At the end of this topic, studentsshould be able to:

a) Identify symbol for logic gate

Chapter Two

Computer System2.4.2 Logic Gate

Logic Gates• An electronic circuit operates on one or

more input signals to produce an outputsignal.Gates are digital (two-state) circuits and can•be analyzed withThe circuit whichcalled OR gateThe circuit which

Boolean algebra.• performs OR operation is

• performs AND operationis called AND gate.

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Electrical Switches• Electrical switches are good examples to

illustrate OR, ANDtheorems.

and many Boolean

• closed = 1, open = 0, ON = 1 and OFF = 0

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Behaviourparallel

of two switches in

Truth table for OR operation/gate

• 0 (false) and 1 (true)

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Cont....• When two switches connected in series as

shown below, the lamp will light up whenboth A and B are closed. Table 6 shows thebehaviour of two switches in series circuit.

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Behaviour of Two Switches in Series

Truth Table for AND gate

• 0 (false) and 1 (true)

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Definition Boolean Algebra• The basic rules for simplifying and combining logic

gates are called Boolean algebra in honour ofGeorge Boole (1815-1864).

••

has either of two values: true or falseThere are two types of operator:

Unary – NOT Binary – AND, OR

(l or 0).

Eg : Y = A • B, Y = AB, Y = A + B, Y = Ā1 = 1.1 , 1 = 1x1 , 1 = 1+0, 1 = Ō

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Logic Gates

These gates are:

AND gate OR gate NOT gate

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Logic Gates

More gates

– Universal gates :

NAND-gate

NOR-gate

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Truth Table• A truth table is a good way to show the

function of a logic gate.It shows the output states for every possible•combination of inputThe symbols 0 (false)

states.and 1 (true) are used• in

truthFor a

tableslogic gate with n inputs, there are• 2n

entries in the truth table.Example: A logic gate with three inputs, A,• B

23and C will contain = 8 entries.10

AND ( Logicoperation)

Gate , Truth Table, Boolean

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OR ( Logicoperation)

Gate , Truth Table, Boolean

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NOT ( Logic Gate , Truthoperation)

Table, Boolean

• The NOT gate has one binaryinput and one binary output.The NOT gate's output is theinverse of its input.~0 = 1 is read as NOT 0equals to 1line over A is pronouncedNOT

•

•

•

• Y = Ā is read as “Y equals NOT

(¬A), (A’),

A”(~A),(Ā)

(!A ),13

NAND Operator

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NOR Operator

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Explain the following logic gates:

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Exercise

Write a boolean expression and draw the truth table to represent thislogic circuit diagram.

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