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An introduction to basic logic gates, including NOT, AND, OR, NAND, NOR, XOR, and XNOR. It explains how to represent logic gates using symbols and truth tables, and provides instructions for creating truth tables for specific gates using Yenka software. The document also includes assignments and exercises for practicing logic gate design and simplification.
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There are seven different logic gates; these are the NOT, AND, OR, NAND, NOR, XOR and the XNOR.
When drawing circuits containing logic gates it is common to use logic symbols.
(‘X’ stands for exclusive)
The easiest way to represent how each gate behaves is to make use of Truth Tables.
A Truth Table shows all possible combinations of inputs and outputs to a logic gate.
Electronics is concerned with the processing of electrical signals.
INPUT PROCESS OUTPUT
Input signals come from a variety of sources - a switch from a keyboard; a bar code reader; a temperature sensor; another part of a computer.
Output signals can have a variety of destinations - a monitor; a modem; an alarm; another part of a computer.
Digital signals can be at a HIGH voltage level or a LOW voltage level.
In logic circuits a LOW signal is said to be at logic '0' a HIGH signal at logic ' 1'.
The results can be recorded and used in a number of formats, the most common being shown below.
LOGIC GATE
PROCESS A B
INPUTS OUTPUTS
INPUTS OUTPUTS A B 0 0 1 1
0 1 0 1
0 1 1 0
Results displayed in this way are known as TRUTH TABLES.
It is possible to use circuit simulation software such as ‘Yenka’ to investigate electric and electronic circuits.
Use ‘Yenka’ to determine the truth table for each of the following gates
Use latching logic inputs and a logic indicator at the output.
WATER LEVEL SENSOR
CONTROL PROGRAM
MOTOR
Which logic gate should be used for this operation?
LIGHTLEVEL SENSOR
HEADLAMPS SWITCH
WARNING INDICATOR
Which logic gate should be used for this operation?
TEMPERATURE SENSOR
PULSERATE SENSOR
WARNING ALARM
Which logic gate should be used for this operation?
Complete a truth table for each of the combinations of gates shown below.
Use Yenka to determine the truth table for each of the following network of NAND gates.
Compare the truth table you obtain with truth tables for the individual gates and decide which gate is the equivalent to the NAND network.
In some of the networks the two inputs of the NAND gate have been connected together to make a single input.
(^1 )
3
4 5
6
A
B
C
D
Z
As has previously been stated it is possible to make all logic circuits from NAND gates only.
This section will examine a method for converting circuits that contain a number of different types of gates into one that uses NAND gates only.
Consider the circuit shown.
A
B
B D
C Z
The system is made from an AND gate an OR gate and a NOT gate.
The problem is to design a system with the same Truth Table, but made from NAND gates only.
Redraw the circuit, replacing each gate with its NAND gate equivalent.
This method is not very elegant and can be very demanding in terms of paper use and does not always lead to a very efficient use of NAND gates. The next section on Boolean algebra should allow us to design circuits more effectively and use fewer gates.
The following logic diagrams are constructed from basic gates. Using the method shown, construct equivalent circuits using NAND gates only.
a) Construct a truth table for the logic circuit shown.
A
B
C
b) Redraw the circuit using NAND gates only.
c) Simplify the NAND circuit. d) Construct a truth table for the finished NAND circuit.
Boolean algebra is a special form of algebra that has been developed for binary systems. It was developed by George Boolean in 1854 and can be very useful for simplifying and designing logic circuits.
VARIABLES:
The most commonly used variables in logic circuit design are capital letters; such as A, B, C, Z and so on and are used to annotate inputs and outputs to systems.
In digital electronics we consider situations where the variables can only have one of two possible values, i.e. 'Logical 0' or 'Logical 1'.
The statement A = 1 means that the variable A has the value of Logic 1. Similarly, if B = 0 it means that variable B has the value of logic 0.
Logical Operations: In Boolean algebra there are three logical operators, these are the AND operation, the OR operation and the Inversion.
The NAND gate is made up from a combination of an AND gate followed by a NOT gate.
A B Z
C
The signal at point C would be A B. This signal is then inverted by the NOT gate to give
A B Z
This reads as output Z is equal to A AND B all NOT
NOR GATE
The NOR gate is made up from a combination of an OR gate followed by a NOT.
A B Z
C
The signal at point C would be A+B. This signal is then inverted by the NOT gate to give
A B Z
This reads as output Z is equal to A OR B all NOT
Write down the Boolean expression for each of the following logic gates.
A B
Z
a)
A B
Z
d)
A B (^) Z C
g)
A B
Z
b)
A (^) Z
e)
A B (^) Z C D
h)
A B
Z
c)
A B Z C
f)
A B (^) Z C D
i)
The following is a summary of the basic laws of Boolean algebra.
A represents A bar i.e. NOT A ( the inverse of A)
Consider the following circuit.
a) b)
c) d)
A B
C D
e) f)
A B
C
A
B
A B
C
A B
C
(i) Write a Boolean expression for each of these circuits; (ii) By constructing a truth table for each of them, show that they are equivalent; (iii) Draw the equivalent arrangements using only 2-input NAND gates.
a)
A B
A B
b)
A B
A
B
B
A
B
B
A
B
B
A
B
B A
B
B
