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# Introduction to Digital Electronics

Introduction to Digital Electronics in Preparation for Computer Fundamentals (Hardware)
by

## Dennis Garcia

on 29 January 2017

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#### Transcript of Introduction to Digital Electronics

INTRODUCTION
TO
DIGITAL ELECTRONICS
(Computer Hardware) Digital Signal Lecture 3 Lecture 4 Flip Flops By Engr. D. Garcia Digital electronics, or digital (electronic) circuits, represent signals by discrete bands of analog levels, rather than by a continuous range. ANALOG SIGNAL
- continuous
- Infinite set of value
- can easily affected by noise
- high resolution DIGITAL SIGNAL
- discrete values
- switches between two voltage levels to represent the two states of Bolean Value "1" and "0".
- noise Immunity
- signal regeneration BINARY SYSTEM (BASE 2) DECIMAL SYSTEM (BASE 10) 0 1 2 3 4 5 6 7 8 9 1 0 ON OFF
HIGH LOW
CLOSE OPEN
PULL PUSH
TRUE FALSE 0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001 Counting
in Base 10 Counting
in Base 2 Binary Counting 10^7 10^6 10^5 10^4 10^3 10^2 10^1 10^0 10,000,000 1,000,000 100,000 10,000 1,000 100 10 1 1 2 3 4 5 6 7 8 TWELVE MILLION THREE HUNDRED FORTY FIVE THOUSAND SIX HUNDRED SEVENTY EIGHT THIS IS EQUAL TO:
1X10,000,00 +
2X1,000,000 +
3X100,000 +
4X10,000 +
5X1000 +
6X100 +
7X10 +
8X1 BASE 10 BASE 2 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0 128 64 32 16 8 4 2 1 1 0 0 1 0 1 1 1 = 128+0+0+16+0+4+2+1
= 151 IN YOUR POINT OF VIEW
WHY COMPUTERS USES BINARY? Some reasons are:
1.) Binary switches and devices that show two states either ON or OFF is much easier to build and cheap.
2.) Creating a computer higher than Binary might be very expensive since it must be very sensitive to store different value/states.
3.) You will be needing a very stable current to supply your computer.
4.) Transmitting data in a long distance will diminish the current. Signal regeneration is much more effective in binary. Boolean algebra (logic) Developed by
George Boole 1854 -the algebra of truth values 0 and 1 -based on two-valued or binary systems Binary systems
were known in the ancient Chinese civilization and by the classical Greek philosophers who created a well structured binary system, called propositional logic. Propositions may be TRUE or FALSE, and are stated as functions of other propositions which are connected by the three basic logical connectives: AND, OR, and NOT. For example the statement: “I will take a raincoat with me if it is raining or the sky is cloudy." OR Rain Cloudy Sky Raincoat Cloudy Raining Umbrella
False False False
False True True
True False True
True True True “If I do not take the car then I will take the raincoat if it is raining or the atmosphere is cloudy” Rain Cloudy Sky Car Raincoat
False False False
False False True
False True False
False True True
True False False
True False True
True True False
True True True OR Rain Cloudy
Sky NOT CAR AND Take Raincoat (Take Raincoat (U)) = ( NOT (Take Car (C) ) ) AND ( (Cloudy Sky (S) ) OR (Raining (R) ) ) 1.) Logic Operation Precedence
( ) Parenthesis - Highest
' NOT
. AND
+ OR - Lowest

2.) NOT Operator
(A')' = A (Double Negation or Involution
law,)
A . A' = 0 (Complement)
A + A' = 1 (Complement)

3.) Associative
(A B) C = A (B C)
(A + B) + C = A + (B + C)

4.) Commutative
A B = B A
A + B = B + A

5.) Distributive
A (B + C) = A B + A C
A + (B C) = (A + B) (A + C)

6.) Indempotent
A A = A
A + A = A

7.) Annulment
A 0 = 0
A + 1 = 1

8.) Identity
A , 1 = A
A + 0 = A

9.) de Morgan’s theorem
(A + B)' = A' B'
(A B)' = A' + B'

Ex. Simplifying
A + A (B) = A (proof: A + A B = A (1 + B) = A 1 = A)
A (A + B) = A (proof: A A + A B = A + A B = A ) Rules in Boolean Expressions U = C' . (S+R) Logic Gates Circuit Graphic Symbol Relay Transistor Boolean Function Truth Table Buffer X = A Inverter
(NOT) X = A' AND X=AB OR X = A + B NAND X = (AB)' NOR X = (A+B)' Exclusive OR
XOR Exclusive NOR
XNOR These gates are the fundamental building blocks of digital circuits. In fact it would be possible to build any digital circuit using just NAND gates or just NOR gates. NOR and NAND gate
Building Blocks of Digital Circuits NOT Gate Indempotent law:
A.A = A therefore (A.A)' = A' To create an AND gate we apply the Involution
law,
(A')' = A
making use of our newly designed inverter: AND gate OR gate To make an OR gate we need to apply de
Morgan's theorem:
A+B = (A' . B')' SEAT WORK

Can you build every gate you need from the
NOR gate? Source: http://www.doc.ic.ac.uk
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