Transcript Steering Gates

Steering Gates, Timing
Diagrams & Combinational
Logic
Technician Series
©Paul Godin
Created Jan 2014
Steering 1.1
Timing Diagrams
Steering 1.2
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
Timing Diagram sample: AND
A
Y
B
Logic 1
Logic 0
The output Y is determined by
looking at the input A and B
states and comparing them to
the truth table for the gate.
A
B
Y
Steering 1.4
Timing Diagram sample: OR
A
Z
B
A
B
Z
0
1 1
0
0
0 1 1
0
1
1
0
0
0
0
1
1
0
0
Steering 1.5
Complete the Timing Diagram: Exercise 1
A
Z
B
A
B
Z
Steering 1.6
Complete the Timing Diagram: Exercise 2
A
Z
B
A
B
Z
Steering 1.7
Steering or Control Gates
Steering 1.8
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
Steering Gates
◊ Digital gates can be used to control the flow of
one digital signal with another.
1
0
Signal
Output
Control 1
Signal
Output
Control 1
Animated
Steering 1.10
Steering Gates
Signal
1
0
0
Output
Control 0
Signal
0
Output
Control 0
Animated
Steering 1.11
Exercise:
Control Gates Worksheet (AND, OR)
Control
Y
Z
Z’
Signal
Control
Signal
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
Control
Signal
0
Y
Status
Z
Z’
Status
Steering 1.12
Combinational Logic
Steering 1.13
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
Combinational Logic Example 1
The circuit below is a combinational logic circuit.
A
B
C
Y
Steering 1.15
Combinational Logic Example 1
It can be described in English terms:
A AND B, OR C equals output Y
A
B
Y
C
A AND B
Steering 1.16
Combinational Logic Example 1
It can be described using a Boolean equation:
(A ● B) + C = Y
A
B
Y
C
A●B
Steering 1.17
Combinational Logic Example 1
It can be described using a Truth Table:
A
A B C Y
B
0 0 0 0
Y
C
If C is 1, Y
is 1
0 0 1 1
0 1 0 0
(A ● B) + C = Y
0 1 1 1
1 0 0 0
1 0 1 1
Only instances where the
output of the AND gate = 1
1 1 0 1
1 1 1 1
Steering 1.18
Combinational Logic Example 1
It can be described using a Timing Diagram:
A
B
C
(A ● B) + C = Y
Y
A B C Y
0 0 0 0
0 0 1 1
A
0 1 0 0
B
0 1 1 1
C
Y
1 0 0 0
1 0 1 1
1 1 0 1
1 1 1 1
Steering 1.19
Combinational Logic Example 2
This is a combinational Logic equation:
A●B●C=Y
It can be described as “NOT A AND B AND C equals Y”.
It can be drawn this way:
A
A
B
C
Y
Steering 1.20
Combinational Logic Example 2
The Truth Table and Timing diagram describes its function
A●B●C=Y
A
A A’ B C Y
0 1
0 0 0
0 1
0 1 0
0 1
1 0 0
A
0 1
1 1 1
B
1 0
0 0 0
C
1 0
0 1 0
1 0
1 0 0
1 0
1 1 0
A
B
C
Y
Y
Steering 1.21
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
Example 1: Circuit to Boolean
Step 1:
AB
Step 2:
AB
Step 3:
AB+C
Steering 1.23
Circuit to Boolean Exercise 1:
Convert the following circuit to its Boolean Expression
Step 1:
Step 2:
Steering 1.24
Circuit to Boolean Exercise 2:
Convert the following circuit to its Boolean Expression
Step 1:
Step 2:
Step 3:
Step 4:
Steering 1.25
Circuit to Boolean Exercise 3:
Convert the following circuit to its Boolean Expression
Step 1:
Step 3:
Step 2:
Steering 1.26
Circuit to Boolean Exercise 4:
Convert the following circuit to its Boolean Expression
Steering 1.27
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
Step 1: ABC is OR’d with BC
ABC
BC
Y
Steering 1.28
Boolean to Circuit Conversion Example
Step 3: Other side, BC
Step 2: One side, ABC
A
B
C
B
C
ABC
BC
Step 4: Put it all together
(ABC) + BC = Y
Steering 1.29
Boolean to Circuit Conversion Example
Step 5: Tidy up the circuit (inputs on left, outputs on right)
A
B
C
B
C
ABC
(ABC) + BC = Y
BC
Steering 1.30
Boolean to Circuit Conversion Example
Step 6: Common the B and the C inputs
A
B
C
ABC
(ABC) + BC = Y
BC
Done
Steering 1.31
Boolean to Circuit Exercise 1:
Draw the circuit whose expression is: (AB)+(CD)
Steering 1.32
Boolean to Circuit Exercise 2:
Draw the circuit whose expression is: (A+B)•(BC)
Steering 1.33
Boolean to Circuit Exercise 3:
Draw the circuit whose expression is: (AB) + (AC)
Steering 1.34
The Resistor and his Ohmies
END
©Paul R. Godin
prgodin°@ gmail.com
Steering 1.35