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TLE Exploratory Course in Grades 7 & 8 (ICT – Computer System Servicing)
Alternative Delivery Mode
Quarter 1 – Module 2 : Perform Mensuration and Calculation
First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the
Government of the Philippines. However, prior approval of the government agency or office
wherein the work is created shall be necessary for exploitation of such work for profit. Such
agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks,
etc.) included in this module are owned by their respective copyright holders. Every effort has
been exerted to locate and seek permission to use these materials from their respective
copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education
Superintendent:
Natividad P. Bayubay, CESO VI
Asst. Superintendent:
Loida Palay- Olavario, Ph. D
Felix M. Pamaran
Printed in the Philippines by ________________________
Department of Education – MIMAROPA Region- Division of Palawan
Office Address: PEO Rd. Bancao Bancao, Puerto Princesa City
Telefax: (048) 433 6392
E-mail Address: palawan@deped.gov.ph
www.depedpalawan.com
Development Team of the Module
Writer: Johndel L. Cueto
Language Editor:
Content Editor:Pedro J Da
Illustrator:
Layout Artist:
Management Team: Aurelia B. Marquez
Rodgie S. Demalinao
Pedro J. Dandal
Clemencia G. Paduga
Orencio M. Abadiano
iii
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Introductory Message
For the facilitator:
Welcome to TLE - Information and Communication Technology (Computer
Systems Servicing) Exploratory Course in Grades 7 and 8, Alternative Delivery Mode
(ADM) Module:3 on Quarter 1 - Week 3: Perform Mensuration and Calculation.
This learning resource hopes to engage the learners into guided and independent learning
activities at their own pace and time. Furthermore, this also aims to help learners acquire the
needed 21st century skills while taking into consideration their needs and circumstances.
For the learner:
Welcome to the TLE - Information and Communication Technology (Computer
Systems Servicing) Exploratory Course in Grades 7 and 8, Alternative Delivery Mode
(ADM) Module: 3 Perform Mensuration and Calculation. .
This module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to process
the contents of the learning resource while being an active learner.
In addition to the material in the main text, you will also see this box in the body of the module:
As a facilitator, you are expected to orient the learners on how to use this module. You also
need to keep track of the learners’ progress while allowing them to manage their own learning.
Furthermore, you are expected to encourage and assist the learners as they do the tasks
included in the module.
This module has the following parts and corresponding icons:
Notes to the Teacher
This contains helpful tips or strategies that will
help you in guiding the learners.
v
What I Need to Know This will give you an idea of the skills or
competencies you are expected to learn in the
module.
What I Know This part includes an activity that aims to check
what you already know about the lesson to take. If
you get all the answers correct (100%), you may
decide to skip this module.
What’s In This is a brief drill or review to help you link the
current lesson with the previous one.
What’s New In this portion, the new lesson will be introduced to
you in various ways; a story, a song, a poem, a
problem opener, an activity or a situation.
What is It This section provides a brief discussion of the
lesson. This aims to help you discover and
understand new concepts and skills.
What’s More This comprises activities for independent practice
to solidify your understanding and skills of the
topic. You may check the answers to the exercises
using the Answer Key at the end of the module.
What I Have Learned This includes questions or blank
sentence/paragraph to be filled in to process what
you learned from the lesson.
What I Can Do This section provides an activity which will help
you transfer your new knowledge or skill into real
life situations or concerns.
Assessment
This is a task which aims to evaluate your level of
mastery in achieving the learning competency.
Additional Activities In this portion, another activity will be given to you
to enrich your knowledge or skill of the lesson
learned.
Answer Key This contains answers to all activities in the
module.
At the end of this module you will also find:
The following are some reminders in using this module:
References This is a list of all sources used in developing this
module.
vi
1. Use the module with care. Do not put unnecessary mark/s on any part of the module.
Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities included
in the module.
3. Read the instruction carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not hesitate to
consult your teacher or facilitator. Always bear in mind that you are not alone.
We hope that through this material, you will experience meaningful learning and gain deep
understanding of the relevant competencies. You can do it!
What I Need to Know
The Most Essential Learning Competency you are about to learn from this module is
to perform mensuration and calculation. This module covers the knowledge, skills, attitudes
and values needed to perform mensuration and calculation. It is also designed and written
with you in mind. It is here to help you measure different storage device applying the four (4)
basic mathematical operation and carry out mensuration and calculation.
After going through this module, you are expected to perform calculation needed to
complete task using the four mathematical fundamental operations addition (+), subtraction (-
), multiplication (x), and division (÷). (TLE_IACSS9-12PMC-IIb-d-11)
In this lesson you are expected to be able to:
1. Identify objects/s or components to be measured.
2. Convert Decimal to Binary.
3. Compute the actual storage capacity of a Hard disk, Memory, Compact Disk, USB
Flash Drive, SD Card, and the actual speed of a Processor.
4. Apply different techniques in checking the conversion from Decimal to Binary, and the
computation of the ideal storage capacity and speed.
5. Maintain measuring Instruments.
1
What I Know
Pre- Assessment:
MULTIPLE CHOICE
Directions: Choose the correct answer. Write the chosen letter on your TLE-CSS Activity
notebook.
1. What decimal number is represented by the binary number 00010001?
A. 18 B. 16 C.15 D. 17
2. What decimal number is represented by the binary number 00000101?
A. 4 B. 5 C.6 D. 3
3. What decimal number is represented by the binary number 00001001?
A. 12 B. 10 C.11 D. 9
4. What decimal number is represented by the binary number 00000011?
A. 1 B. 3 C.2 D. 4
5. What decimal number is represented by the binary number 00000111?
A. 8 B. 7 B.6 D. 9
6. What decimal number is represented by the binary number 00001000?
A. 4 B. 5 C.6 D. 8
7. A measuring instrument that use moving pointer to display rating.
A. Cable Tester B. Loopback Adapter
C. Logic probe D. Analog Multi-tester
8. A measuring instrument that indicates high digital and low digital state.
A. Logic Probe B. Multi-tester
C. Digital tester D Cable Tester
9. Use digital display to display rating.
A. Multi-tester B. Logic Probe
C. Cable Tester D. Digital Tester
10. Verify the electrical connections in a signal cable or other wired
assembly.
2
A. Digital Tester B. Analog Tester
C. Cable Tester D. Loopback Adapter
B. IDENTIFICATION
Direction: Fill in the blanks with a correct word or numbers to correctly complete each
sentence.
11. _____________ is equivalent to 8 bits.
12. A ______________ also known as a VOM, is an electronic measuring instrument that
combines several measurement functions in one unit.
13. _________________ is the primary language for computers that is made up of only two
numbers: 0 and 1
14. Store Instruments in an Appropriate __________________.
15. Always ________ your instruments before and after use.
What’s in
In the previous lesson, you have learned the different components of the computer and
their uses. You have also learned the ways on how to input data in the computer using different
application software, store data using different storage devices. Do you think learning about
them is helpful? Keep on track because the next lesson will show you more interesting and
helpful things which you could use in the modern world especially if you want to know the data
capacity of your storage device.
Can you still remember those storage devices?
Do you still remember their definitions?
3
What’s New
Before we identify the objects or components to be measured, let us first find out what these
measuring/testing intruments are?
Do you know any measuring/testing instruments?
Can you name them and give their functions?
What is It
MEASURING INSTRUMENTS AND THEIR FUNCTIONS:
1. LOGIC PROBE - is a very simple circuit that is designed to measure digital systems and it
is also used for analyzing and troubleshooting the logical states (Boolean 0 or 1) of a digital
circuit. Logic probes are often only equipped with three output LEDs that indicate the following
states:
1 – (Digital High)
0 – (Digital Low)
Z – (High impedance)
P – (Signal is pulsing / switching)
LESSON
1
MEASURING/TESTING
INSTRUMENTS USED IN
COMPUTER SYSTEM
SERVICING
4
2. CABLE TESTER - is an electronic device used to verify the electrical connections in a
signal cable or other wired assembly. Basic cable testers are continuity testers that verify the
existence of a conductive path between ends of the cable, and verify the correct wiring of
connectors on the cable.
www.google.com.wikipedia.org
3. LOOPBACK, OR LOOP-BACK ADAPTER - is a groovy little tool originally designed for
testing network configurations.
www.google.com
www.google.com
5
4. Multimeter (VOM) - A multimeter or a multitester, also known as a VOM, is an electronic
measuring instrument that combines several measurement functions in one unit. A typical
multimeter can measure voltage (Volt), current (Ampere), and resistance (Ohm). Analog
multimeter uses a micro ammeter with a moving pointer to display readings.
Voltmeter - an instrument for measuring electric potential in volts.
Ex. 220 volts
Ohmmeter - an instrument for measuring electrical resistance.
Ex.20 Ohms
Ammeter - an instrument for measuring electric current in amperes.
Ex. 15 amperes
Types of Multi-meter or Multi-tester:
1. Analog Multi-meter or multi-tester (VOM) - use a microammeter with a moving
pointer to display readings
www.google.com.wikipedia.org
6
2. Digital multimeters (DMM, DVOM) - have a numeric display, and may also show a
graphical bar representing the measured value.
www.google.com.wikipedia.org
What’s more
ACTIVITY 1. WHAT AM I?
Directions: Identify what measuring/testing instrument each function refers to. Write your
answer on the circle provided before the question.
7
What is It
Definition of Terms
Mensuration – the act of measuring something ( Merriam- Webster Dictionary)
Measurement – the process of associating numbers with physical quantities and
phenomena. (https://www.britannica.com/technology/measurement)
Calculation – the process of using information you already have and adding, taking away,
multiplying , or dividing numbers to judge the number or amount of something.
(https://dictionary.cambridge.org/us/dictionary/english/calculation)
Bit (b) – short for binary digit (Computer Hope, 2020), either 0 or 1.
Byte (B) – a unit of computer information consisting of eight (8) bits (Merriam-Webster, n.d.)
Binary – the primary language for computers that is made up of only two numbers: 0 and 1
(Computer Hope, 2019).
Binary Prefix – used to represent the quantity in terms of byte or bit in computing
(SearchStorage, n.d.)
Decimal – a base 10 number system (Yadav, 2018)
Giga Hertz (GHz) – also known as clock rate or clock speed of the processor (Computer
Hope, 2018).
What Is Binary and How Does It Work?
Binary is a system of representing numbers using a pattern of ones and zeroes. First invented
by Gottfried Leibniz in the 17th century, the binary number system became widely used once
computers required a way to represent numbers using mechanical switches. It is a base-2
number system, where the number two (2) is raised by an exponent (n-1). The exponent is
denoted by the digits’ place (n) and subtracted by 1, wherein it increases as you move through
each position starting from the right going to the left.
LESSON
2
CARRY OUT MEASUREMENTS
AND CALCULATIONS
8
For example, number 2 on the first position, so that is 2 raised by n-1, wherein n=1.
2(n-1) = 2(1-1) = 20
What Is Binary Code?
Early computer systems had mechanical switches that turned on to represent 1, and turned
off to represent 0. By using switches in series, computers could represent numbers using
binary code. Modern computers still use binary code in the form of digital ones and zeroes
inside the CPU and RAM.
Considering the given table below, the first position is the rightmost cell and the leftmost
position is the last cell.
Position
(n-1)
7 6 5 4 3 2 1 0
Exponent
2(Position)
27
26
25
24
23
22
21
20
Value 128 64 32 16 8 4 2 1
Note: The first place should be 1 but since it is (n-1) subtracted by 1, it becomes 0.
The first value is equivalent to 1 because 20
is equal to 1.
Note: Any value with an exponent of 0 is always equal to 1.
The second value is 21
is 2 because it is just 2 itself multiplied by 1.
The third value is 4 because 22
= 2 x 2 = 4, 23
= 8 because 23
= 2 x 2 x 2 = 8, and so on and
so forth.
In binary system, 1 is equal to ON/TRUE and 0 is OFF/FALSE.
To read a binary number, get the turn - ON value/s only and sum it up, no need to include the
turned-OFF value/s. For example:
Value 128 64 32 16 8 4 2 1
ON/OFF 0 0 0 0 0 0 0 1
0000 0001 = 1
Get the sum: 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 = 1
9
Or simply get the turn - ON value which is 1.
Multiple values example:
Value 128 64 32 16 8 4 2 1
ON/OFF 0 0 0 0 0 1 0 1
0000 0101 = 5
The binary number 0000 0101 is equivalent to 5 because the turned-on values are: (ALWAYS
START FROM THE RIGHT)
1 and 4
Then get the sum: 1 + 4 = 5
Number 5 and the “Value” in the tables are examples of decimal numbers, the number system
that we have known since we learned how to count numbers.
For us humans,
1
+ 2
----------------------------
3
but for computers,
0000 0001
+ 0000 0010
------------------------------------------------
0000 0011
Note: Each group of eight bits is known as a byte.
8 bits = 1 byte
That is how the computer represented the letters and numbers, and all the data that
you can see in the computer like images and videos.
Decimal to Binary Conversion
Rule: If the fraction is = ½ or .5, it is equivalent to 1.
In converting a decimal number to binary, all you have to do is:
1. Divide the number by 2.
2. Write the quotient and multiply the remainder by 2.
10
3. Divide the remainder by 2.
4. Repeat steps 2 and 3 until you get a quotient of 0.
5. Read the values of the remainder from the bottom to top. Write the values to get the
binary value of the decimal number.
Example:
Convert 19 to binary
Decimal number / 2 Quotient Remainder
19 / 2 9 1
9 / 2 4 1
4 / 2 2 0
2 / 2 1 0
1 / 2 0 1
19 = 10011
Note: A byte has 8 binary digits. Add 0s from the left to complete the 8 digits. The final
answer is 19 = 00010011.
For a more detailed discussion, watch this video through this link: ________
Checking:
There are two ways to check if the conversion is accurate.
Method 1: Binary Table
1. Create a binary table.
2. Input the binary value into the table properly. Each digit should be entered on the
correct column starting from right to the left.
Decimal 128 64 32 16 8 4 2 1
Binary
State
0 0 0 1 0 0 1 1
3. Then add the decimal values with 1.
16 + 2 + 1 = 19
11
Method 2: Binary to Decimal Conversion
1. Multiply the bits with its corresponding value.
Note: Always start from the right.
2. Get the sum.
(1 x 1) + (1 x 2) + (0 x 4) + (0 x 8) + (1 x 16) + (0 x 32) + (0 x 64) + (0 x 128)
1 + 2 + 0 + 0 + 16 + 0 + 0 + 0
= 19
Therefore: 19 = 0001 0011
Binary Prefixes
Also called as prefix multipliers consisting of a one-letter abbreviation and the prefix it stands
for.
Unit Symbol Power of 2 (bytes) VALUE in Bytes
Kilobyte KB 210
1,204
Megabyte MB 220
1,048,576
Gigabyte GB 230
1,073,741,824
Terabyte TB 240
1,009,511,627,776
For example:
1 kilobyte = 210
bytes
210
bytes = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 bytes
210
bytes = 1,024 bytes
Therefore: 1 KB = 1,024 bytes
If you have noticed, a 1 KB is not an exact 1,000 bytes but actually its 1,024 bytes because
the computer uses binary code in translating capacity and speed. So, if you have a hard disk
12
with a capacity of 500 GB, its actual size is 536,870,912,000 bytes, and not 500,000,000,000
bytes.
On the contrary, you cannot view a 1 KB file as an actual 1,024 bytes in your computer
because it’s just how Windows represented it. There are a lot of factors involved in it and it will
not be tackled in this lesson.
The presented capacity of a file or component when viewing in your computer is dependent
on the OS and the manufacturer. What you have learned here is the actual values in computing
and is how computers are being engineered in terms of capacity and speed.
Data Storage Capacity Calculation
In a storage device, you need to know its capacity as well as how much space is used and
free.
For example, you have an 8 GB flash drive. You want to copy a file with a size of 1 GB and
your flash drive’s free space is 2 GB. How much free space will be left after you copied that
file to your flash drive?
Computation:
Let FSAC = free space of flash drive after copying
FS = 1 GB (size of the file you want to copy)
FSBC = 2 GB (free space of flash drive before copying)
FSAC = FS – FSBC
FSAC = 2 GB – 1 GB
FSAC = 1 GB
Therefore, there will be only 1 GB of free space in your flash drive after copying the file.
Checking:
Use the equation FSAC = FS – FSBC:
FSAC = FS – FSBC
1 GB = 2 GB – 1 GB
13
1 GB = 1 GB
Therefore, your computation is correct!
CALCULATING BINARY USING THE FOUR FUNDAMENTAL OPERATIONS
Binary Addition
Binary addition follows the same rules as addition in the decimal system except that
rather than carrying a 1 over when the values added equal 10, carry over occurs when
the result of addition equals 2. Refer to the example below for clarification.
Note that in the binary system:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, carry over the 1, i.e. 10
EX:
1
0 1
1 1
1 1
0 1
+ 1 0 1 1 1
= 1 0 0 1 0 0
The only real difference between binary and decimal addition is that the value 2 in the binary
system is the equivalent of 10 in the decimal system. Note that the superscripted 1's represent
digits that are carried over. A common mistake to watch out for when conducting binary
addition is in the case where 1 + 1 = 0 also has a 1 carried over from the previous column to
its right. The value at the bottom should then be 1 from the carried over 1 rather than 0. This
can be observed in the third column from the right in the above example.
Binary Subtraction
Similarly, to binary addition, there is little difference between binary and decimal subtraction
except those that arise from using only the digits 0 and 1. Borrowing occurs in any instance
where the number that is subtracted is larger than the number it is being subtracted from. In
binary subtraction, the only case where borrowing is necessary is when 1 is subtracted from
0. When this occurs, the 0 in the borrowing column essentially becomes "2" (changing
the 0-1 into 2-1 = 1) while reducing the 1 in the column being borrowed from by 1. If the
following column is also 0, borrowing will have to occur from each subsequent column until a
column with a value of 1 can be reduced to 0. Refer to the example below for clarification.
Note that in the binary system:
0 - 0 = 0
0 - 1 = 1, borrow 1, resulting in -1 carried over
1 - 0 = 1
1 - 1 = 0
14
EX1:
-1
1 2
0 1 1 1
– 0 1 1 0 1
= 0 1 0 1 0
EX2:
-1
1 2-1
0 0
– 0 1 1
= 0 0 1
Note that the superscripts displayed are the changes that occur to each bit when borrowing.
The borrowing column essentially obtains 2 from borrowing, and the column that is borrowed
from is reduced by 1.
Binary Multiplication
Binary multiplication is arguably simpler than its decimal counterpart. Since the only values
used are 0 and 1, the results that must be added are either the same as the first term, or 0.
Note that in each subsequent row, placeholder 0's need to be added, and the value shifted to
the left, just like in decimal multiplication. The complexity in binary multiplication arises from
tedious binary addition dependent on how many bits are in each term. Refer to the example
below for clarification.
Note that in the binary system:
0 × 0 = 0
0 × 1 = 0
1 × 0 = 0
1 × 1 = 1
EX:
1 0 1 1 1
× 1 1
1 0 1 1 1
+ 1 0 1 1 1 0
= 1 0 0 0 1 0 1
As can be seen in the example above, the process of binary multiplication is the same as it is
in decimal multiplication. Note that the 0 placeholder is written in the second line. Typically,
the 0 placeholder is not visually present in decimal multiplication. While the same can be done
in this example (with the 0 placeholder being assumed rather than explicit), it is included in
this example because the 0 is relevant for any binary addition / subtraction calculator, like the
one provided on this page. Without the 0 being shown, it would be possible to make the
mistake of excluding the 0 when adding the binary values displayed above. Note again that in
the binary system, any 0 to the right of a 1 is relevant, while any 0 to the left of the last 1 in the
value is not.
15
EX:
1 0 1 0 1 1 0 0
= 0 0 1 0 1 0 1 1 0 0
≠ 1 0 1 0 1 1 0 0 0 0
Binary Division
The process of binary division is similar to long division in the decimal system. The dividend
is still divided by the divisor in the same manner, with the only significant difference being the
use of binary rather than decimal subtraction. Note that a good understanding of binary
subtraction is important for conducting binary division. Refer to the example below, as well as
to the binary subtraction section for clarification.
What’s more
ACTIVITY 1. GUESS THE WHAT?
Direction: Identify what each sentence refers to.
1. If Bit (b) is the short for binary digit either 0 or 1, I am the unit of computer information
consisting of eight (8) bits. What am I?
2. I am a base 10 number system. What am I?
3. If mensuration is the act of measuring something, I am the process associating numbers
with physical quantities and phenomena. What am I?
4. I am the primary language for computers that is made up of only two numbers: 0 and 1.
What am I?
5. I am used to represent the quantity in terms of byte or bit in computing. What am I?
6. I invented the binary system.
7. I am the number equivalent to 16 bits.
8. I represent the symbol TB. What am I?
9. I am the number equivalent to 1KB.
10. I represent the symbol MB. What am I?
16
ACTIVITY 3. FINDING THE RIGHT ONE
Direction: Find the decimal number based on the given input.
1.
Decimal 128 64 32 16 8 4 2 1
Binary
State
0 0 1 0 1 0 1 1
Decimal value/number: ________
2.
Decimal 128 64 32 16 8 4 2 1
Binary
State
0 0 1 1 1 0 0 1
Decimal value/number: ________
3.
Decimal 128 64 32 16 8 4 2 1
Binary
State
0 1 1 0 0 1 1 1
Decimal value/number: _________
4.
Decimal 128 64 32 16 8 4 2 1
Binary State 1 0 0 0 1 1 1 0
ACTIVITY 2. YOU COMPLETE ME!
Direction: Complete the table below.
Position
(n-1)
12 10 8 6 4 2 1 0
Exponent
2(Position)
Value
17
Decimal value/number: _________
5.
Decimal 128 64 32 16 8 4 2 1
Binary
State
0 1 0 1 1 0 1 1
Decimal value/number: _________
What is It
HOW TO PROPERLY CARE FOR AND HANDLE PRECISION MEASURING
INSTRUMENTS
1. Store Instruments in an Appropriate Environment
Whenever you place an instrument in its storage location, be sure the location is well-protected
from destructive elements. Do not store precision instruments where they can jostle against
one another in a drawer; instead, separate instruments from one another using dividers or
place them in padded cases. Avoid stacking instruments on top of each other, unless they are
well-protected in cases.
2. Know How to Properly Handle Instruments During Use
Once you have a precise measuring instrument in your hand, it becomes that much more
important to protect that tool from harm or providing false readings. There are a few things you
should do that will help prevent damage or miscalibration during use, including avoiding
sudden shocks or rough treatment. Do not drop, throw, or bang measuring instruments against
hard surfaces. Regularly check parts and batteries.
3. Always keep your tools used for measuring at or around room temperature
Never lay them on a heat source or in direct sunlight as doing so could really mess them up
so that their accuracy is affected.
LESSON
3
MEASURING
INSTRUMENTS
MAINTENANCE
18
4. Always be wary of laying or using your tools too close to a magnet or magnetized
surface.
Magnets can wreak havoc with many of these precision tools.
5. Always clean your instruments before and after use.
6. Obtain Professional Recalibration Assistance
Some measuring instruments require occasional recalibration to ensure they continue to
function as designed, and that is why it is important to have a professional relationship with a
precision instrument manufacturer and supplier. They can keep your instruments in top-notch
condition so they'll provide years of reliable service.
What’s more
ACTIVITY 1. TRUE OR FALSE
Directions: Read and understand the statements below. Write SANA ALL if the statement
is TRUE and IKAW NA if the statement is FALSE.
1. Lay your measuring instruments on a heat source or in direct sunlight as doing so could
really mess them up so that their accuracy is affected.
2. Drop, throw, or bang measuring instruments against hard surfaces.
3. Measuring instruments are cleaned before and after using.
4. It is important to have a professional relationship with a precision instrument manufacturer
and supplier.
5.Avoid stacking instruments on top of each other, unless they are well-protected in cases.
What I have Learned
Directions: Fill in the blanks with a correct word or numbers to correctly complete each
sentence.
1. In a storage device, you need to know its ______________ as well as how much space is
used and free.
19
2 – 3. Binary is a system of representing numbers using a pattern of ___________ and
__________.
4. _____________ is equivalent to 8 bits.
5. A ______________ also known as a VOM, is an electronic measuring instrument that
combines several measurement functions in one unit.
What I Can Do
ACTIVITY 1. BINARY INITIAL
Directions: Get the binary value of the initial word of the following:
1. Information
2. Communication
3. Technology
Show your solutions and checking.
Ex. First name: JOHNDEL
First name initial: J - 74
Convert: J = 01001010
Please refer to the table below.
Character Decimal Character Decimal
A 65 N 78
B 66 O 79
C 67 P 80
D 68 Q 81
E 69 R 82
F 70 S 83
G 71 T 84
H 72 U 85
20
I 73 V 86
J 74 W 87
K 75 X 88
L 76 Y 89
M 77 Z 90
Assessment
MULTIPLE CHOICE
Directions: Choose the correct answer. Write the chosen letter on your TLE-CSS Activity
notebook.
1. How many bytes are there in 5 kilobytes?
A. 5210 B. 5120 C.5024 D. 5124
2. How do we represent 9 in binary form?
A. 00001001 C.00010100
B. 00001101 D. 00001011
3. If the size of the file is 20KB, then how many bytes will it occupy in the storage
device?
A. 24080 B.24008 C.20408 D. 20480
4. How many 10MB files can be stored on a 1 gigabyte USB Flash drive?
A. 120 B. 104 C.102 D. 130
5. What decimal number is represented by the binary number 00011001?
A. 25 B. 35 C.26 D. 15
6. What decimal number is represented by the binary number 00000101?
A. 4 B. 5 C.6 D. 3
7. What decimal number is represented by the binary number 00001001?
A. 12 B. 10 C.11 D. 9
How are you? I hope you enjoyed the THREE LESSONS. Okay let’s see how much
you have learned.
Write your answer on your test notebook.
21
Congratulations! You did a great job! Rest and relax for a while then wait for the
next module. Good luck!
8. What decimal number is represented by the binary number 00000011?
A. 1 B. 3 C.2 D. 4
9. What decimal number is represented by the binary number 00000111?
A. 8 B. 7 C.6 D. 9
10. What decimal number is represented by the binary number 00001000?
A. 4 B. 5 C.6 D. 8
11. A measuring instrument that use moving pointer to display rating.
A. Cable Tester C. Logic probe
B. Loopback Adapter D. Analog Multi-tester
12. A measuring instrument that indicates high digital and low digital state.
A. Logic Probe C. Digital tester
B. Multi-tester D. Cable Tester
13. Use digital display to display rating.
A. Multi-tester C. Cable Tester
B. Logic Probe D. Digital Tester
14. Verify the electrical connections in a signal cable or other wired
assembly.
A. Digital Tester C. Cable Tester
B. Analog Tester D. Loopback Adapter
15. Primarily a means of testing / measuring the communications infrastructure.
A. Cable Tester C. Digital Tester
B. Loopback Adapter D. Logic probe
22
Additional Activities
ACTIVITY 1. MIND YOUR OWN PROBLEM!
Directions: Perform the indicated binary operations: Find your binary vale and decimal value.
Show your solutions.
A. Binary Addition
1. 010100100 + 11001100
B. Binary Multiplication
1. 01011100 * 11010001
23
Answer Key
PRE
ASSESSMENT
A.
MULTPILE
CHOICE
1.D
2.B
3.D
4.B
5.
B
6.
D
7.D
8.
A
9.D
10.C
B.
IDENTIFICATION
11.
1
BYTE
12.
MULTITESTER/MULTIMETER
13.
BINARY
14.
ENVIRONMENT
15.
CLEAN
LESSON
1
–
WHAT’S
MORE
ACTIVITY
1.
What
am
I?
1.
CABLE
TESTER
2.
LOGIC
PROBE
3.
LOOPBACK
ADAPTER
4.
VOLTMETER
5.
AMMETER
LESSON
2
:
WHAT’S
MORE
ACTIVITY
1.
GUESS
THE
WHAT!
1.
BYTE(B)
2.
DECIMAL
3.
MEASUREMENT
4.
BINARY
5.
BINARY
PREFIX
6.
GOTTFRIED
LEIBNIZ
7.
2
BYTES
8.
TEREBYTE
9.
1024
BYTES
10
MEGABYTE
LESSON
2.
ACTIVITY
2.
YOU
COMPLETE
ME!
Position
(n-1)
12
10
8
6
4
2
1
0
Exponent
2
(Position)
2
12
2
10
2
8
2
6
2
4
2
2
2
1
2
0
Value
4,096
1024
256
64
16
4
2
1
24
LESSON
2.
ACTIVITY
3.
FINDING
THE
RIGHT
ONE
1.
43
2.
57
3.103
4.
142
5.
91
LESSON
3.
WHAT’S
MORE
ACTIVITY
1.
TRUE
OR
FALSE
1.
IKAW
NA
2.
IKAW
NA
3.
SANA
ALL
4.
SANA
ALL
5.
SANA
ALL
WHAT
I
HAVE
LEARNED
1.
CAPACITY
2-3
(ONES
AND
ZEROES/1
AND
2)
4.
I
BYTE
5.
MULTIMETER/MULTITESTER
WHAT
I
CAN
DO
1.
I
I
=
73
I
=
01001001
2.
C
C
=
67
C
=
01000011
3.
T
T
=
84
T
=
01010100
FINAL
ASSESSMENT
1.
B
11.
D
2.
A
12.
A
3.
D
13.
D
4.C
14.
C
5.
D
15.
B
6.B
7.D
8.B
9.
B
10.
D
ADDITIONAL
ACTIVITIES:
A.
BINARY
ADDITION
Binary
value:
01010100
+
11001100
=
0100100000
Decimal
value:
84
+
204
=
288
B.
BINARY
MULTIPLICATION
Binary
value:
01011100
×
11010001
=
0100101100011100
Decimal
value:
92
×
209
=
19228
25
Reference:
BOOKS/MODULES
___________________________________________________________________
K to 12 Basic Education Curriculum-Technology and Livelihood Education Learning
Module-Computer Hardware Servicing-RONALDO V. ROMULO and DEOVER M.
PASCO
ELECTRONIC RESOURCES
______________________________________________________________
Computer Hope. 2020. "Bit". Accessed August 20, 2020.
https://www.computerhope.com/jargon/b/bit.html
Merriam-Webster. n.d. "byte". Accessed AUGUST 20,2020.
https://www.merriam-webster.com/dictionary/byte.
Calora, Alvin. 2014. "Carry Out Mensuration and Calculation".
Accessed AUGUST 20,2020.
https://prezi.com/sxp3xaehyb2u/lo-2-carry-out-mensuration-and-calculation/.
Computer Hope. 2019. "Binary". Accessed AUGUST 20,2020.
https://www.computerhope.com/jargon/b/binary.html
SearchStorage. n.d. "Kilo, mega, giga, tera, peta, exa, zetta and all
that". Accessed AUGUST 20, 2020.
https://searchstorage.techtarget.com/definition/Kilo-mega-giga-tera- peta-and-
all-that.
Computer Hope. 2018. "GHz". Accessed AUGUST 20,2020.
https://www.computerhope.com/jargon/g/ghz.htm.
https://google.com.wikipedia.org.
https://www.calculator.net/binary-calculator.html - Accessed AUGUST 21,2020.
https://westportcorp.com/blogs/calibration-repair-services/how-to-properly-care-for-
and-handle-precision-measuring-instruments - Accessed AUGUST 21,2020.
https://dictionary.cambridge.org/us/dictionary/english/calculation
https://www.britannica.com/technology/measurement
26
For inquiries or feedback, please write or call:
Department of Education – SDO Palawan
Curriculum Implementation Division Office
2nd
Floor Deped Palawan Building
Telephone no. (048) 433-3292
Learning Resources Management Section
LRMS Building, PEO Compound
Telephone np. (048) 434-0099

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TLE ICT Module on Mensuration and CalculationTITLE Performing Mensuration and Calculation in TLE ICTTITLE Measuring and Computing in TLE ICT Module 3TITLE TLE CSS Module on Storage Measurement and Calculation

  • 2. ii TLE Exploratory Course in Grades 7 & 8 (ICT – Computer System Servicing) Alternative Delivery Mode Quarter 1 – Module 2 : Perform Mensuration and Calculation First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Department of Education Superintendent: Natividad P. Bayubay, CESO VI Asst. Superintendent: Loida Palay- Olavario, Ph. D Felix M. Pamaran Printed in the Philippines by ________________________ Department of Education – MIMAROPA Region- Division of Palawan Office Address: PEO Rd. Bancao Bancao, Puerto Princesa City Telefax: (048) 433 6392 E-mail Address: palawan@deped.gov.ph www.depedpalawan.com Development Team of the Module Writer: Johndel L. Cueto Language Editor: Content Editor:Pedro J Da Illustrator: Layout Artist: Management Team: Aurelia B. Marquez Rodgie S. Demalinao Pedro J. Dandal Clemencia G. Paduga Orencio M. Abadiano
  • 4. iv Introductory Message For the facilitator: Welcome to TLE - Information and Communication Technology (Computer Systems Servicing) Exploratory Course in Grades 7 and 8, Alternative Delivery Mode (ADM) Module:3 on Quarter 1 - Week 3: Perform Mensuration and Calculation. This learning resource hopes to engage the learners into guided and independent learning activities at their own pace and time. Furthermore, this also aims to help learners acquire the needed 21st century skills while taking into consideration their needs and circumstances. For the learner: Welcome to the TLE - Information and Communication Technology (Computer Systems Servicing) Exploratory Course in Grades 7 and 8, Alternative Delivery Mode (ADM) Module: 3 Perform Mensuration and Calculation. . This module was designed to provide you with fun and meaningful opportunities for guided and independent learning at your own pace and time. You will be enabled to process the contents of the learning resource while being an active learner. In addition to the material in the main text, you will also see this box in the body of the module: As a facilitator, you are expected to orient the learners on how to use this module. You also need to keep track of the learners’ progress while allowing them to manage their own learning. Furthermore, you are expected to encourage and assist the learners as they do the tasks included in the module. This module has the following parts and corresponding icons: Notes to the Teacher This contains helpful tips or strategies that will help you in guiding the learners.
  • 5. v What I Need to Know This will give you an idea of the skills or competencies you are expected to learn in the module. What I Know This part includes an activity that aims to check what you already know about the lesson to take. If you get all the answers correct (100%), you may decide to skip this module. What’s In This is a brief drill or review to help you link the current lesson with the previous one. What’s New In this portion, the new lesson will be introduced to you in various ways; a story, a song, a poem, a problem opener, an activity or a situation. What is It This section provides a brief discussion of the lesson. This aims to help you discover and understand new concepts and skills. What’s More This comprises activities for independent practice to solidify your understanding and skills of the topic. You may check the answers to the exercises using the Answer Key at the end of the module. What I Have Learned This includes questions or blank sentence/paragraph to be filled in to process what you learned from the lesson. What I Can Do This section provides an activity which will help you transfer your new knowledge or skill into real life situations or concerns. Assessment This is a task which aims to evaluate your level of mastery in achieving the learning competency. Additional Activities In this portion, another activity will be given to you to enrich your knowledge or skill of the lesson learned. Answer Key This contains answers to all activities in the module. At the end of this module you will also find: The following are some reminders in using this module: References This is a list of all sources used in developing this module.
  • 6. vi 1. Use the module with care. Do not put unnecessary mark/s on any part of the module. Use a separate sheet of paper in answering the exercises. 2. Don’t forget to answer What I Know before moving on to the other activities included in the module. 3. Read the instruction carefully before doing each task. 4. Observe honesty and integrity in doing the tasks and checking your answers. 5. Finish the task at hand before proceeding to the next. 6. Return this module to your teacher/facilitator once you are through with it. If you encounter any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator. Always bear in mind that you are not alone. We hope that through this material, you will experience meaningful learning and gain deep understanding of the relevant competencies. You can do it! What I Need to Know The Most Essential Learning Competency you are about to learn from this module is to perform mensuration and calculation. This module covers the knowledge, skills, attitudes and values needed to perform mensuration and calculation. It is also designed and written with you in mind. It is here to help you measure different storage device applying the four (4) basic mathematical operation and carry out mensuration and calculation. After going through this module, you are expected to perform calculation needed to complete task using the four mathematical fundamental operations addition (+), subtraction (- ), multiplication (x), and division (÷). (TLE_IACSS9-12PMC-IIb-d-11) In this lesson you are expected to be able to: 1. Identify objects/s or components to be measured. 2. Convert Decimal to Binary. 3. Compute the actual storage capacity of a Hard disk, Memory, Compact Disk, USB Flash Drive, SD Card, and the actual speed of a Processor. 4. Apply different techniques in checking the conversion from Decimal to Binary, and the computation of the ideal storage capacity and speed. 5. Maintain measuring Instruments.
  • 7. 1 What I Know Pre- Assessment: MULTIPLE CHOICE Directions: Choose the correct answer. Write the chosen letter on your TLE-CSS Activity notebook. 1. What decimal number is represented by the binary number 00010001? A. 18 B. 16 C.15 D. 17 2. What decimal number is represented by the binary number 00000101? A. 4 B. 5 C.6 D. 3 3. What decimal number is represented by the binary number 00001001? A. 12 B. 10 C.11 D. 9 4. What decimal number is represented by the binary number 00000011? A. 1 B. 3 C.2 D. 4 5. What decimal number is represented by the binary number 00000111? A. 8 B. 7 B.6 D. 9 6. What decimal number is represented by the binary number 00001000? A. 4 B. 5 C.6 D. 8 7. A measuring instrument that use moving pointer to display rating. A. Cable Tester B. Loopback Adapter C. Logic probe D. Analog Multi-tester 8. A measuring instrument that indicates high digital and low digital state. A. Logic Probe B. Multi-tester C. Digital tester D Cable Tester 9. Use digital display to display rating. A. Multi-tester B. Logic Probe C. Cable Tester D. Digital Tester 10. Verify the electrical connections in a signal cable or other wired assembly.
  • 8. 2 A. Digital Tester B. Analog Tester C. Cable Tester D. Loopback Adapter B. IDENTIFICATION Direction: Fill in the blanks with a correct word or numbers to correctly complete each sentence. 11. _____________ is equivalent to 8 bits. 12. A ______________ also known as a VOM, is an electronic measuring instrument that combines several measurement functions in one unit. 13. _________________ is the primary language for computers that is made up of only two numbers: 0 and 1 14. Store Instruments in an Appropriate __________________. 15. Always ________ your instruments before and after use. What’s in In the previous lesson, you have learned the different components of the computer and their uses. You have also learned the ways on how to input data in the computer using different application software, store data using different storage devices. Do you think learning about them is helpful? Keep on track because the next lesson will show you more interesting and helpful things which you could use in the modern world especially if you want to know the data capacity of your storage device. Can you still remember those storage devices? Do you still remember their definitions?
  • 9. 3 What’s New Before we identify the objects or components to be measured, let us first find out what these measuring/testing intruments are? Do you know any measuring/testing instruments? Can you name them and give their functions? What is It MEASURING INSTRUMENTS AND THEIR FUNCTIONS: 1. LOGIC PROBE - is a very simple circuit that is designed to measure digital systems and it is also used for analyzing and troubleshooting the logical states (Boolean 0 or 1) of a digital circuit. Logic probes are often only equipped with three output LEDs that indicate the following states: 1 – (Digital High) 0 – (Digital Low) Z – (High impedance) P – (Signal is pulsing / switching) LESSON 1 MEASURING/TESTING INSTRUMENTS USED IN COMPUTER SYSTEM SERVICING
  • 10. 4 2. CABLE TESTER - is an electronic device used to verify the electrical connections in a signal cable or other wired assembly. Basic cable testers are continuity testers that verify the existence of a conductive path between ends of the cable, and verify the correct wiring of connectors on the cable. www.google.com.wikipedia.org 3. LOOPBACK, OR LOOP-BACK ADAPTER - is a groovy little tool originally designed for testing network configurations. www.google.com www.google.com
  • 11. 5 4. Multimeter (VOM) - A multimeter or a multitester, also known as a VOM, is an electronic measuring instrument that combines several measurement functions in one unit. A typical multimeter can measure voltage (Volt), current (Ampere), and resistance (Ohm). Analog multimeter uses a micro ammeter with a moving pointer to display readings. Voltmeter - an instrument for measuring electric potential in volts. Ex. 220 volts Ohmmeter - an instrument for measuring electrical resistance. Ex.20 Ohms Ammeter - an instrument for measuring electric current in amperes. Ex. 15 amperes Types of Multi-meter or Multi-tester: 1. Analog Multi-meter or multi-tester (VOM) - use a microammeter with a moving pointer to display readings www.google.com.wikipedia.org
  • 12. 6 2. Digital multimeters (DMM, DVOM) - have a numeric display, and may also show a graphical bar representing the measured value. www.google.com.wikipedia.org What’s more ACTIVITY 1. WHAT AM I? Directions: Identify what measuring/testing instrument each function refers to. Write your answer on the circle provided before the question.
  • 13. 7 What is It Definition of Terms Mensuration – the act of measuring something ( Merriam- Webster Dictionary) Measurement – the process of associating numbers with physical quantities and phenomena. (https://www.britannica.com/technology/measurement) Calculation – the process of using information you already have and adding, taking away, multiplying , or dividing numbers to judge the number or amount of something. (https://dictionary.cambridge.org/us/dictionary/english/calculation) Bit (b) – short for binary digit (Computer Hope, 2020), either 0 or 1. Byte (B) – a unit of computer information consisting of eight (8) bits (Merriam-Webster, n.d.) Binary – the primary language for computers that is made up of only two numbers: 0 and 1 (Computer Hope, 2019). Binary Prefix – used to represent the quantity in terms of byte or bit in computing (SearchStorage, n.d.) Decimal – a base 10 number system (Yadav, 2018) Giga Hertz (GHz) – also known as clock rate or clock speed of the processor (Computer Hope, 2018). What Is Binary and How Does It Work? Binary is a system of representing numbers using a pattern of ones and zeroes. First invented by Gottfried Leibniz in the 17th century, the binary number system became widely used once computers required a way to represent numbers using mechanical switches. It is a base-2 number system, where the number two (2) is raised by an exponent (n-1). The exponent is denoted by the digits’ place (n) and subtracted by 1, wherein it increases as you move through each position starting from the right going to the left. LESSON 2 CARRY OUT MEASUREMENTS AND CALCULATIONS
  • 14. 8 For example, number 2 on the first position, so that is 2 raised by n-1, wherein n=1. 2(n-1) = 2(1-1) = 20 What Is Binary Code? Early computer systems had mechanical switches that turned on to represent 1, and turned off to represent 0. By using switches in series, computers could represent numbers using binary code. Modern computers still use binary code in the form of digital ones and zeroes inside the CPU and RAM. Considering the given table below, the first position is the rightmost cell and the leftmost position is the last cell. Position (n-1) 7 6 5 4 3 2 1 0 Exponent 2(Position) 27 26 25 24 23 22 21 20 Value 128 64 32 16 8 4 2 1 Note: The first place should be 1 but since it is (n-1) subtracted by 1, it becomes 0. The first value is equivalent to 1 because 20 is equal to 1. Note: Any value with an exponent of 0 is always equal to 1. The second value is 21 is 2 because it is just 2 itself multiplied by 1. The third value is 4 because 22 = 2 x 2 = 4, 23 = 8 because 23 = 2 x 2 x 2 = 8, and so on and so forth. In binary system, 1 is equal to ON/TRUE and 0 is OFF/FALSE. To read a binary number, get the turn - ON value/s only and sum it up, no need to include the turned-OFF value/s. For example: Value 128 64 32 16 8 4 2 1 ON/OFF 0 0 0 0 0 0 0 1 0000 0001 = 1 Get the sum: 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 = 1
  • 15. 9 Or simply get the turn - ON value which is 1. Multiple values example: Value 128 64 32 16 8 4 2 1 ON/OFF 0 0 0 0 0 1 0 1 0000 0101 = 5 The binary number 0000 0101 is equivalent to 5 because the turned-on values are: (ALWAYS START FROM THE RIGHT) 1 and 4 Then get the sum: 1 + 4 = 5 Number 5 and the “Value” in the tables are examples of decimal numbers, the number system that we have known since we learned how to count numbers. For us humans, 1 + 2 ---------------------------- 3 but for computers, 0000 0001 + 0000 0010 ------------------------------------------------ 0000 0011 Note: Each group of eight bits is known as a byte. 8 bits = 1 byte That is how the computer represented the letters and numbers, and all the data that you can see in the computer like images and videos. Decimal to Binary Conversion Rule: If the fraction is = ½ or .5, it is equivalent to 1. In converting a decimal number to binary, all you have to do is: 1. Divide the number by 2. 2. Write the quotient and multiply the remainder by 2.
  • 16. 10 3. Divide the remainder by 2. 4. Repeat steps 2 and 3 until you get a quotient of 0. 5. Read the values of the remainder from the bottom to top. Write the values to get the binary value of the decimal number. Example: Convert 19 to binary Decimal number / 2 Quotient Remainder 19 / 2 9 1 9 / 2 4 1 4 / 2 2 0 2 / 2 1 0 1 / 2 0 1 19 = 10011 Note: A byte has 8 binary digits. Add 0s from the left to complete the 8 digits. The final answer is 19 = 00010011. For a more detailed discussion, watch this video through this link: ________ Checking: There are two ways to check if the conversion is accurate. Method 1: Binary Table 1. Create a binary table. 2. Input the binary value into the table properly. Each digit should be entered on the correct column starting from right to the left. Decimal 128 64 32 16 8 4 2 1 Binary State 0 0 0 1 0 0 1 1 3. Then add the decimal values with 1. 16 + 2 + 1 = 19
  • 17. 11 Method 2: Binary to Decimal Conversion 1. Multiply the bits with its corresponding value. Note: Always start from the right. 2. Get the sum. (1 x 1) + (1 x 2) + (0 x 4) + (0 x 8) + (1 x 16) + (0 x 32) + (0 x 64) + (0 x 128) 1 + 2 + 0 + 0 + 16 + 0 + 0 + 0 = 19 Therefore: 19 = 0001 0011 Binary Prefixes Also called as prefix multipliers consisting of a one-letter abbreviation and the prefix it stands for. Unit Symbol Power of 2 (bytes) VALUE in Bytes Kilobyte KB 210 1,204 Megabyte MB 220 1,048,576 Gigabyte GB 230 1,073,741,824 Terabyte TB 240 1,009,511,627,776 For example: 1 kilobyte = 210 bytes 210 bytes = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 bytes 210 bytes = 1,024 bytes Therefore: 1 KB = 1,024 bytes If you have noticed, a 1 KB is not an exact 1,000 bytes but actually its 1,024 bytes because the computer uses binary code in translating capacity and speed. So, if you have a hard disk
  • 18. 12 with a capacity of 500 GB, its actual size is 536,870,912,000 bytes, and not 500,000,000,000 bytes. On the contrary, you cannot view a 1 KB file as an actual 1,024 bytes in your computer because it’s just how Windows represented it. There are a lot of factors involved in it and it will not be tackled in this lesson. The presented capacity of a file or component when viewing in your computer is dependent on the OS and the manufacturer. What you have learned here is the actual values in computing and is how computers are being engineered in terms of capacity and speed. Data Storage Capacity Calculation In a storage device, you need to know its capacity as well as how much space is used and free. For example, you have an 8 GB flash drive. You want to copy a file with a size of 1 GB and your flash drive’s free space is 2 GB. How much free space will be left after you copied that file to your flash drive? Computation: Let FSAC = free space of flash drive after copying FS = 1 GB (size of the file you want to copy) FSBC = 2 GB (free space of flash drive before copying) FSAC = FS – FSBC FSAC = 2 GB – 1 GB FSAC = 1 GB Therefore, there will be only 1 GB of free space in your flash drive after copying the file. Checking: Use the equation FSAC = FS – FSBC: FSAC = FS – FSBC 1 GB = 2 GB – 1 GB
  • 19. 13 1 GB = 1 GB Therefore, your computation is correct! CALCULATING BINARY USING THE FOUR FUNDAMENTAL OPERATIONS Binary Addition Binary addition follows the same rules as addition in the decimal system except that rather than carrying a 1 over when the values added equal 10, carry over occurs when the result of addition equals 2. Refer to the example below for clarification. Note that in the binary system: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0, carry over the 1, i.e. 10 EX: 1 0 1 1 1 1 1 0 1 + 1 0 1 1 1 = 1 0 0 1 0 0 The only real difference between binary and decimal addition is that the value 2 in the binary system is the equivalent of 10 in the decimal system. Note that the superscripted 1's represent digits that are carried over. A common mistake to watch out for when conducting binary addition is in the case where 1 + 1 = 0 also has a 1 carried over from the previous column to its right. The value at the bottom should then be 1 from the carried over 1 rather than 0. This can be observed in the third column from the right in the above example. Binary Subtraction Similarly, to binary addition, there is little difference between binary and decimal subtraction except those that arise from using only the digits 0 and 1. Borrowing occurs in any instance where the number that is subtracted is larger than the number it is being subtracted from. In binary subtraction, the only case where borrowing is necessary is when 1 is subtracted from 0. When this occurs, the 0 in the borrowing column essentially becomes "2" (changing the 0-1 into 2-1 = 1) while reducing the 1 in the column being borrowed from by 1. If the following column is also 0, borrowing will have to occur from each subsequent column until a column with a value of 1 can be reduced to 0. Refer to the example below for clarification. Note that in the binary system: 0 - 0 = 0 0 - 1 = 1, borrow 1, resulting in -1 carried over 1 - 0 = 1 1 - 1 = 0
  • 20. 14 EX1: -1 1 2 0 1 1 1 – 0 1 1 0 1 = 0 1 0 1 0 EX2: -1 1 2-1 0 0 – 0 1 1 = 0 0 1 Note that the superscripts displayed are the changes that occur to each bit when borrowing. The borrowing column essentially obtains 2 from borrowing, and the column that is borrowed from is reduced by 1. Binary Multiplication Binary multiplication is arguably simpler than its decimal counterpart. Since the only values used are 0 and 1, the results that must be added are either the same as the first term, or 0. Note that in each subsequent row, placeholder 0's need to be added, and the value shifted to the left, just like in decimal multiplication. The complexity in binary multiplication arises from tedious binary addition dependent on how many bits are in each term. Refer to the example below for clarification. Note that in the binary system: 0 × 0 = 0 0 × 1 = 0 1 × 0 = 0 1 × 1 = 1 EX: 1 0 1 1 1 × 1 1 1 0 1 1 1 + 1 0 1 1 1 0 = 1 0 0 0 1 0 1 As can be seen in the example above, the process of binary multiplication is the same as it is in decimal multiplication. Note that the 0 placeholder is written in the second line. Typically, the 0 placeholder is not visually present in decimal multiplication. While the same can be done in this example (with the 0 placeholder being assumed rather than explicit), it is included in this example because the 0 is relevant for any binary addition / subtraction calculator, like the one provided on this page. Without the 0 being shown, it would be possible to make the mistake of excluding the 0 when adding the binary values displayed above. Note again that in the binary system, any 0 to the right of a 1 is relevant, while any 0 to the left of the last 1 in the value is not.
  • 21. 15 EX: 1 0 1 0 1 1 0 0 = 0 0 1 0 1 0 1 1 0 0 ≠ 1 0 1 0 1 1 0 0 0 0 Binary Division The process of binary division is similar to long division in the decimal system. The dividend is still divided by the divisor in the same manner, with the only significant difference being the use of binary rather than decimal subtraction. Note that a good understanding of binary subtraction is important for conducting binary division. Refer to the example below, as well as to the binary subtraction section for clarification. What’s more ACTIVITY 1. GUESS THE WHAT? Direction: Identify what each sentence refers to. 1. If Bit (b) is the short for binary digit either 0 or 1, I am the unit of computer information consisting of eight (8) bits. What am I? 2. I am a base 10 number system. What am I? 3. If mensuration is the act of measuring something, I am the process associating numbers with physical quantities and phenomena. What am I? 4. I am the primary language for computers that is made up of only two numbers: 0 and 1. What am I? 5. I am used to represent the quantity in terms of byte or bit in computing. What am I? 6. I invented the binary system. 7. I am the number equivalent to 16 bits. 8. I represent the symbol TB. What am I? 9. I am the number equivalent to 1KB. 10. I represent the symbol MB. What am I?
  • 22. 16 ACTIVITY 3. FINDING THE RIGHT ONE Direction: Find the decimal number based on the given input. 1. Decimal 128 64 32 16 8 4 2 1 Binary State 0 0 1 0 1 0 1 1 Decimal value/number: ________ 2. Decimal 128 64 32 16 8 4 2 1 Binary State 0 0 1 1 1 0 0 1 Decimal value/number: ________ 3. Decimal 128 64 32 16 8 4 2 1 Binary State 0 1 1 0 0 1 1 1 Decimal value/number: _________ 4. Decimal 128 64 32 16 8 4 2 1 Binary State 1 0 0 0 1 1 1 0 ACTIVITY 2. YOU COMPLETE ME! Direction: Complete the table below. Position (n-1) 12 10 8 6 4 2 1 0 Exponent 2(Position) Value
  • 23. 17 Decimal value/number: _________ 5. Decimal 128 64 32 16 8 4 2 1 Binary State 0 1 0 1 1 0 1 1 Decimal value/number: _________ What is It HOW TO PROPERLY CARE FOR AND HANDLE PRECISION MEASURING INSTRUMENTS 1. Store Instruments in an Appropriate Environment Whenever you place an instrument in its storage location, be sure the location is well-protected from destructive elements. Do not store precision instruments where they can jostle against one another in a drawer; instead, separate instruments from one another using dividers or place them in padded cases. Avoid stacking instruments on top of each other, unless they are well-protected in cases. 2. Know How to Properly Handle Instruments During Use Once you have a precise measuring instrument in your hand, it becomes that much more important to protect that tool from harm or providing false readings. There are a few things you should do that will help prevent damage or miscalibration during use, including avoiding sudden shocks or rough treatment. Do not drop, throw, or bang measuring instruments against hard surfaces. Regularly check parts and batteries. 3. Always keep your tools used for measuring at or around room temperature Never lay them on a heat source or in direct sunlight as doing so could really mess them up so that their accuracy is affected. LESSON 3 MEASURING INSTRUMENTS MAINTENANCE
  • 24. 18 4. Always be wary of laying or using your tools too close to a magnet or magnetized surface. Magnets can wreak havoc with many of these precision tools. 5. Always clean your instruments before and after use. 6. Obtain Professional Recalibration Assistance Some measuring instruments require occasional recalibration to ensure they continue to function as designed, and that is why it is important to have a professional relationship with a precision instrument manufacturer and supplier. They can keep your instruments in top-notch condition so they'll provide years of reliable service. What’s more ACTIVITY 1. TRUE OR FALSE Directions: Read and understand the statements below. Write SANA ALL if the statement is TRUE and IKAW NA if the statement is FALSE. 1. Lay your measuring instruments on a heat source or in direct sunlight as doing so could really mess them up so that their accuracy is affected. 2. Drop, throw, or bang measuring instruments against hard surfaces. 3. Measuring instruments are cleaned before and after using. 4. It is important to have a professional relationship with a precision instrument manufacturer and supplier. 5.Avoid stacking instruments on top of each other, unless they are well-protected in cases. What I have Learned Directions: Fill in the blanks with a correct word or numbers to correctly complete each sentence. 1. In a storage device, you need to know its ______________ as well as how much space is used and free.
  • 25. 19 2 – 3. Binary is a system of representing numbers using a pattern of ___________ and __________. 4. _____________ is equivalent to 8 bits. 5. A ______________ also known as a VOM, is an electronic measuring instrument that combines several measurement functions in one unit. What I Can Do ACTIVITY 1. BINARY INITIAL Directions: Get the binary value of the initial word of the following: 1. Information 2. Communication 3. Technology Show your solutions and checking. Ex. First name: JOHNDEL First name initial: J - 74 Convert: J = 01001010 Please refer to the table below. Character Decimal Character Decimal A 65 N 78 B 66 O 79 C 67 P 80 D 68 Q 81 E 69 R 82 F 70 S 83 G 71 T 84 H 72 U 85
  • 26. 20 I 73 V 86 J 74 W 87 K 75 X 88 L 76 Y 89 M 77 Z 90 Assessment MULTIPLE CHOICE Directions: Choose the correct answer. Write the chosen letter on your TLE-CSS Activity notebook. 1. How many bytes are there in 5 kilobytes? A. 5210 B. 5120 C.5024 D. 5124 2. How do we represent 9 in binary form? A. 00001001 C.00010100 B. 00001101 D. 00001011 3. If the size of the file is 20KB, then how many bytes will it occupy in the storage device? A. 24080 B.24008 C.20408 D. 20480 4. How many 10MB files can be stored on a 1 gigabyte USB Flash drive? A. 120 B. 104 C.102 D. 130 5. What decimal number is represented by the binary number 00011001? A. 25 B. 35 C.26 D. 15 6. What decimal number is represented by the binary number 00000101? A. 4 B. 5 C.6 D. 3 7. What decimal number is represented by the binary number 00001001? A. 12 B. 10 C.11 D. 9 How are you? I hope you enjoyed the THREE LESSONS. Okay let’s see how much you have learned. Write your answer on your test notebook.
  • 27. 21 Congratulations! You did a great job! Rest and relax for a while then wait for the next module. Good luck! 8. What decimal number is represented by the binary number 00000011? A. 1 B. 3 C.2 D. 4 9. What decimal number is represented by the binary number 00000111? A. 8 B. 7 C.6 D. 9 10. What decimal number is represented by the binary number 00001000? A. 4 B. 5 C.6 D. 8 11. A measuring instrument that use moving pointer to display rating. A. Cable Tester C. Logic probe B. Loopback Adapter D. Analog Multi-tester 12. A measuring instrument that indicates high digital and low digital state. A. Logic Probe C. Digital tester B. Multi-tester D. Cable Tester 13. Use digital display to display rating. A. Multi-tester C. Cable Tester B. Logic Probe D. Digital Tester 14. Verify the electrical connections in a signal cable or other wired assembly. A. Digital Tester C. Cable Tester B. Analog Tester D. Loopback Adapter 15. Primarily a means of testing / measuring the communications infrastructure. A. Cable Tester C. Digital Tester B. Loopback Adapter D. Logic probe
  • 28. 22 Additional Activities ACTIVITY 1. MIND YOUR OWN PROBLEM! Directions: Perform the indicated binary operations: Find your binary vale and decimal value. Show your solutions. A. Binary Addition 1. 010100100 + 11001100 B. Binary Multiplication 1. 01011100 * 11010001
  • 31. 25 Reference: BOOKS/MODULES ___________________________________________________________________ K to 12 Basic Education Curriculum-Technology and Livelihood Education Learning Module-Computer Hardware Servicing-RONALDO V. ROMULO and DEOVER M. PASCO ELECTRONIC RESOURCES ______________________________________________________________ Computer Hope. 2020. "Bit". Accessed August 20, 2020. https://www.computerhope.com/jargon/b/bit.html Merriam-Webster. n.d. "byte". Accessed AUGUST 20,2020. https://www.merriam-webster.com/dictionary/byte. Calora, Alvin. 2014. "Carry Out Mensuration and Calculation". Accessed AUGUST 20,2020. https://prezi.com/sxp3xaehyb2u/lo-2-carry-out-mensuration-and-calculation/. Computer Hope. 2019. "Binary". Accessed AUGUST 20,2020. https://www.computerhope.com/jargon/b/binary.html SearchStorage. n.d. "Kilo, mega, giga, tera, peta, exa, zetta and all that". Accessed AUGUST 20, 2020. https://searchstorage.techtarget.com/definition/Kilo-mega-giga-tera- peta-and- all-that. Computer Hope. 2018. "GHz". Accessed AUGUST 20,2020. https://www.computerhope.com/jargon/g/ghz.htm. https://google.com.wikipedia.org. https://www.calculator.net/binary-calculator.html - Accessed AUGUST 21,2020. https://westportcorp.com/blogs/calibration-repair-services/how-to-properly-care-for- and-handle-precision-measuring-instruments - Accessed AUGUST 21,2020. https://dictionary.cambridge.org/us/dictionary/english/calculation https://www.britannica.com/technology/measurement
  • 32. 26 For inquiries or feedback, please write or call: Department of Education – SDO Palawan Curriculum Implementation Division Office 2nd Floor Deped Palawan Building Telephone no. (048) 433-3292 Learning Resources Management Section LRMS Building, PEO Compound Telephone np. (048) 434-0099