Transcript Power Point - Computer Science

Chapter 4: The Building
Blocks: Binary Numbers,
Boolean Logic, and Gates
Invitation to Computer Science,
C++ Version, Third Edition
Spring 2005: Additions by S. Steinfadt
Objectives
In this chapter, you will learn about:

The binary numbering system

Boolean logic and gates

Building computer circuits

Control circuits
Invitation to Computer Science, C++ Version, Third Edition
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Introduction

Chapter 4 focuses on hardware design (also
called logic design)

How to represent and store information inside a
computer

How to use the principles of symbolic logic to
design gates

How to use gates to construct circuits that perform
operations such as adding and comparing
numbers, and fetching instructions
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The Binary Numbering System

A computer’s internal storage techniques are
different from the way people represent
information in daily lives

Information inside a digital computer is stored as
a collection of binary data
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Binary Representation of Numeric and
Textual Information

Binary numbering system



Base-2
Built from ones and zeros
Each position is a power of 2
1101 = 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20

Decimal numbering system


Base-10
Each position is a power of 10
3052 = 3 x 103 + 0 x 102 + 5 x 101 + 2 x 100
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Figure 4.2
Binary-to-Decimal
Conversion Table
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Binary Representation of Numeric and
Textual Information (continued)

Representing integers

Decimal integers are converted to binary integers

Given k bits, the largest unsigned integer is
2k - 1


Given 4 bits, the largest is 24-1 = 15
Signed integers must also represent the sign
(positive or negative) - Sign/Magnitude notation
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Binary Representation of Numeric and
Textual Information (continued)

Representing real numbers

Real numbers may be put into binary scientific
notation: a x 2b
(or ±M x B±E)


Number then normalized so that first significant
digit is immediately to the right of the binary point


Example: 101.11 x 20
Example: .10111 x 23
Mantissa and exponent then stored
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Binary Representation of Numeric and
Textual Information (continued)

Characters are mapped onto binary numbers

ASCII code set


UNICODE code set


8 bits per character; 256 character codes
16 bits per character; 65,536 character codes
Text strings are sequences of characters in
some encoding
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Binary Representation of Textual Information (cont’d)
Decimal
ASCII
8 bits long
Binary
Val.
Dec.
Unicode
Charac.
48
00110000
0
0x30
0x0030
[0]
49
00110001
1
0x31
0x0031
[1]
50
00110010
2
0x32
0x0032
[2]
51
00110011
3
0x33
0x0033
[3]
52
00110100
4
0x34
0x0034
[4]
53
00110101
5
0x35
0x0035
[5]
54
00110110
6
0x36
0x0036
[6]
55
00110111
7
0x37
0x0037
[7]
0x0038
[8]
56
00111000
8
0x38
57
00111001
9
0x39
0x0039
[9]
58
00111010
:
0x3A
0x003A
[:]
59
00111011
;
0x3B
0x003B
[;]
60
00111100
<
0x3C
0x003C
[<]
61
00111101
=
0x3D
0x003D
[=]
62
00111110
>
0x3E
0x003E
[>]
63
00111111
?
0x3F
0x003F
[?]
64
01000000
@
0x40
0x0040
[@]
65
01000001
A
0x41
0x0041
[A]
66
01000010
B
0x42
0x0042
[B]
Invitation to Computer Science, C++ Version, Third Edition
Unicode
16 bits long
Partial
listings
only!
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Binary Representation of Sound and
Images

Multimedia data is sampled to store a digital
form, with or without detectable differences

Representing sound data

Sound data must be digitized for storage in a
computer

Digitizing means periodic sampling of amplitude
values
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Binary Representation of Sound and
Images (continued)

From samples, original sound may be
approximated

To improve the approximation:

Sample more frequently (increase sampling rate)

Use more bits for each sample value ( bit depth)
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Figure 4.5
Digitization of an Analog
Signal
(a) Sampling the Original
Signal
(b) Recreating the
Signal from the Sampled
Values
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Binary Representation of Sound (cont’d)
MP3 format discussed in text, AAC format here
AAC (Advanced Audio Coding) advantages over
MP3





Improved compression provides higher-quality results with
smaller file sizes
Higher resolution audio, yielding sampling rates up to 96
kHz
Improved decoding efficiency, requiring less processing
power for decode
http://www.apple.com/mpeg4/aac/
http://www.aac-audio.com/
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Binary Representation of Sound and
Images (continued)

Representing image data

Images are sampled by reading color and
intensity values at even intervals across the image

Each sampled point is a pixel

Image quality depends on number of bits at each
pixel
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Binary Representation of Images (cont’d)

Representing image data

Images are sampled by reading color and
intensity values at even intervals across the image

Each sampled point is a pixel

Image quality depends on number of bits at each
pixel

More image information:
http://cat.xula.edu/tutorials/imaging/grayscale.php
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The Reliability of Binary
Representation

Electronic devices are most reliable in a bistable
environment

Bistable environment


Distinguishing only two electronic states

Current flowing or not

Direction of flow
Computers are bistable: hence binary
representations
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Binary Storage Devices

Magnetic core

Historic device for computer memory

Tiny magnetized rings: flow of current sets the
direction of magnetic field

Binary values 0 and 1 are represented using the
direction of the magnetic field
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Figure 4.9
Using Magnetic Cores to Represent Binary Values
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Binary Storage Devices (continued)

Transistors

Solid-state switches: either permits or blocks
current flow

A control input causes state change

Constructed from semiconductors
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Figure 4.11
Simplified Model of a Transistor
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