Lecture 1
Class Overview
and
Appendix A -- Number Systems
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Other courses in computer sequence
 ELEN 350
 ELEN 449
 ELEN 450
 ELEN 454
 ELEN 468
 ELEN 472
 ELEN 473
 ELEN 474
 ELEN 475
Computer Architecture and Design
Microprocessor Systems Design
Computer Interfacing and Communications
Digital Integrated Circuit Design
Advanced Logic Design
Microelectronic Circuit Fabrication (electronics)
Microelectronic Device Design (electronics)
VLSI Circuit Design (electronics)
Introduction to VLSI Systems Design
Careers related to Computers
 VLSI
 Fabrication
 Programmers
 System engineers
 Micro-programmers (micro-processor controllers)
 Others
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Appendix A
Number Systems
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Positional Number Notation
• Positional Number Notation
– Decimal , Binary, Octal, Hexadecimal
– A digit’s place in the sequence determines its
weight
• Decimal Numbers - Base 10 -- Digits 0-9
– Example
– 15410 =
=
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Positional Number Notation
• Binary- Base 2 - Digits 0 and 1. Binary
Digits (bits)
• Example
• 100110102 =
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Positional Number Notation
• Octal- Base 8 - Digits 0 - 7.
• Example
• 2328 =
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Positional Number Notation
• Hexadecimal- Base 16 - Digits 0 - 9, A-F
• A16 = 1010
B16 = 1110
C16 = 1210
• D16 = 1310
E16 = 1410
F16 = 1510
• Example
• 9A16 =
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Conversion Between Binary, Octal, and
Hexadecimal Systems
• Conversion from Binary to Octal or
Hexadecimal.
– Octal
– Group into 3 bit groupings, starting at right.
– Ex.
100110102
– Hexadecimal
– Group into 4-bit groupings, starting at right.
– Ex.
100110102
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Conversion from Octal to Hexadecimal and
Hexadecimal to Octal
(1) Convert to binary
(2) Convert from binary to hexadecimal or
octal.
• Ex.
2328
Convert to hexadecimal
• (1)
• (2)
• Ex.
• (1)
• (2)
9A16
Convert to octal
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Conversion from Decimal to Binary
(1) Perform successive division -successively divide the base 10 number by
the base to which it is to be converted
(2) Collect the remainder to form the
number in the target base
(3) 1st division yields the least significant
bit as its remainder
(4) Continue until the quotient is 0.
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Conversion from Decimal to Binary
(1) Ex. Convert 15410 to binary
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Conversion from Decimal to Octal
(2) Ex. Convert 15410 to octal
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Conversion from Decimal to Hexadecimal
(3) Ex. Convert 15410 to hexadecimal
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Binary Arithmetic Operations
• Base 10 (review) -- addition
9510
+_1610
11110
• Base 10 (review) -- subtraction
9510
-_1610
7910
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Binary Arithmetic Operations
•
•
•
•
•
•
Addition in Base 2 -- Laws
0+0=0
0+1=1
1+0=1
1 + 1 = 0 with a carry of 1
Ex.
1 0 12
1 0 1 1 1 1 12
11
10000
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Binary Arithmetic Operations
•
•
•
•
•
•
Subtraction in Base 2 -- Laws
0-0=0
0 - 1 = 1 with borrow of 1
1-0=1
1-1=0
Ex.
1 0 0 0 02
1 0 1 1 1 1 12
1
10000
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Homework Assignment
HW #1 -- Appendix A
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