Q2-ICT7-1
ICT LESSON 1
NUMBER SYSTEMS
What I Need to Know.
1. Understand the different number systems used by computers in its operation.
2. Realize how decimals and binary numbers work.
3. Learn how to compute the binary equivalent of decimal numbers.
What I Know.
Instruction: Choose the letter of the best answer and write it on the space
provided.
___1. Which of the following is an example of a binary number?
A. 357110 B. 11010101 C. 7586616 D. AE14
___2. Which of the following is not true about number systems?
A. Number systems are numbers.
B. Number systems have different bases.
C. Number systems are used by computers in performing calculations.
D. None of the above.
___3. In a binary number system translated into a digital data, what do 0 and 1 mean
respectively?
A. Yes and No B. True or False C. Right and Left D. On and Off
___4. Which number system is the most commonly used?
A. Decimal Number System C. Binary Number System
B. Octal Number System D. Hexadecimal Number System
___5. Which of the following is not a characteristics of the binary number system?
A. It uses 0 and 1. C. It uses letters.
B. It is a base 2 number system. D. None of the above.
___6. Who among the following described and wrote the first binary number system?
A. Aristotle B. Pingala C. Albert Einstein D. Isaac Newton
___7. Which of the following is true about binary number system used in a computer?
A. Every input in a computer will be translated into a binary number.
B. Every output we see in the monitor IS a translated binary number.
C. Both A and B
D. Only A
___8. If I have a robot that can only read 1 and 0, what number system is it using?
A. It uses 0 and 1. C. It uses letters.
B. It is a base 2 number system. D. None of the above
___9. Practically speaking, computers use binary system because of what reason?
Address: SICAT Rd., Calaocan, Santiago City 3311
Telephone No.: (078) 305-0110
Email Address: 300599@deped.gov.ph
Always Practice Proper Hygiene at ALL TIMES.
1
Q2-ICT7-1
A. It is more practical since 0 and 1 are cool numbers.
B. In the field of electronics, it is easier to program using binary because circuits or
hardware can only be turned on and off.
C. In the field of electronics, it is easier to program using binary because circuits or
hardware can only be turned on and off but also cannot be disabled and enabled.
D. None of the above
___10. Which of the following number systems uses NOT MORE THAN 2 bases?
A. Decimal Number System C. Binary Number System
B. Octal Number System D. Hexadecimal Number System
Address: SICAT Rd., Calaocan, Santiago City 3311
Telephone No.: (078) 305-0110
Email Address: 300599@deped.gov.ph
Always Practice Proper Hygiene at ALL TIMES.
2
Q2-ICT7-1
Number Systems in Computers
We learned in the previous lessons that computers speak through numbers. Different
number systems will be discussed in this lesson and on to the next lessons. We have to understand
how these computers communicate if we want to learn something from them and use it to our
advantage per se. Furthermore, understanding the substance of things makes us better understand
the world we live in. This is particularly at this time, the digital age.
Types of Number Systems
Number System Base Characters
Binary 2 0, 1
Decimal 10 0,1,2,3,4,5,6,7,8,9
Octal 8 0,1,2,3,4,5,6,7
Hexadecimal 16 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
Binary Number System
As mentioned above, the binary number system uses 2 bases which are 0 and 1. Every
character, string and number has a binary equivalent. For example, red. Red has a binary equivalent
of 1011110011001010011111. Interesting, right? Every data has a binary equivalent.
For the remainder of this lesson, you will be dealing with the methods on how to compute
and calculate the binary equivalent of decimal (base 10) numbers.
Brief History of Binary Number System
According to historians, Egyptians were said to be the earliest to use the Binary numbers as
well as the ones who introduced the Decimal Number System (the numbers we are using today),
although, the Binary Number System were first described in the 2 nd – 3rd century BCE by Acrharya
Pingala.
REMEMBER
Decimal Number System has 10 characters: 0,1,2,3,4,5,6,7,8,9
Binary Number System has 2 characters: 0, 1
Address: SICAT Rd., Calaocan, Santiago City 3311
Telephone No.: (078) 305-0110
Email Address: 300599@deped.gov.ph
Always Practice Proper Hygiene at ALL TIMES.
3
Q2-ICT7-1
GETTING THE BINARY EQUIVALENT OF A DECIMAL NUMBER
There are 3 steps in converting a Decimal Number into a Binary Number:
1. Divide the decimal number by 2
2. Multiply the remainder by 2, (if there’s any).
3. Divide the succeeding whole number by 2.
Repeat the steps until you get a quotient of ZERO WITH NO REMAINDERS.
Example 1
Let’s take the number 9:
Step 1 Step 2
9 ÷ 2 = 4.5 .5 x 2 = 1
Step 3 Hence, we get 01001 as the binary
4 ÷ 2 = 2.0 0x2=0 equivalent of 9.
2 ÷ 2 = 1.0 0x2=0
1 ÷ 2 = 0.5 .5 x 2 = 1 Notice MEEEE: You should see that we
0÷2=0 0x2=0 translated the binary number from
bottom to top.
Example 2
Let’s get the binary equivalent of 19.
19 ÷ 2 = 9.5 .5 x 2 = 1
9 ÷ 2 = 4.5 .5 x 2 = 1 Notice MEEEE: Again we translate the
4 ÷ 2 = 2.0 0x2=0 binary number from bottom to top. Hence
2 ÷ 2 = 1.0 0x2=0 we get 10011 as the answer.
1 ÷ 2 = 0.5 .5 x 2 = 1
Thus, 19 has an equivalent binary number 10011. And we read this binary equivalent as
(one-zero-zero-one-one base 2)1 0 0 1 1p. Or the most common way to put it is 10011 especially if
we are working with different /specific bases.
Address: SICAT Rd., Calaocan, Santiago City 3311
Telephone No.: (078) 305-0110
Email Address: 300599@deped.gov.ph
Always Practice Proper Hygiene at ALL TIMES.
4
Q2-ICT7-1
How to convert a Binary number back to a Decimal Number
You can convert any Binary number back to its decimal equivalent using this method.
Step 1: Remember this table of values.
212 211 210 29 28 27 26 25 24 23 22 21 20
4096 2048 1024 512 256 128 64 32 16 8 4 2 1
Step 2: Align the Binary Number you want to convert starting from RIGHT to LEFT.
Let’s take the one we had just converted in the previous page. 10011 (we should be able to get 19)
212 211 210 29 28 27 26 25 24 23 22 21 20
4096 2048 1024 512 256 128 64 32 16 8 4 2 1
1 0 0 1 1
As you can see, I just wrote them below the values, starting from right to left.
Step 3: Multiply the Binary number that has a value of 1 to the value above it.
212 211 210 29 28 27 26 25 24 23 22 21 20
4096 2048 1024 512 256 128 64 32 16 8 4 2 1
1 0 0 1 1
In this case we get the products of:
16x1 = 16
2x1 = 2
1x1 = 1
Step 4: Lastly, we add the products
Let’s sum up 16 + 2 + 1 = 19
Hence, the Decimal Value of the Binary 10011 is 19.
References
Computer - Number System - Tutorialspoint. (2020). Retrieved 29 December 2020, from
https://www.tutorialspoint.com/computer_fundamentals/computer_number_system.htm
Porubsky, S. (2020). BinarySystem. Retrieved 31 December 2020, from
https://www.cs.cas.cz/portal/AlgoMath/NumberTheory/Arithmetics/NumeralSystems/PositionalNu
meralSystems/BinarySystem.htm#:~:text=The%20modern%20binary%20number%20system,used
%20symbols%200%20and%201.
Pingala. (2020). Retrieved 31 December 2020, from https://en.wikipedia.org/wiki/Pingala
Address: SICAT Rd., Calaocan, Santiago City 3311
Telephone No.: (078) 305-0110
Email Address: 300599@deped.gov.ph
Always Practice Proper Hygiene at ALL TIMES.
5
Q2-ICT7-LAS-2.1
This sheet will be submitted. Please separate it from the Self Learning Module (Pages 1-5)
INFORMATION AND COMMUNICATIONS TECHNOLOGY 1
Name: _________________________________
Grade and Section: _______________________
LEARNING ACTIVITY SHEET 1
NUMBER SYSTEMS
Activity 1. Instruction: Convert the following number into a Binary Number. Show you solution on
a separate sheet of paper to be attached and passed along with this LAS.
1. 29 = __________________ 6. 33 = _____________________
2. 17 = __________________ 7. 77 = _____________________
3. 45 = __________________ 8. 56 = _____________________
4. 21 = __________________ 9. 11 = _____________________
5. 35 = __________________ 10. 32 = ____________________
Activity 2 – Convert the following binaries into a decimal number. Show you solution on a
separate sheet of paper.
1. 111001 = _______________ 6. 00110101101 = _______________
2. 1010101 = _______________ 7. 11111111111 = _______________
3. 11001100 = _______________ 8. 11111100111 = _______________
4. 11010101 = _______________ 9. 11000111100 = _______________
5. 000111101 = _______________ 10. 1111111101 = _______________
GUIDELINES IN USING LAS (Learning Activity Sheet)
1. Always keep your answer sheets clean and organized.
2. Do not write anything irrelevant on the papers.
3. Do not fold or crumple the pages.
4. Please take your time in reading these modules for you to understand the lesson.
5. If you need help from your teacher, do any of the following:
a. If you have Facebook: Look for Cj Verona
b. Call +639171270834 from 8am-5pm only.
6. Please Return your ANSWERED LAS to its respective drop-off point on the date scheduled in your
respective barangay.
Address: SICAT Rd., Calaocan, Santiago City 3311
Telephone No.: (078) 305-0110
Email Address: 300599@deped.gov.ph
Always Practice Proper Hygiene at ALL TIMES.
6
Q2-ICT7-LAS-2.1
This sheet will be submitted. Please separate it from the Self Learning Module (Pages 1-5)
Performance Task 1
Instructions:
1. Decipher the equation below by converting the decimal or binary number.
2. Given are decimal numbers. Convert them into binary numbers.
3. Look for the letter corresponding to the value you get on the table. (Refer to the table on
Page 7.)
4. Complete the equation. You can use a separate sheet of paper for your solving.
Letter:
Given 80 65 83 83 73 79 78
Binary:
Letter:
Given: 80 69 82 83 73 83 84 69 78 67 69
Binary:
Letter:
Given: 71 82 73 84
Binary:
Write the complete equation here:
__________________________ + ________________________ = ___________________________
Good Job!!!!!!
Look for the letter corresponding to the binary number you got.
Letter Binary Letter Binary
A 1000001 N 1001110
B 1000010 O 1001111
C 1000011 P 1010000
D 1000100 Q 1010001
E 1000101 R 1010010
F 1000110 S 1010011
G 1000111 T 1010100
H 1001000 U 1010101
I 1001001 V 1010110
J 1001010 W 1010111
K 1001011 X 1011000
L 1001100 Y 1011001
M 1001101 Z 1011010
Acknowledgement:
Learner’s Name and Signature: ________________________________________
Parent/Guardian’s Name and Signature: ________________________________
Address: SICAT Rd., Calaocan, Santiago City 3311
Telephone No.: (078) 305-0110
Email Address: 300599@deped.gov.ph
Always Practice Proper Hygiene at ALL TIMES.
7
