LOGIC, CIRCUITS,
AND TRUTH TABLES
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CS 147
Dr. Sin-Min Lee
Presented by
Kristina Miguel
INTRODUCTION
The CPU is constructed from logic gates.
 The basic activity of the control unit is decoding
instructions.
 Decoder circuits use an input binary number to
select an output line, or several lines.
 Logic circuits can be implemented directly from
truth table information.

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REVIEW: BASIC LOGIC GATES WITH
TRUTH TABLES
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TRAFFIC LIGHT CONTROLLERS –
IMPOSSIBLE TO AVOID!
Traffic controllers are an
example of decoder
circuits.
 Integrated urban traffic
management schemes
depend on communication
links between the traffic
light controllers and a
central control computer.

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EXAMPLE SYSTEM
Traffic light controllers found at British road
junctions have the sequence Red, Red/Amber,
Green, Amber, and then Red again.
 We will analyze the corresponding truth tables.

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CIRCUIT IMPLEMENTATION FROM TRUTH
TABLES – SOME PRACTICAL TIPS
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TIP #1: IDENTICAL COLUMNS

The input is directly connected to the output if an
output column is identical to an input column. No
logic is required.

The level crossing Amber output and Y input are
identical and can be expressed as
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TIP #2: NEARLY IDENTICAL COLUMNS

An output can be generated by a simple logic
function from only some of the inputs.

The level crossing Red is the inverse of input X.
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TIP #3: SOLO ROW

Use an AND gate to detect the input row if an
output column only has a single ‘1’.

The level crossing Green can be expressed as
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TIP #3: SOLO ROW (CONT.)

The crossroads Green can be expressed as
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TIP #4: INVERTED SOLO ROW

Use an AND gate to detect the input row pattern, and
then a NOT inverter when an output column only has
a single ‘0’.

Crossroads Red can be expressed as
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TIP #5: STANDARD PATTERNS
Sometimes it is possible to utilize an existing
logic circuit, with minimum modification.
 Let us consider a simple washing machine
controller.


XOR can be used as a ‘difference detector’ as seen in
the motor control output from the following washing
machine example.
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TIP #5: STANDARD PATTERNS (CONT.)

Motor can be expressed as
Motor = (X XOR Y) AND
Z
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TIP #6: ELIMINATION

A shortcut can be taken when considering the Crossroads
truth table.
There are two rows where both X and Z contains ‘1’ and the value of Y
has no effect in determining the output.
 Crossroads Amber can be expressed as

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TIP #7: SUM-OF-PRODUCTS

When these short cuts do not work out, the brute
force method remains:
Run down each output column and mark every row
which contributes a ‘1’.
 Next set up an AND gate pattern detector for each
marked row, using NOT gates on inputs if ‘0’ is
detected.
 Then allocate an OR gate to each output column.

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DECODER LOGIC – ESSENTIAL FOR
CONTROL UNITS AND MEMORIES
The essential purpose of a decoder is to recognize
a code number and invoke the corresponding
action.
 The schematic diagram for a decoder is a box
with more output than input lines.
 ‘Proper’ decoders select a single output line at a
time.
 Example: 74F138 Decoder

3 to 8 line decoder
 Accepts three binary weighted inputs.
 The output selected depends on the input number.
 Ideal for memory chip select decoding.

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EXAMPLE: 74F138 DECODER
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ANOTHER EXAMPLE: SEVEN-SEGMENT
CONVERTER

The seven-segment decoder
has three inputs and eight
outputs and could be
modified to implement a
binary to seven-segment
display converter.

The unit is constructed from
seven LEDs (Light-Emitting
Diodes).
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APPLYING THE BRUTE FORCE METHOD
Using logic
expressions you can
design a sevensegment display
converter driver
circuit.
 The truth table logic
terms for each output
column can be directly
implemented by the
brute force method.

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APPLYING THE BRUTE FORCE METHOD
(CONT.)
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APPLYING THE BRUTE FORCE METHOD
(CONT.)
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USING LOGIC EXPRESSIONS TO DESIGN A
LOGIC CIRCUIT


Logic circuit
for the ‘a’
segment of a
sevensegment
LED driver.
‘a’ can be
derived by
taking the
complement
of ‘inverse a’
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SUMMARY
Truth tables can clearly express logic circuit
functionality by displaying input-output
relationships.
 Some short cuts can be used to speed up the
process of deriving logic circuits from truth
tables.
 Logic minimization may not be the priority when
building circuits.

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