Raul CruzCano

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Lecture 3

• Raul Cruz-Cano
• CIS 340 Computer Architecture
• Texas AM University Texarkana
• Fall 2008

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Announcements

• Exam 1 October 6, 2008
• Material from first session to ½ next session.
• Next session after recess we will have a review

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Characters Representation

• Each character is encoded by 8 bits
• American Standards Committee on Information
  Interchange (ASCII) encoding system 7 bits
  encoding
• The 8th (most significant) bit is used to encode
  characters from different alphabets and some
  extra special symbols

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T
ABLE
E.1
Binary-Coded Decimal (BCD)
encoding
of
decimal
digits
digit
Decimal
BCD
co
de
0
0000
1
0001
2
0010
3
0011
4
0100
5
0101
6
0110
7
0111
8
1000
9
1001
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Hexadecimal Numbers

• Base 16 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
• (Z3Z2Z1Z0)H
• (Z3x 163)(Z3x 162)(Z3x 161)(Z3x 160)
• (Z3x4096)(Z3x 256)(Z3x 16)(Z3x
  1)
• Example (A34E)H
• (A x 163)(3 x 162)(4 x
  161)(E x 160)
• (Ax4096)(3x 256)(4x
  16)(E x 1)
• (10x4096)(3x 256)(4x 16)(14
  x 1)
• 40960768641441806.
  

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Hexadecimal Numbers Advantages

• Easier to represent large numbers in compact
  manner
• Close relationship to binary numbers
• Ex. Find the binary representation of
  110101101011101
• 110 1011
  0101 1101
• 6D6H 11DBH 5D5H
  13DCH
• (110101101011101)B(6B5C)H
• and vice versa
• OS used it to represent the values of registers,
  contents of memory address, etc

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Conversion Hexadecimal-Decimal

• Same old, same old!!!!
• Hexadecimal to Decimal Already studied during
  the definition of HEX numbers.
• Decimal to HEX Same process as with binary.
• Example (1574)D(?)H
• 1974 / 16 123 rem 6
• 123 / 16 7 rem 11
• Hence (1574)D(7B6)H

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Table of ASCII Characters
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Review

• If you want to know more
• Appendix E1(pp. 790-793)

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Boolean Operations (Irvine Book, Chapter 1)

• NOT
• AND
• OR
• Operator Precedence
• Truth Tables

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Boolean Algebra

• Based on symbolic logic, designed by George Boole
• Boolean expressions created from
• NOT, AND, OR

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NOT

• Inverts (reverses) a boolean value
• Truth table for Boolean NOT operator

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AND

• Truth table for Boolean AND operator

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OR

• Truth table for Boolean OR operator

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Operator Precedence

• Examples showing the order of operations

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Truth Tables (1 of 3)

• A Boolean function has one or more Boolean
  inputs, and returns a single Boolean output.
• A truth table shows all the inputs and outputs of
  a Boolean function

Example ?X ? Y
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Truth Tables (2 of 3)

• Example X ? ?Y

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Truth Tables (3 of 3)

• Example (Y ? S) ? (X ? ?S)

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Why do we bother with digital logic?
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Translating Languages
English Display the sum of A times B plus C.
C cout ltlt (A B C)
Assembly Language mov eax,A mul B add eax,C call
WriteInt
Intel Machine Language A1 00000000 F7 25
00000004 03 05 00000008 E8 00500000
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Specific Machine Levels
(descriptions of individual levels follow . . . )