steering gates, timing diagrams & combinational logic technician series steering 1.1 ©paul...
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Steering Gates, Timing Diagrams & Combinational
Logic
Technician Series
Steering 1.1
©Paul GodinCreated Jan 2014
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Timing Diagrams
Steering 1.2
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Timing
◊ Timing diagrams are the best means of comparing the input and output logic values of a digital circuit over time, such as would be found in a functioning circuit.
◊ The output of digital circuit analysis tools such as oscilloscopes and logic analyzers essentially display timing diagrams.
Steering 1.3
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Timing Diagram sample: AND
A
B
Y
A
The output Y is determined by looking at the input A and B
states and comparing them to the truth table for the gate.
Logic 0
B
Y
Logic 1
Steering 1.4
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Timing Diagram sample: OR
A
B
Z
A
B
Z
0 0 0
0
0
0 0
0 01
1
1
1 1
1 1
0 01
Steering 1.5
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Complete the Timing Diagram: Exercise 1
A
B
Z
A
B
Z
Steering 1.6
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Complete the Timing Diagram: Exercise 2
A
B
Z
A
B
Z
Steering 1.7
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Steering or Control Gates
Steering 1.8
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Introduction
◊ An application for a logic circuit is to control one digital signal with another digital signal.
◊ The AND and the OR gates can function as signal Control, or Steering Gates.
Steering 1.9
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Steering Gates
◊ Digital gates can be used to control the flow of one digital signal with another.
1
1
Control
Output
10Signal
1Control
Signal
Output
Animated
Steering 1.10
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Steering Gates
0
1
Control
Output
10Signal
0Control
Signal
Output
0
0
Animated
Steering 1.11
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Exercise:Control Gates Worksheet (AND, OR)
Control Signal Y Status
0 0
0 1
1 0
1 1
Control Signal Z Z’ Status
0 0
0 1
1 0
1 1
Control
Signal
Y
Z
Z’
Steering 1.12
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Combinational Logic
Steering 1.13
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Combinational Logic
◊ Combinational logic describes digital logic circuits that are based on arrays of logic gates. Combinational logic circuits have no retention of states.
◊ Combinational logic circuits can be described with: ◊ English Terms◊ Boolean equations◊ Truth Tables◊ Logic diagrams◊ Timing Diagrams
Steering 1.14
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Combinational Logic Example 1
The circuit below is a combinational logic circuit.
A
B
CY
Steering 1.15
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Combinational Logic Example 1
It can be described in English terms:
A
B
CY
A AND B, OR C equals output Y
A AND B
Steering 1.16
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Combinational Logic Example 1
It can be described using a Boolean equation:
A
B
CY
(A ● B) + C = Y
A ● B
Steering 1.17
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Combinational Logic Example 1
It can be described using a Truth Table:
A
B
CY
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
(A ● B) + C = Y
Only instances where the output of the AND gate = 1
If C is 1, Y is 1
Steering 1.18
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Combinational Logic Example 1
It can be described using a Timing Diagram:
A
B
CY
(A ● B) + C = Y
A
B
C
Y
A B C Y
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
Steering 1.19
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Combinational Logic Example 2
This is a combinational Logic equation:
It can be described as “NOT A AND B AND C equals Y”.It can be drawn this way:
A ● B ● C = Y
ABC
Y
A
Steering 1.20
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Combinational Logic Example 2
The Truth Table and Timing diagram describes its function
A ● B ● C = Y
ABC
Y
A A A’
B C Y
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 0
1 0 1 0 0
1 0 1 1 0
A
B
C
Y
Steering 1.21
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Boolean from a Circuit Diagram
◊ A step-by-step process is used to determine the Boolean equation from a circuit diagram.
◊ Begin at the inputs and include the logic expressions while working toward the outputs.
Steering 1.22
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Example 1: Circuit to Boolean
Step 1: AB Step 2: AB Step 3: AB+C
Steering 1.23
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Circuit to Boolean Exercise 1:
Step 1: Step 2:
Convert the following circuit to its Boolean Expression
Steering 1.24
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Circuit to Boolean Exercise 2:
Step 1: Step 2:
Convert the following circuit to its Boolean Expression
Step 3:
Step 4:
Steering 1.25
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Circuit to Boolean Exercise 3:
Step 1:
Step 2:
Convert the following circuit to its Boolean Expression
Step 3:
Steering 1.26
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Circuit to Boolean Exercise 4:
Convert the following circuit to its Boolean Expression
Steering 1.27
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Boolean to Circuit Conversion Example
◊ Take a step-by-step approach when converting from Boolean to a circuit. Work outward from the expression that brings together groupings found within the expression.
◊ Example: Convert (ABC) + BC = Y
YABC
BC
Steering 1.28
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Step 2: One side, ABC
BC
Boolean to Circuit Conversion Example
ABC
Step 3: Other side, BC
BC
ABC
(ABC) + BC = Y
Step 4: Put it all together
Steering 1.29
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Step 5: Tidy up the circuit (inputs on left, outputs on right)
BC
Boolean to Circuit Conversion Example
ABC
BC
ABC(ABC) + BC = Y
Steering 1.30
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Step 6: Common the B and the C inputs
BC
Boolean to Circuit Conversion Example
ABC
ABC(ABC) + BC = Y
Done
Steering 1.31
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Boolean to Circuit Exercise 1:
Draw the circuit whose expression is: (AB)+(CD)
Steering 1.32
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Boolean to Circuit Exercise 2:
Draw the circuit whose expression is: (A+B)•(BC)
Steering 1.33
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Boolean to Circuit Exercise 3:
Draw the circuit whose expression is: (AB) + (AC)
Steering 1.34
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END©Paul R. Godin
prgodin°@ gmail.com
The Resistor and his Ohmies
Steering 1.35