Chapter1_1 - Chapter 1 (Lect1) Working with Binary, Octal,...

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Chapter 1 (Lect1) Working with Binary, Octal, and Hexadecimal numbers Review Bases Conversions Addition and subtraction Number complements Signed and Unsigned representations (Base 2) Addition and Subtraction revisited (Base 2) Unsigned numbers Signed numbers
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Base 10 Numbers Number of discrete symbols: 10 Allowed values 0 to (Base – 1): 0 1 2 3 4 5 6 7 8 9 (542.75) 10 = 500 + 40 + 2 + 0.7 + 0.05 = 5x10 2 +4x10 1 +2x10 0 +7x10 -1 +5x10 -2 Counting 0 – 9 Reset , increment 10 – 19 Reset , increment 20 – 29 … 99 Reset, Reset, increment
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Base 2 – Binary numbers 2 –state Digital (electronic) numbering systems Number of discrete symbols: 2 Allowed values 0 to (Base – 1): 0 1 Counting Base 10 Base 2 0 1 2 3 4 5 6 7 8 9 10
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Base 8 – Octal numbers Number of discrete symbols: 8 Allowed values 0 to (Base – 1): 0 1 2 3 4 5 6 7 Counting Base 10 Base 8 0 1 2 3 4 5 6 7 8 9 10
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Base 16 – Hexadecimal numbers Number of discrete symbols: 16 Allowed values 0 to (Base – 1): 0 1 2 3 4 5 6 7 8 9 A B C D E F Counting Base 10 Base 16 Base 10 Base 16 01 1 11 2 21 3 31 4 41 5 51 6 6 7 8 9 10
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Decimal Binary Octal Hexadecimal 0 0000 00 0 1 0001 01 1 2 0010 02 2 3 0011 03 3 4 0100 04 4 5 0101 05 5 60 1 1 00 6 6 7 0111 07 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 1011 13 B 12 1100 14 C 13 1101 15 D 14 1110 16 E 15 1111 17 F
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Conversions ANY Base to Base 10 Write in the form: a i x b i +… a 2 x b 2 + a 1 x b 1 + a 0 x b 0 .
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This note was uploaded on 12/15/2011 for the course E 202 taught by Professor Staff during the Fall '11 term at University of Alabama - Huntsville.

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Chapter1_1 - Chapter 1 (Lect1) Working with Binary, Octal,...

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