Steering Gates, Timing Diagrams & Combinational

Logic

Technician Series

Steering 1.1

©Paul GodinCreated Jan 2014

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

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

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

Complete the Timing Diagram: Exercise 1

A

B

Z

A

B

Z

Steering 1.6

Complete the Timing Diagram: Exercise 2

A

B

Z

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

1

Control

Output

10Signal

1Control

Signal

Output

Animated

Steering 1.10

Steering Gates

0

1

Control

Output

10Signal

0Control

Signal

Output

0

0

Animated

Steering 1.11

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

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

CY

Steering 1.15

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

Combinational Logic Example 1

It can be described using a Boolean equation:

A

B

CY

(A ● B) + C = Y

A ● B

Steering 1.17

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

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

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

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

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:

Step 1: Step 2:

Convert the following circuit to its Boolean Expression

Steering 1.24

Circuit to Boolean Exercise 2:

Step 1: Step 2:

Convert the following circuit to its Boolean Expression

Step 3:

Step 4:

Steering 1.25

Circuit to Boolean Exercise 3:

Step 1:

Step 2:

Convert the following circuit to its Boolean Expression

Step 3:

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

YABC

BC

Steering 1.28

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

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

Step 6: Common the B and the C inputs

BC

Boolean to Circuit Conversion Example

ABC

ABC(ABC) + BC = Y

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

END©Paul R. Godin

prgodin°@ gmail.com

The Resistor and his Ohmies

Steering 1.35