2 - ECSE-2610 Computer Components & Operations (CoCO) Fall...

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ECSE-2610 Computer Components & Operations (CoCO) Fall 2006 Part 2: Number Systems
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Decimal Representation: 10 digits = {0,1,2,. ..,9} Positional Number Notation: Weight of each digit determined by its position. Positional Number Notation: Positional Number Notation: Weight of each digit determined by its position. Example: 246 = 200 + 40 + 6 = 2 x 10 2 + 4 x 10 1 + 6 x 10 0 In general, for the Base 10 representation: N = Σ N i x 10 i where each N i {0, 1, 2, . . . , 9} is the weight on the base raised to the exponent i . Note: Decimal fractions occur when i is negative: 0.35 = 3 x 10 -1 + 5 x 10 -2 In general, for the Base 10 representation: N = Σ N i x 10 i where each N i {0, 1, 2, . . . , 9} is the weight on the base raised to the exponent i . Note: Decimal fractions occur when i is negative: 0.35 = 3 x 10 -1 + 5 x 10 -2
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Binary Representation: 2 digits = {0, 1} Positional Number Notation for the Binary Representation Positional Number Notation for the Binary Representation Positional Number Notation for the Binary Representation N = Σ N i x 2 i with each N i {0,1} Example (Converting from binary to decimal) 111001 2 = 100000 2 + 10000 2 + 1000 2 + 000 2 + 00 2 + 1 2 = 1 x 2 5 + 1 x 2 4 + 1 x 2 3 + 0 x 2 2 + 0 x 2 1 + 1 x 2 0 = 1 x 32 + 1 x 16 + 1 x 8 + 0 x 4 + 0 x 2 + 1 x 1 = 57 10
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Quote of the Day There are 10 kinds of people in this world: Those who understand binary … and those who don’t.
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Hexadecimal (Hex) Representation: 16 digits = {0,1,2,. ..,9,A,B,C,D,E,F} Positional Number Notation for the Hexadecimal Representation Positional Number Notation for the Hexadecimal Representation Positional Number Notation for the Hexadecimal Representation Note : A - F represent the decimal values 10 - 15, respectively. Note : A - F represent the decimal values 10 - 15, respectively. N = Σ N i x 16 i with each N i {0,1,2,. . .,9,A,B,C,D,E,F} Example (Converting from Hex to Decimal representation) 8A9B 16 = 8000 16 + A00 16 + 90 16 + B 16 = 8 x 16 3 + A x 16 2 + 9 x 16 1 + B x 16 0 = 8 x 4096 + 10 x 256 + 9 x 16 + 11 x 1 = 35483 10
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Converting Decimal to Binary: Successive Division Successive Division Idea : Use remainders from dividing the decimal number by powers of 2. Idea : Use remainders from dividing the decimal number by powers of 2.
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This homework help was uploaded on 04/22/2008 for the course ECSE 2610 taught by Professor Ji during the Spring '08 term at Rensselaer Polytechnic Institute.

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2 - ECSE-2610 Computer Components & Operations (CoCO) Fall...

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