**FULL EDITION** A comprehensive summary of IT Theory on a Grade 11 Level. It contains all the necessary information in a colourful, table format. Diagrams of complex topics have been included. All information has been typed for improved legibility. These notes have been used by hundreds of learner...
exploring it theory grade 11 2nd ed isbn 9780639903682
data representation and boole
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Zeyn Mahomed LV 2021
Adapted from - EXPLORING IT: THEORY Gr 11 2ND ED (Funworks Publication)
Complete Notes
IT Theory - Grade 11
LU1 Data Representation and Boolean Logic
1. Word Size
2. Possible Combinations of a Fixed Number of Bits
3. Binary Addition
4. Representing Integers in a Fixed Number of Bits
5. Representing Real Numbers
6. Compression Techniques
7. Screen Resolution
8. Truth Tables
LU2 Hardware
1. CPU Design
2. RAM
3. Motherboard
4. Secondary Storage
5. Other Types of Caching
LU4 Local Area Networks
1. Overview of Physical Aspects
2. Bounded Connection Media
3. Unbounded Connection Media
4. Broadcast vs Point-to-Point Communication
5. Topology
6. Ethernet
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7. Network Addressing
8. Internet Protocols
9. LAN Network Devices
10. OSI Model
11. Wireless LAN
LU5 Wide Area Networks
1. Fibre Optic Backbone
2. WAN
3. Devices
4. Transmission
5. Internet Connection Technologies
6. Protocols
LU6 Internet
1. Evolution of the Internet
2. Web-Based Applications
3. Mobile Websites
4. Mobile Applications
5. Design Factors for Mobile Technology
6. Plug-Ins and Extensions
7. Search Engines
8. Using Multimedia Online
9. Compression Technology
LU7 Errors, Threats and Security
1. Sources of Errors
2. Solutions for Errors
3. Database Management System Integrity
4. Threats to Computer Systems
5. Security Solutions
LU8 Social Implications
1. Effect on Workplace and Employment Practices
2. Effects of Computer Crime
3. Safeguards against Computer Crimes
4. Evaluating Information
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LU1 - Data Representation and Boolean Logic
1. Word Size
Word Size ● The number of bits that the CPU of a computer can work with at one time -
amount of data that a CPU register can hold and manipulate at any one time.
● A word is a unit of data defining the number of bits that move around a
computer from one component to another. They are stored in components and
are processed.
● Buses (transporters of data) are built with 32 bits (4 bytes) and 64 bits (8 bytes).
● CPUs, components and OS are built to accommodate the bus sizes and allow the
computer to function as efficiently as possible.
2. Possible Combinations of a Fixed Number of Bits
Possible ● 0 = “off”, 1 = “on”
Combinations ● Bits are grouped in multiples of 8 in registers or buses
● Number of combinations is calculated as 2n where n is the number of bits: (24) =
16 combinations
3. Binary Addition
Rules
Carry: 1
02 02 12 12 1 + 1, the answer cannot be 2, so a 0
is written down and the 2 is carried
+ 02 + 12 + 02 + 12
as 1 in the column to the left
______ ______ ______ _______
02 12 12 1 02
Steps Add 47 and 31 by converting them to binary, then convert them to decimal after
addition.
Step 1: Step 2: Step 3:
Convert to Binary: Add: Convert to Binary:
Binary to Decimal
Decimal to Binary
● Continuously divide by 2 ● Order the binary number
in columns with
● Write down the 111111 increasing powers of 2
remainder 1011112
● Going from right to left,
● Repeat until the quotient + 111112
starting at 0
is 0 __________
= 10011102 ● Multiply the bit by the
● Read the remainders
power of 2 in its column
from bottom to top
10011102 = 7810
4710 = 1011112
3110 = 111112
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4. Representing Integers in a Fixed Number of Bits
Representing Integers ● All numbers that are stored in a computer are represented by a fixed
number of bits usually dictated by the word size
● Integers and their subtypes (byte, short, long) are all allocated a fixed
number of bits
● By limiting the number of bits to store the number, the number can no
longer be infinite, but has a minimum and maximum value associated
with the type - negative numbers cannot be represented (unsigned)
Positive Numbers ● Uses all of the allocated bits to represent the value of the number
● Can only be a positive whole number or 0
● We can write the number with leading 0s to match the required number
of bits
Negative Numbers ● The first bit is used to represent the sign of the number (0 = +; 1 = -)
● Can be any whole number
-9+9=0 Sign and Size
● The left-most bit indicates the sign (0 = +ve, 1 = -ve)
Sign and Size ● Cannot be used in arithmetic
Represent -47 in 8 bits using Sign and Size
0 0 0 0 1 0 0 12
+ 1 0 0 0 1 0 0 12 Step 1: Step 2: Step 3:
________________ Convert Decimal to Add extra bits to Add a 1 to the first bit to
1 0 0 1 0 0 1 02 Binary: make up 8 bits: show the number is negative:
≠ 010
4710 = 1011112 001011112 -4710 = 101011112
Two’s Complement Two’s Complement
● 0 will be represented as 000000002
● -1 will be represented as 111111112
0 0 0 0 1 0 0 12 ● Can be used in arithmetic
+ 1 1 1 1 0 1 1 12
________________ Represent -47 in 8 bits using Two’s Complement
1 0 0 0 0 0 0 0 02 If we add 47 in binary and the answer we get below (-47 in binary) we get
= 010 1000000002
Step 1: Step 2: Step 3: Step 4:
(Ignore 9th bit - not Convert Add extra One’s Complement Two’s Complement
considered an error) Decimal to bits to (drop the minus sign (add 1):
Binary make up 8 and swap 1s and 0s):
bits: 110100002
001011112 + 12
-4710 -ve = ______________
= -1011112 001011112 110100002 110100012
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