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Lecture1000-2 - ITEC 1000 Introduction to Information...

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1 Lecture 2 Lecture 2 Number Systems Number Systems ITEC 1000 “Introduction to Information Technology” Prof. Peter Khaiter Hexadecimal Decimal Octal Binary
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2 Lecture Template: Lecture Template: Types of number systems Types of number systems Number bases Number bases Range of possible numbers Range of possible numbers Conversion between number bases Conversion between number bases Common powers Common powers Arithmetic in different number bases Arithmetic in different number bases Shifting a number Shifting a number
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3 Types of Number Systems Types of Number Systems Additive: Numbers have intrinsic value: e.g.:  Roman Numerals: LVIII  = 50 + 5 + 1 + 1 + 1 = 58 Positional: Value depends on position: e.g.:  Decimal system: 55 = 5 x 10 + 5 x 1 Additive Number Systems  are not used much  any more: Awkward to use. Prone to errors.
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4 Definitions Definitions The Base  of a number system – how  many different digits (incl. zero) are used  in the system. Base 2: 0, 1 Base 5: 0, 1, 2, 3, 4 Base 8: 0, 1, 2, 3, 4, 5, 6, 7 Base 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 Base 16: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
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5 Definitions Definitions Bit  – a cell holding a single binary number  (0 or 1) Byte  = 8 bits (can hold 2 8  = 256 different  patterns/values) Word  – a fixed-sized group of bits that the  computer handles together. Typical word  sizes: 4, 8, 16, 32, 64, 128 bits 1K  = 1024 bytes
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6 Magnetic Core Memory Magnetic Core Memory http://en.wikipedia.org/wiki/Computer
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7 Common Number Systems Common Number Systems System Base Symbols Used by  humans? Used in  computers? Decimal 10 0, 1, … 9 Yes No Binary 2 0, 1 No Yes Octal 8 0, 1, … 7 No Yes Hexa- decimal 16 0, 1, … 9, A, B, … F No Yes
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8 Positional decimal system Positional decimal system The number 125 means:    1 group of 100   (100 = 10 2 )    2 groups of 10        (10 = 10 1 )    5 groups of 1        (1 = 10 0 )
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9 Place values (1 of 2) Place values (1 of 2) In our usual positional number system, the meaning of a  digit depends on where it is located in the number 3 groups of 1000 7 groups of 100 3 groups of 10 2 groups of 1 Example: 3 7 3 2
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10 Place values (2 of 2) Place values (2 of 2) 125 10 => 5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125 Base Weight
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Representing in bases:  Representing in bases:  10 10 2 2 8 8 16 16 865 10  = 8 x 10 2  + 6 x 10 1  + 5 x 10 0  = 800 + 60 + 5 1011 2  = 1 x 2 3  + 0 x 2 2  + 1 x 2 1  + 1 x 2 0  = 8 + 2 +  1 = 11 10 25 8  = 2 x 8 1  + 5 x 8 0  = 16 + 5 = 21 10  A7 16  = 10 x 16 1  + 7 x 16 0  = 160 + 7 = 167 10 Note:       The subscript naming the base is itself  given in base ten (10), by convention. Base
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Lecture1000-2 - ITEC 1000 Introduction to Information...

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