

1 21 = 2

2 22 = 4

3 23 = 8

4 24 = 16

5 25 = 32

6 26 = 64

7 27 = 128

8 28 = 256

n 2n

9

Encoding Text

How many bits would it take to encode…? 26 lower case letters 26 upper case letters 10 digits 10 arithmetic characters 20 punctuation characters 3 non-printable characters 95 characters

10

How Many Bits to Encode 95 Characters?

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This many bits Will encode this many items

1 21 = 2

2 22 = 4

3 23 = 8

4 24 = 16

5 25 = 32

6 26 = 64

7 27 = 128

8 28 = 256

n 2n

Encoding Text

• The original ASCII code was a 7-bit code.

• A widely used encoding scheme today is the Extended ASCII code or ISO-8859-1

• The Extended ASCII code is an 8-bit code.

• So, the code for one character will fit exactly into one byte.

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ASCII code p. 235

• What is the ASCII code for each character?• H• &• 3

• What ASCII character is represented by each code?

• 0110 1010• 0011 1111• 1111 0001

13

ASCII Code

• The ASCII code is for encoding text only.

• ASCII 62 is 0011 0110 0011 0010

• The number 62 is 0000 0000 0011 1110

• The computer cannot do arithmetic with ASCII digits.

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Encoding Text• Becoming more wide spread is a new multibyte (one

to four bytes) code called the Unicode

• It can handle all symbols in all languages

• To see other languages go to http://www.unicode.org/standard/WhatIsUnicode.html

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कम्प्यू�टर, मू�ल रूप से , नं�बर� से सेम्ब�ध रखते हैं�। यू प्रत्यू क अक्षर और वर्ण क लिलए एक नं�बर निनंध$ रिरते करक अक्षर और वर्ण से�ग्रनिहैंते करते हैं�। यू�निनंक'ड क$ आनिवष्क$र हैं'नं से पहैंल , ऐसे नं�बर दे नं क लिलए से�कड� निवभि.न्न से�क ते लिलनिप

प्रर्ण$लिलयू$� थीं1। निकसे2 एक से�क ते लिलनिप मू3 पयू$ प्ते अक्षर नंहैं1 हैं' सेकते हैं� : उदे$हैंरर्ण क लिलए, यू�र'निपयू से�घ क' अक ल हैं2, अपनं2 से.2 .$षा$ऒं क' कवर करनं क लिलए अनं क निवभि.न्न से�क ते लिलनिपयू� क9 आवश्यूकते$ हैं'ते2 हैं;। अ�ग्र जी2 जी;से2 .$षा$ क लिलए .2, से.2 अक्षर�, निवर$मूलि=न्हैं� और से$मू$न्यू प्रयू'ग क तेकनं2क9 प्रते2क� हैं ते@ एक हैं2 से�क ते लिलनिप पयू$ प्ते

नंहैं1 थीं2।

Encoding Other Things

In chapter 11 we will look at encoding numbers, images and video.

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Do you remember color codes?

Would you rather type this color code? 3 E C 5 A 7

Or this? 0011 1110 1100 0101 1010 0111

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Hexadecimal

• Since the earliest days of computing, two hexadecimal digits have been used as a shorthand notation for 8 bits (one byte)

• If two hexadecimal digits symbolize one byte, then one hexadecimal digit must correspond in some way to 4 bits

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Hexadecimal

• Base 16

• 16 symbols for building numbers: (0 – 9, A – F)

• Examples of hexadecimal numbers:• 387• 4AFFCC

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Hexadecimal – Binary Equivalents0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

A 1010

B 1011

C 1100

D 1101

E 1110

F 1111

• What would be the hexadecimal shorthand for this 2 byte binary code?

0011 1100 1111 0110

answer: 3CF6

• What would the one byte binary code that corresponds to this hexadecimal shorthand?

B5

answer: 1011 0101

20

Hexadecimal – Binary Equivalents0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

A 1010

B 1011

C 1100

D 1101

E 1110

F 1111

• First column of bits: 8 zeros, 8 ones• Second column of bits: 4 zeros, 4 ones• Third column of bits: 2 zeros, 2 ones• Fourth column of bits: 1 zero, 1 one

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Tags: A Higher Level of Encoding

• HTML tags are also a form of encoding– Formatting– Special non-text items

• Tags can also be used to encode – Structure– See the Oxford English Dictionary example in the

chapter

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