Logic Gates

Logic Design and Switching

* Property of STI

Page 1 of 26

used to process information in computers

operate on the binary variables that are

symbolically represented by the values 0 and 1

(LOW and HIGH logic)

deals with binary variables and logic operations

applied on these variables

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Logic Gates

Logic Design and Switching

* Property of STI

Page 3 of 26

Two Unary Operators:

buffer

NOT

the symbol “ ” can be used interchangeably with

the symbol “ ’ ”

A = A’ = C

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Logic Gates

Logic Design and Switching

* Property of STI

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a special kind of electronic device which can be

used for many important functions

in computers, it is used to serve as a switch,

either ON or OFF

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Logic Gates

Logic Design and Switching

* Property of STI

Page 4 of 26

Logic diagram

composed of logic gates which are the visual

representation of the operators as well as some

of their combinations

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Logic Gates

Logic Design and Switching

* Property of STI

Page 5 of 26

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Logic Gates

Logic Design and Switching

* Property of STI

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Logic Gates

Logic Design and Switching

* Property of STI

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TTL Transistor-Transistor Logic

ECL. Emitter-Coupled Logic

MOS Metal-Oxide Semiconductor

CMOS Complementary MOS

BiCMOS Bipolar CMOS

I2L Integrated-Injection Logic

GaAS Gallium Arsenide

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Logic Gates

Logic Design and Switching

* Property of STI

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has a high output only when all its inputs are

high

F = A • B or F = AB

Truth table:

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Logic Gates

Logic Design and Switching

* Property of STI

Page 9 of 26

The equivalent to the AND gate using switches

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

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Logic Gates

Logic Design and Switching

* Property of STI

Page 11 of 26

Truth table:

XYZ = X(YZ) = (XY)Z is equivalent to

A • B • C = F

Cascade

to connect the output of one gate to one of the

inputs of another making a chain of gates and

effectively creating a product of products

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Logic Gates

Logic Design and Switching

* Property of STI

Page 10 of 26

Consider the Boolean expression

A • B • C = F

where the inputs A, B, and C can have any

binary value. Implement the expression using a

three-input AND gate. Get all possible input

combinations and their corresponding values for

the output F.

Solution:

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Logic Gates

Logic Design and Switching

* Property of STI

Page 12 of 26

Consider the Boolean expression

A • B • C • D • E = F

where we need to implement a digital circuit

using only binary input AND gates. Since

several combinations exist for solving the

problem, consider at least two solutions using a

minimum amount of gates.

Solution:

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Logic Gates

Logic Design and Switching

* Property of STI

Page 13 of 26

output voltage is high if any or all of the input

voltages are high

algebraically represented by a “+” symbol

can be thought of as having switches in parallel,

with each switch corresponding to an input node

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Logic Gates

Logic Design and Switching

* Property of STI

Page 15 of 26

Implement the Boolean expression of Example

3 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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Logic Gates

Logic Design and Switching

* Property of STI

Page 14 of 26

Similar to the case of Example 2, provide the

necessary OR gate implementation for the

Boolean expression

A + 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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Logic Gates

Logic Design and Switching

* Property of STI

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Truth Table for the Three-Input OR Gate

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Logic Gates

Logic Design and Switching

* Property of STI

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a gate with only one input signal and only one

output signal

the output state is always the opposite of the

input state

Ao = A’I

Truth table:

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Logic Gates

Logic Design and Switching

* Property of STI

Page 19 of 26

an abbreviation for NOT AND

can also be represented by an AND gate 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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Logic Gates

Logic Design and Switching

* Property of STI

Page 18 of 26

represented either by a “ ’ “ or “ “ symbol

the sole purpose is to invert (or negate) the fed

to it

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

Two Types of Pushbutton Switches

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Logic Gates

Logic Design and Switching

* Property of STI

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an abbreviation for NOT OR

can be replaced by an OR gate 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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Logic Gates

Logic Design and Switching

* Property of STI

Page 21 of 26

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

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Logic Gates

Logic Design and Switching

* Property of STI

Page 23 of 26

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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Logic Gates

Logic Design and Switching

* Property of STI

Page 22 of 26

Exclusive-OR operator

symbolically represented by “ ”

similar in output to an OR gate except that the

XOR gate produces a 0 output when both

inputs are 1

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Logic Gates

Logic Design and Switching

* Property of STI

Page 24 of 26

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Logic Gates

Logic Design and Switching

* Property of STI

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Truth Table for Three-Input XOR

odd function

the output of the 3-input XOR is 1 if only one

input is equal to 1 or if all the three inputs are

equal to 1 (or when the total number of 1’s is

odd)

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Logic Gates

Logic Design and Switching

* Property of STI

Page 26 of 26

Truth Table for Three-Input XNOR

even function

simply the opposite of the XOR function

when all inputs are 0 or for even occurrences

of a 1 as an input, the output is 1

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