# Introduction: false values for a circuit (true=1,

Introduction:

This is a report based on the
experiments shown above. In the report, information about the different methods
used is presented, as well as the outcome, results, advantages and
disadvantages of the used methods is presented.

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Background:

*Truth table, what is used to determine all the true or
false values for a circuit (true=1, false=0).

To be able to determine the Boolean expression you have to
start by making a truth table.

*Boolean Expression, states what type of gate is used. For
example if the gate used is a NAND gate the Boolean Expression would ”NOT A
AND B” (The output is positive when A and B has different values or both are
negative 0.

A=0, B=0   Output=1

A=0, B=1  Output=1

A=1, B=0  Output=1

A=1, B=1 Output=0

JK Flip Flop

Has 2 inputs (J and K), If J and K are not the same output Q
gets the value of J at the the upcoming clock edge.

If J and K are low, no change is detected. Id J and K are
high at the clock edge, the output= toggle from one position to the next.

Asynchronous Combinational Logic

The JK Flip Flops depend on each other (are daisy chained).
The signal has to travel through all of the JK flip flops to reach the output.

(Hyperphysics.phy-astr.gsu.edu,
2018)

Apparatus:

In this lab the equipment needed is:

Tutor board consisting of 4 distinctive fields set up for
combinational logic experiment.

Field 1 consists of LEDs and switches.

Field 2 consists of gates and resistors

Field 3 consists of Flip Flop (74112) and NAND (7400)

Field 4 consists of seven segment display and driver and
debounced switch section.

Wire connectors

Method:

In the experiment, there was a number of circuits that were
constructed using the material provided.

In part, one of the experiment Field 1 and 2 were used,
along with wire connectors.

After the circuit was constructed:

Using the switches and LEDs, the truth table was filled out
by following what happened on the circuit:

When the LED is turned on the output is 1, if the LED stays
of the output is 0.

When the truth table was filled out the Boolean Expression
could be calculated.

In the second
part of the experiment the used material was Field 3 and 4, along with wire
connectors.

Using the pictures provided the circuits where constructed
to determine which LED represents the LSB and which one the MSB by filling out
the truth table by reading the results of the LEDs.

In the third
part of the experiment the used material was Field 3 and 4, along with wire
connectors.

In this step, the LEDs were still used to get the results to
fill out a truth table but an LED display was added to display what sequences
the circuit went through.

*See figure 9.

The seven segment display was connected to a driver chip
(7447)

Using the 4 LEDs the truth table was determined, the LED
display also showed the numbers that the circuit  clocked through.

Results:

In the first part of the experiments (fig a to e):

The results showed that all the circuits constructed where
combinational logic, this is proved because these types of circuits logical
functions output only depends on the current combination of the input values.

Combinational logic circuits also gave Boolean functions and
only functions based on their inputs.

The circuits to respond the quickest is circuit a and b,
this because there is only one gate, the signal traveling through the circuit
will reach the output faster.

In the second part of the experiment ( table 1, fig7)

It was shown that the circuit resets after 9 steps including
PRESET, CLEAR AND CLOCK 1.

*The circuit goes through 9 steps befor it restarts its
sequence.

(Table 2, fig 8) The circuit resets at 16.

(Table 3, fig 11)
The LED display was added to in more than one way (truth table) also
show what sequence the circuit goes through showing us numbers/figures.

The circuit restarts
at 15. But the display is only capable of displaying numbers up to 9, single
digit numbers (this results in the display showing nonsense signs instead of
numbers when it passes the number 9.

(Table 4, fig 13)

The circuit goes through 0 to 9 (0 = clock 1) and resets
back to 0 directly after 9 unlike figure 11.

*Sequins of 10 numbers, 0 to 9.

In figure 11 the counter counts up to 15 while in figure 13
the counter only counts up to 9 before it resets.

The LED display in both examples can only show one digit,
this result in gibberish/nonsense (signs that are not related to numbers
containing more than one digit) shown on the display.

This is was achieved because of the NAND gate.

Questions:

1)
The results showed that all the circuits
constructed where combinational logic, this is proved because these types of
circuits logical functions output only depends on the current combination of
the input values.

Combinational logic circuits also gave Boolean functions and
only functions based on their inputs.

1)
Circuits a and b will respond the quickest.

2)
Because there is only one gate, the signal
traveling through the circuit will reach the output faster.

1)
In figure 11 the counter counts up to 15 while
in figure 13 the counter only counts up to 9 before it resets.

The LED display in both examples can only
show one digit, this result in gibberish (signs that are not related to numbers
containing more than one digit) shown on the display.

2)
Because of the NAND Gate.

3)
The major disadvantage of asynchronous counters
is that all the JK flip flops depend on each other (are daisy chained). The
signal has to travel through all of the JK flip flops to reach the output.

The signal goes through JK1 to JK2, JK2 to
JK3 and so on. If the one of the JK Flip Flops would have a defect or the
circuit would be broken the outcome would be faulty.

Analysis:

In the experiments one of the things that was discovered was
that if the number of Flip Flop gates used doubles (in this case from 2 to 4)
the counter can go through more segments before it resets (Fig 7 and 8).

If a NAND gate is added to an Asynchronous 4 bit JK Flip
Flop counter with a 7 segment display the counter will go through less segments
of numbers/signs.

Conclusion:

In the experiment it is shown
that adding more parts to a circuit affects the outcome and gives different results.