Lab 1:Logic Gate Systems :

1
Lab 1Logic Gate Systems
Binary Number System
Slide 2
Decimal Numbers
Slide 3
Binary Number Conversion
Slide 4
Switches and LEDs
Slide 5
The NOT gate
Slide 6
The OR gate
Slide 7
The AND gate
Slide 8
NOR Gate
Slide 9
NAND Gate
Slide 10
XOR and XNOR Gate
Slide 11
NOR / NAND Alternate Symbols
Slide 12
Rule for using alternate symbols
Slide 13
Logic Gate Equations
Slide 14
Vending Machine System
Slide 15
2
Lab 1 Binary Number System
We will use a car odometer to learn about the
binary number system. A car odometer
(non-digital) consists of a series of plastic
discs that rotate to track the distance traveled
by a car.
A decimal odometer has the outer edge of each
disc numbered from 0 9. Three discs will allow
the odometer to record a maximum distance
traveled of 999 Kms.
A binary odometer has the outer edge of each disc
numbered with only 0 and 1. Using 3 discs will
allow the odometer to record a maximum distance
traveled of 111 binary Kms or 7 kms.
Proceed to watch the odometer in action.
1
1
1
1
3 Bit Binary
From the odometer example, you can place the 3
bit numbers in a table and see the order of the
first 8 binary numbers.
Slide 2
3
Lab 1 Decimal Numbers
Reviewing some fundamental facts about the
decimal number system will help you learn the
binary number system.
The decimal positional weight chart (PWC). Each
numeral of a decimal number occupies a position
that has a weight. Here is the decimal PWC.
5
3
2
The weight of each position have been given names.
A decimal point is used to separate the whole
part and the fractional part of a number.
Here is the decimal number 235 placed in the PWC.
Slide 3
4
Lab 1 Binary Number Conversions
Digital systems process data in binary format. It
is important to know how to convert back and
forth from binary to decimal.
Binary numbers are part of a base 2 number
system. Only two numerals exist 1 and 0.
Converting binary to decimal Drop the binary
number into the binary PWC to convert it to
decimal. Example convert 11012 to decimal.
Or
Binary PWC
1x8 1x4 0x2 1x1 8401 1310
Converting decimal to binary Example convert
2510 to binary Write down a binary PWC which the
MSB (most significant bit) surpasses the number
you are trying to convert.
Work from MSB and use a 1 to include the bit
position and a 0 to exclude it. The included bits
should have their weight add up to the number
being converted.
Exclude because 16 8 2 will exceed 25.
Include because 16 8 1 will equal 25.
Include because 16 8 does not exceed 25.
Include because 16 does not exceed 25.
Exclude because 16 8 4 will exceed 25.
Exclude because it would make number larger than
25
0
1
1
0
0
1
Slide 4
5
Lab 1 Switches and LEDs
Students can create and test digital systems by
using switches to represent binary input data and
using LEDs (light emitting diode) to represent
binary output data.
Digital systems have an input side and an output
side. Each arrow is a connection wire.
The inputs of a digital system are binary digits
(bits). You either input a binary 1 (logic 1) or
a binary 0 (logic 0). The digital system
processes the signals you have applied to the
input and responds with binary 1 or binary 0 at
the output(s).
5 volts represents a logic 1 and a 0 volts (also
called GROUND or Gnd) represents a logic 0. The
digital system is powered up by a 5 Volt power
supply.
A switch can be used to input a logic 1 and logic
0. An LED can be connected to the output to see
the digital systems response. Continue and you
will see the switch and LED in action.
Slide 5
6
Lab 1The NOT Gate (inverter)
The NOT gate is the first of the three
fundamental logic gates. You will learn its
operation using Truth Table analysis and an
animation.
Truth Table Is a chart that lists the input
condition on the left and the gates output
response on the right. The table shows that the
NOT gate responds at the output with the inverse
of the signal applied to the input.
Animation In order to see how it works, the gate
has been connected to a switch and LED. Continue
to see the system in action
Slide 6
7
Lab 1 The OR Gate
The OR gate is the second of three fundamental
logic gates. You will learn its behaviour using a
Truth Table analysis and an animation.
Truth Table The table shows that the OR gate
responds with a high at the output if the signal
applied to the input A or B is high.
Animation In order to see how it works, the gate
has been connected to 2 switches and LED.
Continue to see the system in action
Slide 7
8
Lab 1 The AND Gate
The AND is the last of the remaining fundamental
logic gates. You will learn its behaviour using a
Truth Table analysis and an animation.
Truth Table The table shows that the AND gate
responds with a high at the output if the signal
applied to the input A and B are both high.
Animation In order to see how it works, the gate
has been connected to 2 switches and LED.
Continue to see the system in action
Slide 8
9
Lab 1 NOR Gate
The NOR gate is equivalent to an OR gate with a
NOT gate connected to its output. NOR comes from
the words Not OR. Continue to see the standard
symbol for NOR.
NOR Symbol
Truth Table The table shows that the NOR gate
responds with a low at the output if the signal
applied to the input A or B is high.
System animation In order to see how it works,
the gate has been connected to 2 switches and
LED. Continue to see the system in action
Boolean Equation here is the equation for the
NOR gate.
Slide 9
10
Lab 1 NAND Gate
The NAND gate is equivalent to an AND gate with a
NOT gate connected to its output. NAND comes from
the words Not AND. Continue to see the standard
symbol for NAND.
NAND Symbol
Truth Table The table shows that the NAND gate
responds with a low at the output if the signal
applied to the input A and B is high.
System animation In order to see how it works,
the gate has been connected to 2 switches and
LED. Continue to see the system in action
Boolean Equation here is the equation for the
NAND gate.
Slide 10
11
Lab 1 XOR Gate
The XOR gate is an exclusive OR gate. It will
output a logic 1 if there is an exclusive logic 1
at input A or B. Exclusive means Only one input
can be high at one time.
Truth Table The table shows that the XOR gate
responds with a high at the output if the signal
applied to the input A or B is high (but not both
high).
XOR Boolean Equation
The XNOR gate is an exclusive OR gate with an NOT
gate at the output. It will output a logic 0 if
there is an exclusive logic 1 at input A or B.
XOR Boolean Equation
Slide 11
12
Lab 1 NOR and NAND Gate Alternate Symbols
The NAND and NOR logic gate symbols you have
studied are called the standard symbols. Each
gate also has an alternate symbol.
The standard logic symbols for the NAND and NOR
gates indicates a gates response to logic 1 at
the input.
Alternate NOR GATE The bubbles at the input of
the NOR gate implies that a logic 0 at input A
and a logic 0 at input B are required to
produce a logic 1 at output X (NO bubble at
output).
Alternate NAND GATE The bubbles at the input of
the NAND gate implies that a logic 0 at input A
or a logic 0 at input B are required to produce
a logic 1 at output X (NO bubble at output).
Slide 12
13
Lab 1 Rule for Using the Alternate symbols
The basic logic gates AND, OR, and NOT have
standard logic symbols and alternate logic
symbols. A general rule for using alternate
symbols exists. The rule is a guide and not a
strict rule. Some designers do not use the rule
but many do.
Standard
Alternate
The rule is simple Active high device connects
to active high symbol Active low device
connects to the active low symbol.
Example Connect an LED to an AND gate There
are two types of LED connections.
Active high device connects to active high symbol
(standard).Active low device connects to the
active low symbol (alternate).
Slide 13
14
Lab 1 Logic Gate Equations
Each logic gate has a Boolean equation to
represent its operation.
Slide 14
15
Lab 1 Vending Machine System
Design a logic system for a vending machine that
will dispense a 75 cent surprise gift package if
any of the following conditions occur Three
quarters are inserted. A dollar is inserted. The
machine can only accept quarters and a dollar
coin / note.
Step 1 Declare Inputs and Outputs Inputs
Quarters (Q1, Q2, Q3). Dollar (L). Logic 1
currency present. Outputs Package (P). Quarter
Change (C). Logic 1 dispense item.
Q1 Q2 Q3

L
L
Step 2 Generate Equation for the
system Dispense Package if Quarter1 and
Quarter2 and Quarter3 OR Dollar is inserted.
Dispense change if dollar is inserted. P Q1
Q2 Q3 L C L
Once the system diagram is complete it can be
used to test the operation of the system. Here is
what happens when someone inserts 3 quarters.
P-Term thus P L
Here is what happens when someone inserts a
dollar.
Here is what happens when someone searches their
pocket finds a quarter and inserts it into the
machine. Then they realize that they do not have
2 more quarters! If they insert a dollar what
would be the result?
Step 3 Draw the Digital System Diagram Group
variables that are ANDed together into a single
block. This block is called product term
(P-Term).
The result The package and the change would be
dispensed. The un-happy user of the machine would
have paid 1 (1.25 - 0.25 change). To resolve
this problem an extra change output could be
added.
Work from output towards input. P must be
connected to an OR gate.
Re-insert the P-Term (Q1 Q2 Q3). A 3 input
AND gate is required.
Slide 15
Connect L to OR gate and connect C to L (CL).