UNIVERSITY OF GONDAR
INSTITUTE OF TECHNOLOGY
Department of Electrical and Computer Engineering
course name: digital logic design
course code: ECEG3141
course instructor: Amare worku
contact information:
email: amareworku2154@gmail.com
consultation hours: Friday: from 8:00-11:00
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CHAPTER THREE
Logic gates
The inverter
The AND gate
The OR gate
The NAND gate
The NOR gate
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BOOLEAN CONSTANTS AND VARIABLES
A Boolean variable is a quantity that may, at different times, be equal
to either 0 or 1.
Boolean variables are often used to represent the voltage level present on a
wire or at the input/output terminals of a circuit.
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Cont.….
Boolean 0 and 1 do not represent actual numbers but instead represent the state of a
voltage variable, or what is called its logic level.
A truth table is a means for describing how a logic circuit’s output depends on the
logic levels present at the circuit’s inputs.
A logic gate is a circuit with several inputs but only one output that is activated by
particular combinations of input conditions.
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NOT Gate (INVERTER)
This gate always has only a single input, and its output logic level is always opposite to the
logic level of this input.
It inverts (complements) the input signal at all points on the waveform so that whenever the
input is 0, output is 1, and vice versa.
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Timing diagram
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AND Gate
The AND gate output is equal to the AND product of the
logic inputs; that is, Y = AB.
In other words, the AND gate is a circuit that operates so that
its output is HIGH only when all its inputs are HIGH.
For all other cases, the AND
gate output is LOW.
This same operation is characteristic of AND gates with more
than two inputs.
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Cont.….
An example of wave form output for wave
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form inputs A and B
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Cont.…
AND logic gate operates similarly to control devices connected in series.
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Cont.….
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Cont.…
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OR gate
The OR operation produces a result (output) of 1 whenever any
input is a 1. Otherwise the output is 0.
An OR gate is a logic circuit that performs an OR operation on the
circuit’s inputs.
The expression x = A + B is read as “x equals A OR B.”
The plus sign is different from the ordinary addition.
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Cont.…
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Cont.….
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NOR Gate
It is the same as the OR gate symbol except that it has a small circle on the
output.
The small circle represents the inversion operation.
Thus, the NOR gate operates like an OR gate followed by an INVERTER.
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Cont.….
Equivalent to NOR gate
Truth table
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Cont.….
An example of wave form output for wave
form inputs A nor B
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NAND gate
The symbol for a two-input NAND gate is the same as the AND gate
symbol except for the small circle on its output.
Once again, this small circle denotes the inversion operation.
Thus, the NAND operates like an AND gate followed by an INVERTER.
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Cont.…
Truth table
Equivalent for NAND gate
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Exclusive-OR gate
The standard symbol for the exclusive-OR gate(XOR in short form) is shown below.
It has only two input.
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Cont.…..
The output of the exclusive OR gate is high only when the two inputs are at opposite
logic level.
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The pulsed wave form of exclusive OR gate is
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Exclusive-NOR gate
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Cont.…..
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Cont.…
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