Tutorial -2

# Tutorial -2 - Number Representations Bases Base 16 10.1116...

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Number Representations

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Bases Base 16 • 10.11 16 = (1*16 1 ) + (0*16 0 ) + (1*16 -1 ) + (1*16 -2 ) = 16.0664 10 Base 10 • 10.11 10 = (1*10 1 ) + (0*10 0 ) + (1*10 -1 ) + (1*10 -2 ) = 10.11 10 Base 7 • 10.11 7 = (1*7 1 ) + (0*7 0 ) + (1*7 -1 ) + (1*7 -2 ) = 7.16327 10 Base 5 • 10.11 5 = (1*5 1 ) + (0*5 0 ) + (1*5 -1 ) + (1*5 -2 ) = 5.24 10 Base 3 • 10.11 3 = (1*3 1 ) + (0*3 0 ) + (1*3 -1 ) + (1*3 -2 ) = 3.4444 10 Base 2 • 10.11 2 = (1*2 1 ) + (0*2 0 ) + (1*2 -1 ) + (1*2 -2 ) = 2.75 10
Binary numbers 1011b = 1*2 3 +0*2 2 +1*2 1 +1*2 0 = (8+2+1) 10 = 11 10 = B 16 Recall that: Binary has digits from set {0,1} Decimal has digits from the set {0,1,2…9} Hexadecimal has digits from {0,1,2. .,9,A…F}

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Decimal, Binary, Hexadecimal Decimal Binary Hex 0 0 0 1 1 1 2 10 2 3 11 3 4 100 4 5 101 5 6 110 6 7 111 7 Decimal Binary Hex 8 1000 8 9 1001 9 10 1010 A 11 1011 B 12 1100 C 13 1101 D 14 1110 E 15 1111 F
Base Conversion CASE 1 From base A to base 10 Simply expand at base A and obtain the value for base 10 Ex: • 23.4 5 = (2*5) + (3*1) + (4*5 -1 ) = 13.8

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Division Remainder 23 2 7 1 2 2 0 Base Conversion CASE 2 From base 10 to base A
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## This note was uploaded on 04/21/2008 for the course ESCE 221 taught by Professor Ferrie during the Spring '08 term at McGill.

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Tutorial -2 - Number Representations Bases Base 16 10.1116...

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