The document discusses number systems and converting between different bases. It begins with learning objectives about understanding number systems and performing basic operations in different bases. It then defines key terms like number system and base. The main number systems covered are decimal, binary, octal, and hexadecimal. Examples are provided for converting between decimal, binary, octal, and hexadecimal bases using division and multiplication. Students are given an activity to practice converting between different number systems.
The document discusses number systems and converting between different bases. It begins with learning objectives about understanding number systems and performing basic operations in different bases. It then defines key terms like number system and base. The main number systems covered are decimal, binary, octal, and hexadecimal. Examples are provided for converting between decimal, binary, octal, and hexadecimal bases using division and multiplication. Students are given an activity to practice converting between different number systems.
The document discusses number systems and converting between different bases. It begins with learning objectives about understanding number systems and performing basic operations in different bases. It then defines key terms like number system and base. The main number systems covered are decimal, binary, octal, and hexadecimal. Examples are provided for converting between decimal, binary, octal, and hexadecimal bases using division and multiplication. Students are given an activity to practice converting between different number systems.
The document discusses number systems and converting between different bases. It begins with learning objectives about understanding number systems and performing basic operations in different bases. It then defines key terms like number system and base. The main number systems covered are decimal, binary, octal, and hexadecimal. Examples are provided for converting between decimal, binary, octal, and hexadecimal bases using division and multiplication. Students are given an activity to practice converting between different number systems.
Department of Education National Capital Region DIVISION OF CITY SCHOOLS – MANILA Manila Education Center Arroceros Forest Park Antonio J. Villegas St. Ermita, Manila
PROGRAMMING .NET NCIII Grade 11
Quarter 1 Week 2 Module 2
Learning Competency: Understand the history of computer and the number system. TLE_ICTCP9-12MC-If-2 Number System
0 Division of City Schools-Manila DEPARTMENT OF EDUCATION K TO 12 BASIC EDUCATION CURRICULUM JUNIOR HIGH SCHOOL TECHNICAL LIVELIHOOD EDUCATION AND SENIOR HIGH SCHOOL - TECHNICAL-VOCATIONAL-LIVELIHOOD TRACK INFORMATION AND COMMUNICATIONS TECHNOLOGY–PROGRAMMING (.NET TECHNOLOGY) NC III
(1st Semester)
By: RHAYMOND M. MONTERDE Master Teacher I C.P. Garcia High School
1 EXPECTATIONS:
At the end of the period, learners should be able to:
LO1. Learn what is number system.
LO2. Compute the basic mathematical operations in number system.
Key Terminologies
• Number system A number system is defined as a system of writing for expressing
numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.
• Base – a subscript place before the number to identify the system of
the number.
• Conversion – the process of changing one base to another base.
LEARNING OUTCOME 1:
Learn what is number system.
2 A. Direction: Multiple Choice: Choose the letter of the correct answer. 1 ___________ any number ranging from 0 to 9. . a. Binary d. Decimal b. Digit e. Hexadecimal c. Octal
2 The base for decimal number.
. a. 1 d. 20 b. 2 e. 11 c. 10
3 The base for Octal number.
. a. 6 d. 8 b. 7 e. 10 c. 9
4 The base for Hexadecimal number
. a. 15 c 14 b. 16 e. 13 c. 10
5 It is a subscript number place each of the number system.
. a. Digit d. Marking b. Base e. unit c. System
B. Direction: Convert the following given. Use the space provided below.
3 There are number of various numbering framework which is being used for the extraordinary capacity to speak to various numbers. Binary, Octal, Decimal and Hexadecimal are number frameworks that are utilized in various perspectives Decimal number is the most usually utilized number framework which is much of the time utilized in day by day life.
Types of Number System
There are various types of the number system in mathematics. The four most common number system types are:
1. Decimal number system (Base- 10)
2. Binary number system (Base- 2) 3. Octal number system (Base-8) 4. Hexadecimal number system (Base- 16)
Decimal Number System (Base 10)
Decimal number system has base 10 because it uses ten digits from 0 to 9. In the decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. This system is expressed in decimal numbers. The base of the decimal is 10. This shows that there are ten symbols, 0 to 9. Similarly, the system using the symbols 0, 1, two will be of base 3, four symbols will be of base 4 and so on. Every position shows a particular power of the base (10). For example, the decimal number 1457 consists of the digit 7 in the units position, 5 in the tens place, 4 in the hundreds position, and 1 in the thousands place whose value can be written as (1×1000) + (4×100) + (5×10) + (7×1) (1×103) + (4×102) + (5×101) + (7×1) 1000 + 400 + 50 + 7 1457
Binary Number System (Base 2)
The base 2 number system is also known as the Binary number system wherein, only two binary digits exist, i.e., 0 and 1. Specifically, the usual base-2 is a radix of 2. The figures described under this system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is a binary number. We can convert any system into binary and vice versa.
4 Octal Number System (Base 8) The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7.
Hexadecimal Number System (Base 16)
The word “Hexadecimal” means sixteen because this type of digital numbering system uses 16 different digits from 0-to-9, and A-to- F. Hexadecimal Numbers group binary numbers into sets of four digits.
CONVERSION OF NUMBER SYSTEM
Decimal to Binary Conversion Examples: 1. 12 10 ___________________ 2 Solution: Division Quotient Remainder 12/2 6 0 6/2 3 0 3/2 1 1 ½ 0 1 Therefore the equivalent binary number is 1100 2 . 2. 42 10 ________________________ 2 Solution: Division Quotient Remainder 42/2 21 0 21/2 10 1 10/2 5 0 5/2 2 1 2/2 1 0 ½ 0 1 Therefore, the equivalent binary number is 101010 2
5 Binary to Decimal Conversion 1. 1100 2____________________10 Solution: To convert binary to decimal number, follow the steps below. 1. Multiply each binary digit from left to right by 2 then add plus sign between binary digits. 1X2+1X2+0X2+0X2. 2. In each term (1X2), add corresponding exponent from right to left starting from 0. 1X23+1X22+0X21+0X20 Since 23 equals to 2X2X2= 8, therefor 1X23 equal to 1X8+1X4+0X2+0X1= 12 10 Note: Any number raised to 1 is equal to the number itself. Any number raised to 0 is equal to 1. 2. 101010 2____________________________10 Solution: To convert binary to decimal number, follow the steps below. 1. Multiply each binary digit from left to right by 2 then add plus sign between binary digits. 1X2+0X2+1X2+0X2+1X2+0X2. 2. In each term (1X2), add corresponding exponent from right to left starting from 0. 1X25+0X24+1X23+0X22+1X21+0X20 Since 25 equals to 2X2X2X2X2= 32, therefore 1X32+0X16+1X8+0X4+1X2+0X1= 42 10 Note: Any number raised to 1 is equal to the number itself. Any number raised to 0 is equal to 1.
Decimal to Octal Conversion
1. 25 10 __________________ 8
6 Solution: Division Quotient Remainder 25/8 3 1 3/8 0 3 Therefore, 31 is the octal equivalent of 25 decimal.
Octal to Decimal Conversion
Solution: To convert Octal to decimal number, follow the steps below. 1. Multiply each octal digit from left to right by 8 then add plus sign between octal digits. 3X8+1X8 2. In each term (1X8), add corresponding exponent from right to left starting from 0. 3X81+1X80 Since 81 equals to 8, therefore 3X8+1X1= 25 10 Note: Any number raised to 1 is equal to the number itself. Any number raised to 0 is equal to 1. Decimal to Hexadecimal Conversion 1. 49 10 __________________ 16 Solution: Division Quotient Remainder 49/16 3 1 3/16 0 3 Therefore, 31 is the Hexadecimal equivalent of 49 decimal. Hexadecimal to Decimal Conversion Solution: To convert Hexadecimal to decimal number, follow the steps below. 1. Multiply each hexadecimal digit from left to right by 16 then add plus sign between Hexadecimal digits. 3X16+1X16
7 2. In each term (1X16), add corresponding exponent from right to left starting from 0. 3X161+1X160 Since 161 equals to 16, therefore 3X16+1X1= 49 10
Note: Any number raised to 1 is equal to the number itself. Any number raised to 0 is equal to 1.
8 Number system consists of 4 different bases namely Decimal number (based 10) which is from 0-9, Binary number (base 2) which is 0-1,Octol number(base 8) which is 0-7 and the Hexadecimal number(base 16) from 0-9 and A,B,C,D,E and F for number 10 to 15.
CHECKING YOUR UNDERSTANDING
Explain the four bases of number system. Used the space below.
9 A. Direction: Multiple Choice: Choose the letter of the correct answer. 1 ___________ any number ranging from 0 to 9. . a. Binary d. Decimal b. Digit e. Hexadecimal c. Octal
2 The base for decimal number.
. a. 1 d. 20 b. 2 e. 11 c. 10
3 The base for Octal number.
. a. 6 d. 8 b. 7 e. 10 c. 9
4 The base for Hexadecimal number
. a. 15 c 14 b. 16 e. 13 c. 10
5 It is a subscript number place each of the number system.
. a. Digit d. Marking b. Base e. unit c. System
10 Acknowledgements
Writer: Rhaymond M. Monterde- MT I/ICT Computer Programming
Editors: Ariel Tosio- EPS, Elena C. Reyes- Principal IV, Gibson J.
Olazo– MT II/ICT Computer Programming Coordinator
Reviewer: Gibson J. Olazo– MT II/ICT Computer Programming
Coordinator, Ariel Tosio- EPS
Management Team: Maria Magdalena M. Lim-Schools Division
Superintendent-Manila, Aida H. Rondilla-Chief Education Supervisor Lucky S. Carpio-EPS and Lady Hannah C Gillo, Librarian II-LRMS
11 Answer Key:
Lesson 2 PRE-TEST L01 A. B. 1. B 1. 10111 2 2. C 2. 710 8 3. D 3. 43 10 4. B 4. 64206 10 5. B 5. 84 10 ACTIVITIY 1.1
