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lecture17 - ECE 4514 Digital Design II Spring 2008 Lecture...

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ECE 4514 Digital Design II Spring 2008 Lecture 17: Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division Hardware Division A Design Lecture Patrick Schaumont
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Overview boxshadowdwn Division algorithms/architectures square4 Division as an 'inverted' multiplication square4 Division one digit at-a-time: digit-recurrence square4 The restoring divider algorithm square4 The non-restoring divider algorithm square4 Designing the non-restoring divider architecture Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division
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Before Division .. look at Multiplication First boxshadowdwn Binary multiplication using shift - and - add 15 1 1 1 1 12 1 1 0 0 X 0 0 0 0 Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 180
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Before Division .. look at Multiplication First boxshadowdwn Binary multiplication using shift - and - add boxshadowdwn 12 x 15 = square4 0 x 1 x 15 + square4 0 x 2 x 15 + square4 1 x 4 x 15 + square4 1 x 8 x 15 Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division boxshadowdwn In multiplication, we look at one bit of the multiplier at a time, and accumulate & shift the multiplicand
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How does division work? boxshadowdwn more or less the opposite way .. divider 1 1 1 1 quotient 1 1 0 0 X 0 0 0 0 Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 dividend
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How does division work? boxshadowdwn We subtract the shifter divider from the dividend .. divider 1 1 1 1 quotient 1 1 0 0 X 0 0 0 0 Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 dividend
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How does division work? boxshadowdwn We subtract the shifter divider from the dividend .. divider 1 1 1 1 quotient 1 1 0 0 X 0 0 0 0 Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 dividend 1 1 1 1 - 0 0 1 1 1 1 0 0
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How does division work? boxshadowdwn We subtract the shifter divider from the dividend .. divider 1 1 1 1 quotient 1 1 0 0 X 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division 1 0 1 1 0 1 0 0 dividend 1 1 1 1 - 0 0 1 1 1 1 0 0 1 1 1 1 0 0 0 0 0 0
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How does division work? boxshadowdwn The problem is: in a real division, we don't know the quotient .. divider 1 1 1 1 quotient X X X X X X X X Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division X X X X X X X X X X X X 1 0 1 1 0 1 0 0 dividend
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How does division work? boxshadowdwn Therefore, we make a tentative subtraction, and look each time if we are left with a positive number divider 1 1 1 1 quotient X X X X X X X X Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division X X X X X X X X X X X X 1 0 1 1 0 1 0 0 dividend
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How does division work? boxshadowdwn Example: Start at the MSB position divider 1 1 1 1 quotient X X X X 1 0 1 1 0 1 0 0 dividend 1 1 1 1 subtract 0 Patrick Schaumont Spring 2008 ECE 4514 Digital Design II Lecture 17: Hardware Division 1 1 0 0 0 1 0 0 ..111 This is an 'overflow' (when considering this as an unsigned number).
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