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ECE 15A
Fundamentals of Logic Design
Lecture 11
Malgorzata MarekSadowska
Electrical and Computer Engineering Department
UCSB
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Overview
Last time:
Timing diagrams
Static hazards
Today:
Mapping word problems to combinational logic
More examples on
Timing diagrams
Static hazards
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Combinational Logic Word Problems
General Design Procedure
1.
Understand the problem
what is the circuit supposed to do?
write down inputs (data, control) and outputs
draw block diagram or other picture
2.
Formulate the problem in terms of a truth table or other suitable
design representation
3.
Follow Implementation Procedure
Kmaps, QM, a CAD tool
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Example: Process Line Control Problem
Statement of the Problem:
•
Rods of varying length (+/10%) travel on conveyor belt,
mechanical arm pushes rods within spec (+/5%) to one side
•
Second arm pushes rods too long to other side
•
Rods too short stay on belt
•
3 light barriers (light source + photocell) as sensors
Design combinational logic to activate the arms
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Example (cont.)
Where to place the light sensors A, B, and C to distinguish among
the three cases?
Assume that A detects the leading edge of the rod on the conveyor
Understanding the Problem
Inputs are three sensors,
outputs are two arm control
signals
Assume sensor reads "1" when
tripped, "0" otherwise
Call sensors A, B, C
Spec
+ 5%
+10%
Too
Long
ROD
Spec
+ 5%
5%
Within
Spec
ROD
Spec
 10%
Too
Short
ROD
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A to B distance place apart at specification  5%
A to C distance placed apart at specification +5%
A
B
C
Spectification
5%
Specification
+ 5%
Too
Long
Too
Short
Within
Spec
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Example (cont.)
Truth table and logic implementation
"too long" = A B C
(all three sensors tripped)
"in spec" =
A B C'
(first two sensors tripped)
0
0
0
1
X
0
0
A
BC
0
1
00
01
11
10
0
0
0
0
X
1
0
0
A
BC
0
1
00
01
11
10
Arm 1 (in spec)
Arm 2 (too long)
0
A
0
0
0
0
1
1
1
1
B
0
0
1
1
0
0
1
1
C
0
1
0
1
0
1
0
1
Function




too short

in spec
too long
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Binary coded decimal (BCD)
Decimal symbol
BCD symbol
0
0000
1
0001
2
0010
3
0011
4
0100
5
0101
6
0110
7
0111
8
1000
9
1001
Example:
(526)
= (0101 0010 0110)
= (1000001110)
10
BCD
2
(16)
10
= (0001 0110)
BCD
= (10000)
2
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Example: BCD to 7 Segment Display
Controller
•
Understanding the problem:
Input:
a 4 bit bcd digit
Output:
the control signals
for the display
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 Winter '08
 M
 Binarycoded decimal, G protein coupled receptors, Comparator, Digital comparator

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