Lecture_10

# Lecture_10 - ECE 331 Digital System Design...

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ECE 331 – Digital System Design Numbers (Lecture #10)

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ECE 331 - Digital System Design 2 52 What does this number represent? What does it mean?
ECE 331 - Digital System Design 3 1011001.101 What does this number represent? Consider the base (or radix ) of the number.

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ECE 331 - Digital System Design 4 Number Systems
ECE 331 - Digital System Design 5 Number Systems R is the radix or base of the number system - Must be a positive number - R digits in the number system: [0 . . R-1] Important number systems for digital systems: - Base 2 (binary): [0, 1] - Base 8 (octal): [0 . . 7] - Base 16 (hexadecimal): [0 . . 9, A, B, C, D, E, F]

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ECE 331 - Digital System Design 6 Number Systems Positional Notation N = a 4 a 3 a 2 a 1 a 0 . a -1 a -2 a -3 a -4 a -5 Power Series expansion in R N = a 4 x R 4 + a 3 x R 3 + a 2 x R 2 + a 1 x R 1 + a 0 x R 0 + a -1 x R -1 + a -2 x R -2 + a -3 x R -3 + a -4 x R -4 + a -5 x R -5
ECE 331 - Digital System Design 7 Number Systems Base Position in Power Series Expansion R 4 3 2 1 0 -1 -2 -3 Decimal 10 10 10000 1000 100 10 1 0.1000 0.0100 0.0010 Binary 2 2 16 8 4 2 1 0.5000 0.2500 0.1250 Octal 8 8 4096 512 64 8 1 0.1250 0.0156 0.0020 Hexadecimal 16 16 65536 4096 256 16 1 0.0625 0.0039 0.0002 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3 2 4 2 3 2 2 2 1 2 0 2 -1 2 -2 2 -3 8 4 8 3 8 2 8 1 8 0 8 -1 8 -2 8 -3 16 4 16 3 16 2 16 1 16 0 16 -1 16 -2 16 -3

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ECE 331 - Digital System Design 8 Conversion between Number Systems
ECE 331 - Digital System Design 9 Conversion of Decimal Integer Use repeated division to convert to any base - N = 57 (decimal) - Convert to binary (R = 2) and octal (R = 8) 57 / 2 = 28: rem = 1 = a0 28 / 2 = 14:

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Lecture_10 - ECE 331 Digital System Design...

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