#3 Number Systems

# #3 Number Systems - 1. Number Systems Location in course...

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ITEC 1011 Introduction to Information Technologies 1. Number Systems Chapt. 2 Location in course textbook

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ITEC 1011 Introduction to Information Technologies 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 No Hexa- decimal 16 0, 1, … 9, A, B, … F No No
ITEC 1011 Introduction to Information Technologies Quantities/Counting (1 of 3) Decimal Binary Octal Hexa- decimal 0 0 0 0 1 1 1 1 2 10 2 2 3 11 3 3 4 100 4 4 5 101 5 5 6 110 6 6 7 111 7 7 p. 33

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ITEC 1011 Introduction to Information Technologies Quantities/Counting (2 of 3) Decimal Binary Octal Hexa- decimal 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F
ITEC 1011 Introduction to Information Technologies Quantities/Counting (3 of 3) Decimal Binary Octal Hexa- decimal 16 10000 20 10 17 10001 21 11 18 10010 22 12 19 10011 23 13 20 10100 24 14 21 10101 25 15 22 10110 26 16 23 10111 27 17 Etc.

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ITEC 1011 Introduction to Information Technologies Conversion Among Bases The possibilities: Hexadecimal Decimal Octal Binary pp. 40-46
ITEC 1011 Introduction to Information Technologies Quick Example 25 10 = 11001 2 = 31 8 = 19 16 Base

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ITEC 1011 Introduction to Information Technologies Decimal to Decimal (just for fun) Hexadecimal Decimal Octal Binary Next slide…
ITEC 1011 Introduction to Information Technologies 125 10 => 5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125 Base Weight

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ITEC 1011 Introduction to Information Technologies Binary to Decimal Hexadecimal Decimal Octal Binary
ITEC 1011 Introduction to Information Technologies Binary to Decimal Technique Multiply each bit by 2 n , where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the right Add the results

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ITEC 1011 Introduction to Information Technologies Example 101011 2 => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = 32 43 10 Bit “0”
ITEC 1011 Introduction to Information Technologies Octal to Decimal Hexadecimal Decimal Octal Binary

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ITEC 1011 Introduction to Information Technologies Octal to Decimal Technique Multiply each bit by 8 n , where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the right Add the results
ITEC 1011 Introduction to Information Technologies Example 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10

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ITEC 1011 Introduction to Information Technologies Hexadecimal to Decimal Hexadecimal Decimal Octal Binary
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## This note was uploaded on 06/14/2011 for the course COMPUTER 091 taught by Professor Rajivsir during the Summer '11 term at MIT.

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#3 Number Systems - 1. Number Systems Location in course...

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