MELJUN CORTES Logic Gates

8/8/2019 MELJUN CORTES Logic Gates

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used to process information in computers

o erate on the binar variables that are

symbolically represented by the values 0 and 1(LOW and HIGH logic)

deals with binary variables and logic operationsapplied on these variables

Logic Gates * Property of STI Page 1 of 26


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a special kind of electronic device which can beused for many important functions

in computers, it is used to serve as a switch,either ON or OFF



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Two Unary Operators:

buffer

NOT


the symbol “ ” can be used interchangeably withthe symbol “ ’ ”

A = A’ = C


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Logic diagram

com osed of lo ic ates which are the visual

representation of the operators as well as someof their combinations



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TTL Transistor-Transistor Logic

-.

MOS Metal-Oxide Semiconductor

CMOS Complementary MOS

BiCMOS Bipolar CMOS

I2L Integrated-Injection Logic

GaAS Gallium Arsenide



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has a high output only when all its inputs arehigh

F = A • B or F = AB

Truth table:



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with (a) two inputs and (b) N inputs with N = 4.


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Consider the Boolean expression

A • B • C =

where the inputs A, B , and C can have anybinary value. Implement the expression using athree-input AND gate. Get all possible inputcombinations and their corresponding values forthe output F .

Solution:



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Truth table:


= =

A • B • C = F

Cascade

to connect the output of one gate to one of theinputs of another making a chain of gates andeffectively creating a product of products


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Consider the Boolean expression

A • B • C • D • E = F

where we need to implement a digital circuitusing only binary input AND gates. Sinceseveral combinations exist for solving theproblem, consider at least two solutions using aminimum amount of gates.

Solution:



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output voltage is high if any or all of the inputvoltages are high

algebraically represented by a “+” symbol

can be thought of as having switches in parallel,with each switch corres ondin to an in ut node



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Similar to the case of Example 2, provide thenecessary OR gate implementation for the

Boolean expressionA + B + C = F

What will the result be if the inputs are:

1) A = logic 0; B = logic 0; C = logic 0

2) A = logic 1; B = logic 1; C = logic 1

Solution:

1) A+ B+ C = 0 + 0 + 0 = 0

2 A+ B+ C = 1 + 1 + 1 = 1



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Implement the Boolean expression of Example3 using only binary gates with the following

configurations:a) using two OR gates in cascade

b) using a two-level hierarchical approach

Solution:



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Truth Table for the Three-Input OR Gate



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a gate with only one input signal and only oneoutput signal

the output state is always the opposite of theinput state

Ao = A’ I

Truth table:



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represented either by a “ ’ “ or “ “ symbol

the sole ur ose is to invert or ne ate the fed

to it

The symbols for (a) NOT and (b) buffer

Two Types of Pushbutton Switches



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an abbreviation for NOT AND

can also be re resented b an AND ate with a

bubble at the output all input signals must be high to produce a low

output

F = A’B’


Truth Table


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an abbreviation for NOT OR

can be re laced b an OR ate with a bubble at

the output all inputs must be low to produce a high

output

F = (A + B)’


Truth Table


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The (a) NAND and (b) NOR used as inverters


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Exclusive-OR operator

s mbolicall re resented b “ ”

similar in output to an OR gate except that theXOR gate produces a 0 output when bothinputs are 1



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XOR Truth Table

XNOR

is simply the XOR followed by an inverter

its operator is usually written as “ “


XNOR Truth Table


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Truth Table for Three-Input XOR


the output of the 3-input XOR is 1 if only oneinput is equal to 1 or if all the three inputs areequal to 1 (or when the total number of 1’s is

odd)


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Truth Table for Three-Input XNOR

even function

simply the opposite of the XOR function

when all inputs are 0 or for even occurrencesof a 1 as an input, the output is 1

MELJUN CORTES Logic Gates

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