Combinational Circuit Design

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Combinational Circuit Design

• ECE-331, Digital Design
• Dr. Ron Hayne
• Electrical and Computer Engineering

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Informal Description

• Word Problem, e.g.,
• Design a dB reading meter with 10 resolution
• dB 10 log ( P1 / P2 )
• Assuming source impedance load impedance
• dB 20 log ( V1 / V2 ), assume V2 1
• 24 16, lt 1/10

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Formal Specification

• Alternatives
• Directly write Boolean algebraic formula
• Difficult to do for this word problem
• Generate truth table
• In this problem, converts real values of dB into
  desired binary coded values

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dB Meter Truth Table
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dB Meter Truth Table
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dB Meter Truth Table
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dB Meter Truth Table
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Minterm Form of Outputs

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Canonical SOP Form

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Minimization Techniques

• Boolean Algebraic Manipulation
• Possible, but no guarantee of minimum
• Karnaugh Maps
• Visual technique suitable for small functions
• Quine-McCluskey
• Tabular method
• Guaranteed minimum
• Implementable on computer

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Theorems of Boolean Algebra

• Involution
• A transformation which is its own inverse
• Idempotent (i dem potent)
• A quantity unchanged under multiplication by
  itself
• x x x
• x x x

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Theorems of Boolean Algebra

• DeMorgans
• Adjacency

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Theorems of Boolean Algebra

• Absorption
• Simplification

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Karnaugh Maps

• Mapping of Function onto Spatial Representation
• H/V Adjacent Cells Differ in Only One Bit
• Hamming distance 1
• If Adjacent Cells (minterms) Are 1, Then They Can
  Be Covered by a Single Term
• Algebraic Principle

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1 2 Variable K-maps
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3 Variable K-map
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Adjacency Theorem
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4 Variable K-map
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Uses for K-map

• Minterms of f
• Maxterms of f
• SOP
• POS
• Truth Table
• Algebraic Representation
• Value of dont cares When Minimized

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dB Meter Example
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dB Meter Example
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dB Meter Example
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dB Meter Example
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dB Meter Example
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dB Meter Example
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dB Meter Example
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Hazards

• Error condition resulting in a momentary change
  of output in response to an input change that
  should not cause the output to change
• Result of non-ideal operation of physical devices
• Can be eliminated by use of extra gates

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Hazards
Hazard free
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End of Lecture

• Word Problems
• Minimization
• Boolean Theorems
• Karnaugh Maps
• Hazards