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CDA 3101 Spring 2016
Introduction to Computer Organization
Digital Logic “102”
12 Jan 2016Mark Schmalz
http://www.cise.ufl.edu/~mssz/CompOrg/Top-Level.html
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Overview
• Review of gates and truth tables
• Boolean algebra
• Complex logic circuits
• Combinational logic systems
• Clocking
• Memory elements
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Transistors
NOT gate (Inverter)
Symbol
Functional Behavior
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NOT Gate NAND Gate
Gate Symbol
Truth Table
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AND, OR, NOR Gates
NOR
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Boolean Algebra
• Basic operators: OR (sum), AND (product), NOT• Boolean laws:
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Circuit Equivalence
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The Majority Function
M = f (A, B, C)
M = ABC + ABC + ABC + ABC
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Step 3. a) Build SOP circuit using minterms (M=1);b) OR minterms
The Majority Function (cont’d)M = f (A, B, C)
Step 1. Build truth table for logic function f.
Step 2. Write logic equation in SOP form.
3a
3b
M = ABC + ABC + ABC + ABC1 1 0
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Combinatorial Logic
• Many inputs and many outputs
• Outputs are uniquely determined by inputs
• Absence of memory elements
• Basic combinatorial circuits– Multiplexers– Demultiplexers– Decoders– Comparators
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Multiplexer
2n data inputs
1 data output
n control inputs
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Decoder
n data inputs
2n data outputs
3-to-8 decoder
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Comparator
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Two-Level Logic
x
PLA 12 inputs 6 outputs
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Clocks
Clock period
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Edge-Triggered Clocking
StateElement
1
StateElement
2
Combinational logic
State
Element
Combinational logic
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NOR SR Latch
State 0 State 1
Inputs S - set
R - resetOutputs: Q and Q
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Clocked SR Latch
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Clocked D Latch
D
C
Q
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D flip-flop
D
C
Q
C
D QD
latchC
D QD
latch
C
D Q
Setup time
hold time
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Conclusions
• Digital logic – lowest level of CDA3101 worldview
• Digital logic circuits– Made from building blocks (AND,OR,NOT,…)– Simple or Complex, Combinatorial– Synchronous (clocked) or Asynchronous
• Know rules for Boolean Algebra
Enjoy your week!!