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