NUMBER SYSTEM.pptx

NUMBERS

1. ICT – CSS 9 NUMBER SYSTEM

2. WHAT IS NUMBER SYSTEM? A number system is 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. It provides a unique representation to every number and represents the arithmetic and algebraic structure of the figures . It also allows us to operate arithmetic operations like addition, subtraction, and division.

3. Characteristics of Numbering Systems The digits are consecutive. The number of digits is equal to the size of the base. Zero is always the first digit. The base number is never a digit. When 1 is added to the largest digit, a sum of zero and a carry of one results. Numeric values are determined by the implicit positional values of the digits.

4. Types of Number System There are various types of number system in mathematics. The four most common number system types are: Decimal number system (Base- 10) Binary number system (Base- 2) Octal number system (Base-8) Hexadecimal number system (Base- 16)

5. = represents no value 1 = represents a unit value THE BINARY NUMBER SYSTEM The binary number system uses 2 digits to encode a number:

6. That means that you can only use the digits 0 and 1 to write a binary number Example: some binary numbers 1 10 11 1010           and so on.

7. Binary Number System Also called the “Base 2 system” The binary number system is used to model the series of electrical signals computers use to represent information 0 represents the no voltage or an off state 1 represents the presence of voltage or an on state

8. Base 2 Number System Base 2 number systems are also known as 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

9. DECIMAL NUMBER SYSTEM Decimal number system has base 10 because it uses ten digits from 0 to 9. In decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. Every position shows a particular power of the base (10). 

10. Base 10 Number System This system is expressed in decimal numbers. The base to 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.

11. Base 10 Number System This system is expressed in decimal numbers. The base to 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.

12. Binary ‒ to ‒ Decimal Process The Process: Weighted Multiplication Multiply each bit of the Binary Number by it corresponding bit-weighting factor (i.e. Bit-0→2 =1; Bit-1→2 1 =2; Bit-2→2 2 =4; etc ). Sum up all the products in step (a) to get the Decimal Number .

13. Decimal ‒ to ‒ Binary Conversion The Process : Successive Division Divide the Decimal Number by 2; the remainder is the LSB of Binary Number. If the quotation is zero, the conversion is complete; else repeat step (a) using the quotation as the Decimal Number. The new remainder is the next most significant bit of the Binary Number.

14. Binary to Decimal B. Decimal to Binary 10110 2 = ____________ 1. 13 10 = ____________ 101010 2 = ____________ 2. 22 10 = ____________ 0100101 2 = ____________ 3. 43 10 = ____________ 010011 2 = ____________ 4. 1 58 10 = ____________ 11010 2 = ____________ 5. 98 10 = ____________

15. Learning Task 2. Write 5-sentence essay focusing on what you have learned. Do not summarize the lesson, instead discuss new ideas and significant insights and how the information can be used. Write your answer on the space provided.

16. ICT – CSS 9 OCTAL TO BINARY

17. In order to  convert octal to binary  number, we must follow a few steps. Octal numbers have base 8 and binary numbers have base 2. We can convert the octal number into decimal and then  convert the decimal number into its equivalent binary number . Also, we can remember the octal to the binary equivalent table to do the quick conversion.

18. Octal Numbers:  Octal numbers are the numbers which have base 8. It is represented as N 8 . It uses the digits 0,1, 2, 3, 4, 5, 6 and 7 to represent the numbers in this number system. For example: 112 8

19. OCTAL TO BINARY 1. 250 2. 434 3. 620 4. 5722 5.1472

20. The Hexadecimal Numbering System The  base 16 , also known as  hexadecimal  (abbreviated to  hex ) numbering system is regularly used in computer coding for conveniently representing a byte or word of data. 

21. Hexadecimal, the Base 16 Numbering System Hexadecimal or "hex" is a numbering system which uses 16 different numerals. We saw that decimal used ten numerals from 0 to 9. Hex expands on this by adding six more, the capital letters A, B, C, D, E and F.

22. ICT – CSS 9 QUIZ

23. ‘ qqqqqqqqqqqqqqqqqqqqqqqqqq Binary to Decimal 1 . 10011011 2 2. 11101110 2 3. 00111000 2 4. 1001011111 2 5.110111001 2

24. ‘ qqqqqqqqqqqqqqqqqqqqqqqqqq Decimal to Binary 1 . 62 10 2. 15 10 3. 86 10 4. 48 10 5.55 10

25. ‘ qqqqqqqqqqqqqqqqqqqqqqqqqq Octal to Binary 1 . 103 8 2. 434 8 3. 1472 8 4. 22645 8 5.5722 8

26. ‘ qqqqqqqqqqqqqqqqqqqqqqqqqq Binary to Octal 1. 101110010 2 2. 010100101010 2 Hexadecimal to Binary 3. 79E 16 4. B04 16 5. 13A 16

27. ‘ qqqqqqqqqqqqqqqqqqqqqqqqqq Octal to Hexadecimal 1 . 1456 8 2. 6620 8 3. 15355 8 4. 1430 8 5.742 8

28. ‘ qqqqqqqqqqqqqqqqqqqqqqqqqq Write an essay focusing on what you have learned. Do not summarize the lesson, instead discuss new ideas and significant insights and how the information can be used. Write your answer on your notebook.

29. ‘ qqqqqqqqqqqqqqqqqqqqqqqqqq Answer the ff. questions below. Write your answer on your notebook How important is binary in the world of digital systems? Why is it important for the students to learn about binary numbers? What are the benefits of using binary? How do you explain binary to a child?